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Topic 5 - Statistics and probability

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Description

The aim of this topic is to introduce basic concepts. It is expected that most of the calculations required will be done using technology, but explanations of calculations by hand may enhance understanding. The emphasis is on understanding and interpreting the results obtained, in context. Statistical tables will no longer be allowed in examinations. While many of the calculations required in examinations are estimates, it is likely that the command terms “write down”, “find” and “calculate” will be used.

Directly related questions

12N.1.sl.TZ0.1a: Find AB .
08N.2.sl.TZ0.3b: Find the interquartile range.
08M.2.sl.TZ1.6a: Find the mean number of defective switches in the sample.
08M.2.sl.TZ1.8a(i) and (ii): One biscuit is chosen at random from the box. Find the probability that this biscuit (i) ...
08M.2.sl.TZ2.4a: Find the value of k.
08M.2.sl.TZ2.5b: Given that the mean height is $6.84{\text{ cm}}$ and the standard deviation...
08M.2.sl.TZ2.6b: In one week, find the probability that she goes to work on a red bus on exactly two days.
12M.1.sl.TZ1.1b(i) and (ii): The cumulative frequency diagram is given below. Use the diagram to estimate (i) the 80th...
12M.2.sl.TZ1.8a(i) and (ii): (i) Write down the value of p and of q . (ii) Write down the median class.
10M.1.sl.TZ1.5a(i), (ii) and (iii): Write down the value of (i) p ; (ii) q ; (iii) r.
09N.1.sl.TZ0.3b: Given that ${\rm{P}}(X < d) = {\rm{P}}(X > 105)$ , find the value of $d$ .
09N.2.sl.TZ0.3a: Find the expected number of questions Jose answers correctly.
09M.1.sl.TZ2.9c: Find the expected value of S.
10N.2.sl.TZ0.1a: Write down the standard deviation.
10N.2.sl.TZ0.9a(i) and (ii): (i) Find E(X ) . (ii) Find the probability that Mark passes the test.
SPNone.1.sl.TZ0.9a(i), (ii) and (iii): (i) Find ${\rm{P}}(X = 6)$ . (ii) Find ${\rm{P}}(X > 6)$ . (iii) Find...
SPNone.2.sl.TZ0.8a: Write down the equation of the regression line of y on x .
SPNone.2.sl.TZ0.8b(i) and (ii): Use your regression line from part (a) as a model to answer the following. Interpret the meaning...
11N.1.sl.TZ0.3a: Write down the probability that the first marble Anna selects is red.
11N.2.sl.TZ0.9b: The sample of caps passes inspection if at most one cap is defective. Find the probability that...
11M.2.sl.TZ1.7a: Find the probability that it passes inspection.
11M.1.sl.TZ2.2b: Find ${\rm{P}}(B')$ .
11M.2.sl.TZ2.6b: Find the standard deviation of X .
11M.2.sl.TZ2.9b: The probability distribution for the sum of the scores on the two dice is shown below. Find...
13M.1.sl.TZ1.9d: Given that the marble is red, find the probability that it was drawn from jar A.
13M.2.sl.TZ1.2a: Find the value of $p$ .
08M.1.sl.TZ1.10b: If the blue face lands down, the die is not rolled again. If the red face lands down, the die is...
14M.2.sl.TZ1.3b(i): Write down the correlation coefficient.
14M.2.sl.TZ1.3b(ii): State which two of the following describe the correlation between the variables. strong ...
14M.2.sl.TZ2.4b: Find ${\text{P}}(A \cup B)$.
14M.2.sl.TZ2.4c(i): On the following Venn diagram, shade the region that represents $A \cap B'$.
13N.1.sl.TZ0.3a: Find the number of students who completed the task in less than 45 minutes.
14M.2.sl.TZ2.10a(ii): A tree is selected at random from the forest. Given that this tree is a giant, find the...
14M.2.sl.TZ2.10b: Two trees are selected at random. Find the probability that they are both giants.
13N.2.sl.TZ0.4a: Given that $A$ and $B$ are mutually exclusive, find ${\text{P}}(B)$.
13N.2.sl.TZ0.10d: After $n$ school days, the probability that Samantha goes to school by bus at least once is...
14N.2.sl.TZ0.10e: $25\% $ of the fish in the lake are salmon. $10\% $ of the salmon are tiddlers. Given that a...
15N.1.sl.TZ0.1b: Find the value of (i) $c$; (ii) $d$.
09M.2.sl.TZ1.7b: If the team does not win the game, find the probability that the game was played at home.
09M.2.sl.TZ1.8c: In order to sell the fish, the fisherman classifies them as small, medium or large. Small fish...
11N.2.sl.TZ0.9a: Find the probability that exactly one cap in the sample will be defective.
15M.1.sl.TZ1.10c: Find the probability that Ann wins the game.
15M.2.sl.TZ1.9d: A sample of $50$ containers is chosen at random. Find the probability that $48$ or more of...
16M.1.sl.TZ1.2b: Find ${\text{P}}(B)$.
16M.2.sl.TZ1.8c: Find ${\text{E}}(B)$.
16M.1.sl.TZ2.8b: (i) Write down the probability that this student owns a laptop. (ii) Find the...
16M.2.sl.TZ2.8d: Find the year when Lina sells her car.
16N.2.sl.TZ0.8b: During week 2, the students worked on a major project and they each spent an additional five...
17M.1.sl.TZ2.3c: Find ${\text{P}}(93 < X < 107)$.
17M.2.sl.TZ1.4b.ii: Hence, find the probability that fewer than $k$ students are left handed.
18M.2.sl.TZ1.2c: The die is rolled 80 times. On how many rolls would you expect to obtain a three?
18M.1.sl.TZ2.8e: Two days next week Pablo will drive to work. Find the probability that he will be late at least...
18M.2.sl.TZ2.1a.i: Find the value of a and of b.
12N.1.sl.TZ0.1b: Given that ${\boldsymbol{X}} - 2{\boldsymbol{A}} = {\boldsymbol{B}}$, find X.
12N.1.sl.TZ0.2a: Find the value of k .
12M.1.sl.TZ2.9b: Bag A contains three white balls and four red balls. Two balls are chosen at random without...
08N.1.sl.TZ0.5c: Hence, explain why A and B are not mutually exclusive.
08M.2.sl.TZ1.1b: Find the median number of sit-ups.
08M.2.sl.TZ1.6c: Find the probability that there is at least one defective switch in the sample.
08M.1.sl.TZ2.1b(i) and (ii): Find (i) the median; (ii) the interquartile range.
08M.1.sl.TZ2.6a(i) and (ii): One student is selected at random. (i) Calculate the probability that the student is a male...
08M.2.sl.TZ2.6c: In one week, find the probability that she goes to work on a red bus on at least one day.
12M.2.sl.TZ1.8c(i) and (ii): Consider the class interval $45 \le T < 55$ . (i) Write down the interval...
09M.1.sl.TZ1.2a: Find ${\rm{P}}(A)$ .
09M.2.sl.TZ1.8a: Calculate an estimate for the standard deviation of the lengths of the fish.
10N.2.sl.TZ0.9b(i) and (ii): (i) Show that $4a + 2b = 0.24$ . (ii) Given that ${\rm{E}}(Y) = 1$ , find a and b .
10N.2.sl.TZ0.9c: Find which student is more likely to pass the test.
10M.2.sl.TZ1.4b: Write down the standard deviation.
10M.2.sl.TZ1.7b: Write down an expression, in terms of p , for the probability that he wins exactly four games.
10M.2.sl.TZ2.1b: Find the mean grade.
SPNone.1.sl.TZ0.2c: For the data in diagram D , which two of the following expressions describe the correlation...
SPNone.2.sl.TZ0.3b: Given that the standard deviation is 20, find a . Give your answer correct to the nearest whole...
SPNone.2.sl.TZ0.8e(i) and (ii): Comment on the appropriateness of using your model to (i) estimate the cost of producing...
11N.1.sl.TZ0.7b: Each value of k is equally likely for $ - 5 \le k \le 5$ . Find the probability that...
11N.1.sl.TZ0.3b: Find the probability that Anna selects two red marbles.
11N.1.sl.TZ0.7a: Find the values of k such that $f(x) = 0$ has two equal roots.
11M.2.sl.TZ1.4a: Find ${\rm{P}}(X \le 24.5)$ .
11M.2.sl.TZ1.4b(i) and (ii): Let ${\rm{P}}(X \le k) = 0.85$ . (i) Represent this information on the following...
11M.1.sl.TZ2.2a(i) and (ii): (i) Write down the value of n . (ii) Find the value of m , of p , and of q .
13M.2.sl.TZ1.2b: Find (i) the mean; (ii) the variance.
14M.2.sl.TZ1.8d: Assume that the weights of these rats are normally distributed with the mean and standard...
14N.1.sl.TZ0.3b: The contestant scores points as shown in the following table. Given that the game is fair,...
14N.2.sl.TZ0.2a: Find the correlation coefficient.
15N.2.sl.TZ0.9b: Use the regression equation to estimate the number of coyotes in the reserve when $t = 7$.
12M.1.sl.TZ2.1a: Find the median mark.
09M.1.sl.TZ1.2c: Find ${\rm{P}}(A \cap B)$ .
15M.2.sl.TZ2.3a: (i) Find the value of $a$ and of $b$. (ii) Write down the value of $r$.
16M.1.sl.TZ1.8d: The students raise $0.10 for each recycled can. (i) Find the largest amount raised by a...
16M.1.sl.TZ1.2a: (i) Write down the value of $q$. (ii) Find the value of $p$.
16M.2.sl.TZ1.1a: On the following diagram, shade the region representing ${\text{P}}(X \leqslant 25)$.
16M.2.sl.TZ1.5b: The equation of the line of best fit is $\ln M = - 0.12t + 4.67$. Given that...
16M.1.sl.TZ2.2a: Find the mean.
16M.2.sl.TZ2.8b: Use the regression equation to estimate the price of Lina’s car, giving your answer to the...
16N.1.sl.TZ0.5a: Find ${\text{P}}(B)$.
16N.2.sl.TZ0.5a: Given that 5.3% of newborn babies have a low birth weight, find $w$.
17M.1.sl.TZ1.4a.ii: Write down the boiling temperature of the liquid.
17M.2.sl.TZ2.10a.i: Find $q$.
17M.2.sl.TZ2.10b.i: Write down the probability of drawing three blue marbles.
17M.2.sl.TZ2.10b.ii: Explain why the probability of drawing three white marbles is $\frac{1}{6}$.
17N.2.sl.TZ0.8d.i: Find the value of $k$;
18M.1.sl.TZ2.3b.ii: Find the value of the new variance.
18M.2.sl.TZ2.10b: Find P(M < 95) .
12N.2.sl.TZ0.10d: At a large school, students are required to learn at least one language, Spanish or French. It is...
08N.2.sl.TZ0.7b(i) and (ii): A student is chosen at random. This student has the same probability of having a score less than...
08M.2.sl.TZ1.8b(i) and (ii): Five percent of the biscuits in the box weigh less than d grams. (i) Copy and complete the...
12M.2.sl.TZ1.8d(i) and (ii): Hence find an estimate for the (i) mean; (ii) standard deviation.
12M.2.sl.TZ1.7a: The probability of obtaining “tails” when a biased coin is tossed is $0.57$. The coin is tossed...
09N.1.sl.TZ0.8d: Show that A and B are not independent.
09N.2.sl.TZ0.6: Consider the independent events A and B . Given that ${\rm{P}}(B) = 2{\rm{P}}(A)$ , and...
10N.2.sl.TZ0.1c: Find the interquartile range.
10M.2.sl.TZ1.10b(i) and (ii): (i) Write down the standardized value, z, for $68{\text{ kg}}$. (ii) Hence, find the...
10M.2.sl.TZ1.10c(i) and (ii): To take part in a tournament, a player’s weight must be within 1.5 standard deviations of the...
10M.2.sl.TZ2.3b: Jan tosses the two dice 8 times. Find the probability that she wins 3 prizes.
SPNone.2.sl.TZ0.5b: Find the probability that the number of heads obtained is less than one standard deviation away...
SPNone.2.sl.TZ0.8c: Estimate the cost of producing 60 boxes.
11N.1.sl.TZ0.3c: Find the probability that one marble is red and one marble is blue.
11N.1.sl.TZ0.5: The random variable X has the following probability distribution. Given that...
11N.2.sl.TZ0.9e: The bottles and caps are manufactured separately. A sample of 10 bottles and a sample of 10 caps...
11M.2.sl.TZ2.9c: Fred plays a game. He throws two fair 4-sided dice four times. He wins a prize if the sum is 5 on...
13M.2.sl.TZ1.7: A random variable $X$ is normally distributed with $\mu = 150$ and $\sigma = 10$ . Find...
13M.2.sl.TZ2.9a: (i) Find ${\rm{P}}(X = 0)$ . (ii) Find ${\rm{P}}(X = 1)$ . (iii) Hence, find...
14M.1.sl.TZ1.9d: Given that Bill wins at least one game, find the probability that he wins both games.
14M.2.sl.TZ1.8c: The same data is presented in the following...
14M.2.sl.TZ2.10c(i): $100$ trees are selected at random. Find the expected number of these trees that are giants.
13N.1.sl.TZ0.3c: Given that 50 students take less than k minutes to complete the task, find the value of $k$.
13N.2.sl.TZ0.10c: In a randomly chosen school week, find the probability that Samantha goes to school by bus on...
13M.2.sl.TZ2.9b: Find the probability that exactly five of the balls are gold.
14N.2.sl.TZ0.2b: The relationship can be modelled by the regression line with equation $y = ax + b$. Write down...
14N.1.sl.TZ0.8a: Find the value of $p$.
15N.2.sl.TZ0.5c: Find ${\text{P}}(C'|D)$.
09M.2.sl.TZ1.8e: Find ${\text{E}}(X)$ .
13M.1.sl.TZ1.9b: Find the expected number of green marbles drawn from the jar.
15M.1.sl.TZ1.1b: Find ${\text{E}}(X)$.
15M.2.sl.TZ1.1b: Elizabeth watches television for an average of $3.7$ hours per day. Use your regression line...
16M.1.sl.TZ1.8c: Sam’s class collected 745 cans. They want an average of 40 cans per student. How many more cans...
16M.1.sl.TZ2.8c: (i) Copy and complete the following tree diagram. (Do not write on this page.) (ii) ...
16M.2.sl.TZ2.6b: Given that 1% of the contestants are disqualified, find the value of $x$.
16M.2.sl.TZ2.8a: (i) Find the correlation coefficient. (ii) Write down the value of $a$ and of $b$.
16N.2.sl.TZ0.8a: Find the mean number of hours spent browsing the Internet.
17M.1.sl.TZ1.1a.ii: Find the value of $q$.
17M.1.sl.TZ1.4a.i: Write down the independent variable.
17M.1.sl.TZ2.8d: Only 10 employees earned more than £$k$. Find the value of $k$.
17M.2.sl.TZ1.1b.ii: Find the variance.
17M.2.sl.TZ2.2a.ii: Write down the value of $r$.
17M.2.sl.TZ2.10d: Grant plays the game until he wins two prizes. Find the probability that he wins his second prize...
17N.2.sl.TZ0.4a: Find the value of $k$.
259340: This is an example question for the example test. You can delete this question.
18M.2.sl.TZ1.8b: Use the regression equation to estimate the value of y when x = 3.57.
18M.2.sl.TZ1.9b.i: Find the standardized value for 289 g.
18M.2.sl.TZ1.9e: The grocer selects two boxes at random. Find the probability that the grocer buys more than half...
18M.2.sl.TZ2.1a.ii: Write down the correlation coefficient.
18M.2.sl.TZ2.1b: Use your equation to estimate the mean weight of a child that is 1.95 years old.
18M.2.sl.TZ2.10d.i: Find the expected number of bags in this crate that contain at most one small apple.
18M.2.sl.TZ2.10a.i: Write down the value of k.
12N.1.sl.TZ0.8a(i) and (ii): (i) Write down the median weekly wage. (ii) Find the interquartile range of the weekly...
12M.2.sl.TZ2.4a: The heights of a group of seven-year-old children are normally distributed with mean...
08N.1.sl.TZ0.5b(i) and (ii): Given that ${\text{P}}(A \cup B) = 0.8$ , (i) find x ; (ii) find...
08N.2.sl.TZ0.3a: Write down the median.
08N.2.sl.TZ0.5a: Find the probability of obtaining exactly two heads.
08M.2.sl.TZ1.1c: Find the mean number of sit-ups.
08M.2.sl.TZ1.8c: The weights of biscuits in another box are normally distributed with mean $\mu $ and standard...
12M.1.sl.TZ1.1a: Find p .
12M.2.sl.TZ1.7b: The probability of obtaining “tails” when a biased coin is tossed is 0.57. The coin is tossed ten...
12M.2.sl.TZ1.8e: John assumes that T is normally distributed and uses this to estimate the probability that a...
10M.1.sl.TZ2.9a(i) and (ii): Find (i) ${\rm{P}}(E \cap F)$ ; (ii) ${\rm{P}}(F)$ .
10M.1.sl.TZ2.9b(i) and (ii): Find the probability that (i) José misses his bus and is not late for school; (ii) José...
09M.2.sl.TZ1.4b: Given that ${\rm{P}}(X > a) = 0.27$ , find $a$.
10M.2.sl.TZ1.7c: Hence, find the values of p such that the probability that he wins exactly four games is 0.15.
10M.2.sl.TZ1.10d: Of the players in the league, $25\% $ are women. Of the women, $70\% $ take part in the...
SPNone.1.sl.TZ0.4b(i) and (ii): Each value in the original data set is multiplied by 10. (i) Write down the value of the new...
SPNone.2.sl.TZ0.8d: The factory sells the boxes for $19.99 each. Find the least number of boxes that the factory...
11M.1.sl.TZ1.4b: Show that $k = 3$ .
11M.1.sl.TZ1.8c: Two students are selected at random, one after the other. Find the probability that the first...
11M.2.sl.TZ1.7b: The company would like the probability that a box passes inspection to be 0.87. Find the...
13M.1.sl.TZ2.8a: Find the value of $p$ and of $q$ .
13M.1.sl.TZ2.8b: A girl is chosen at random. (i) Find the probability that the time she takes is less than...
08M.1.sl.TZ1.10a: Write down (i) P(B);(ii) P(R).
08M.1.sl.TZ1.10c: Guiseppi plays a game where he rolls the die. If a blue face lands down, he scores 2 and is...
14M.2.sl.TZ1.3a(i): The relationship between the variables is modelled by the regression equation \(y = ax +...
14M.2.sl.TZ1.8a(i): Write down the median weight of the rats.
14M.2.sl.TZ2.10c(ii): $100$ trees are selected at random. Find the probability that at least $25$ of these trees...
14N.1.sl.TZ0.8b: Find the probability that Adam will travel by car and be late for school.
09M.2.sl.TZ2.9a: For Route A, find the probability that the journey takes more than $60$ minutes.
16M.2.sl.TZ1.1c: Let ${\text{P}}(X \leqslant c) = 0.7$. Write down the value of $c$.
16M.2.sl.TZ1.5a: State two words that describe the linear correlation between $\ln M$ and $t$.
16M.1.sl.TZ2.2b: (i) Write down the value of the new mean. (ii) Find the value of the new variance.
16M.2.sl.TZ2.6a: A contestant is chosen at random. Find the probability that their $S$ score is less than 50.
17M.1.sl.TZ1.4b: Jim describes the correlation as very strong. Circle the value below which best represents the...
17M.1.sl.TZ2.8a.ii: Write down the number of employees who worked 50 hours or less.
17M.1.sl.TZ2.8c: Find the number of employees who earned £200 or less.
17N.1.sl.TZ0.1a: Complete the following tree diagram.
17N.2.sl.TZ0.7: The heights of adult males in a country are normally distributed with a mean of 180 cm and a...
17N.2.sl.TZ0.4c: Find ${\text{P}}(X = 2|X > 0)$.
18M.2.sl.TZ1.8a: Find the value of a and of b.
18M.2.sl.TZ1.9b.ii: Hence, find the value of σ.
18M.2.sl.TZ2.10a.ii: Show that μ = 106.
12N.1.sl.TZ0.2b: Find ${\text{E}}(X)$ .
12N.2.sl.TZ0.10c(i) and (ii): At a large school, students are required to learn at least one language, Spanish or French. It is...
12M.1.sl.TZ2.1b: Find the interquartile range.
12M.2.sl.TZ2.4b: The heights of a group of seven-year-old children are normally distributed with mean...
12M.2.sl.TZ2.7a: A factory makes lamps. The probability that a lamp is defective is 0.05. A random sample of 30...
12M.2.sl.TZ2.7b: A factory makes lamps. The probability that a lamp is defective is 0.05. A random sample of 30...
08N.2.sl.TZ0.5b: Find the probability of obtaining at least two heads.
08N.2.sl.TZ0.7a: Find the standard deviation of the scores.
08M.2.sl.TZ2.4b: Find the expected value of X.
12M.1.sl.TZ1.4a: Write down the value of t .
09N.1.sl.TZ0.8b: One boy is selected at random. (i) Find the probability that he plays only one...
09N.2.sl.TZ0.3b: Find the probability that Jose answers exactly three questions correctly.
09N.2.sl.TZ0.3c: Find the probability that Jose answers more than three questions correctly.
09M.1.sl.TZ2.9d: Anna plays a game where she wins $\$ 50$ if S is even and loses $\$ 30$ if S is odd. Anna...
09M.2.sl.TZ1.8d: The cost of a small fish is $\$ 4$, a medium fish $\$ 10$, and a large fish $\$ 12$. Copy...
09M.2.sl.TZ2.9c: The van sets out at 06:00 and needs to arrive before 07:00. (i) Which route should it...
10M.2.sl.TZ2.1a(i) and (ii): Find the value of (i) p ; (ii) q .
10M.2.sl.TZ2.3a: Jan tosses the two dice once. Find the probability that she wins a prize.
11N.2.sl.TZ0.2c: Given that $82\% $ of the boys are taller than $h{\text{ cm}}$, find h .
11N.2.sl.TZ0.2b: A boy is chosen at random. Find the probability that he is shorter than $161{\text{ cm}}$.
11M.1.sl.TZ1.4a: Write down ${\rm{P}}(X = 2)$ .
11M.1.sl.TZ1.4c: Find ${\rm{E}}(X)$ .
13M.2.sl.TZ2.2a: Find ${\rm{P}}(X \le 22.9)$ .
13M.2.sl.TZ2.9d: Given that at most five of the balls are gold, find the probability that exactly five of the...
08M.1.sl.TZ1.10d: (i) Construct a probability distribution table for X. (ii) Calculate the expected value...
08M.1.sl.TZ1.10e: If the total score is 3, Guiseppi wins $\$ 10$. If the total score is 2, Guiseppi gets...
14M.1.sl.TZ1.9b: Find the probability that Bill wins the first game and Andrea wins the second game.
14M.1.sl.TZ1.9a: Copy and complete the following tree diagram. (Do not write on this page.)
14M.2.sl.TZ1.8b(ii): The same data is presented in the following...
14M.2.sl.TZ1.8e: Assume that the weights of these rats are normally distributed with the mean and standard...
14M.2.sl.TZ2.3a(ii): Explain what the gradient $a$ represents.
14M.2.sl.TZ2.10a(i): A tree is selected at random from the forest. Find the probability that this tree is a giant.
13N.2.sl.TZ0.6b: The probability that a student takes between $k$ and $21.8$ minutes is $0.3$. Find the...
14N.1.sl.TZ0.8c: Find the probability that Adam will be late for school.
14N.2.sl.TZ0.8b: (i) Write down the number of families who have a monthly income of $2000$ dollars or...
14N.1.sl.TZ0.8d: Given that Adam is late for school, find the probability that he travelled by car.
14N.2.sl.TZ0.10b: (i) Write down the standardized value for $815$ g. (ii) Hence or otherwise, find...
13M.1.sl.TZ1.9c: (i) Write down the probability that the marble is drawn from jar B. (ii) Given that the...
16M.1.sl.TZ1.8b: (i) Write down the value of $a$. (ii) The interquartile range is 14. Find the value...
16M.1.sl.TZ1.8e: (i) Write down the new mean. (ii) Write down the new standard deviation.
16M.2.sl.TZ1.8d: (i) Find the probability that there are exactly two breakdowns on Tuesday. (ii) Given...
16M.2.sl.TZ2.3a: For the graph of f: (i) write down the $y$-intercept; (ii) find the...
16N.2.sl.TZ0.5b: A newborn baby has a low birth weight. Find the probability that the baby weighs at least 2.15 kg.
16N.2.sl.TZ0.8c: During week 3 each student spent 5% less time browsing the Internet than during week 1. For week...
17M.1.sl.TZ1.4c: Jim’s model is $d = - 2.24t + 105$, for $0 \leqslant t \leqslant 20$. Use his model to...
17M.1.sl.TZ2.3a: Write down ${\text{P}}(X > 107)$.
17M.2.sl.TZ1.1a.ii: Find the value of the range.
17M.2.sl.TZ1.4b.i: Hence, find the probability that exactly $k$ students are left handed;
17M.2.sl.TZ1.9c: Find $\lambda $.
17M.2.sl.TZ2.2a.i: Find the value of $a$ and of $b$.
17M.2.sl.TZ2.B10c: Jill plays the game nine times. Find the probability that she wins exactly two prizes.
18M.2.sl.TZ1.5b: Given that P((A ∪ B)′ ) = 0.19, find P(A | B′ ).
18M.2.sl.TZ1.9a: Find the probability that an orange weighs between 289 g and 310 g.
18M.1.sl.TZ2.3b.i: Write down the value of the new mean.
18M.1.sl.TZ2.3a: Find n.
12N.2.sl.TZ0.10b: At a large school, students are required to learn at least one language, Spanish or French. It is...
12M.1.sl.TZ2.9a(i) and (ii): Bag A contains three white balls and four red balls. Two balls are chosen at random without...
08N.1.sl.TZ0.5a: Write down an expression for ${\text{P}}(A \cap B)$ .
08M.2.sl.TZ1.1a(i) and (ii): (i) Write down the value of p. (ii) Find the value of q.
08M.1.sl.TZ2.1a: Calculate the value of k.
10N.1.sl.TZ0.4a: Write down the value of p .
10M.1.sl.TZ2.9d: The cost for each day that José catches the bus is 3 euros. José goes to school on Monday and...
09M.2.sl.TZ1.4a: Find ${\rm{P}}(X \le 475)$ .
09M.1.sl.TZ2.9b: Let S be the sum of the numbers on the two cards. Find the probability of each value of S.
09M.2.sl.TZ2.9b: For Route B, the probability that the journey takes less than $60$ minutes is $0.85$. Find...
10N.2.sl.TZ0.1b: Write down the median score.
SPNone.1.sl.TZ0.2b: Given that $r = 0.95$ , which of the following diagrams best represents the data.
SPNone.1.sl.TZ0.4a(i) and (ii): Each value in the data set has 10 added to it. Write down the value of (i) the new...
SPNone.2.sl.TZ0.5a(i) and (ii): (i) Write down the mean number of heads. (ii) Find the standard deviation of the number...
11N.2.sl.TZ0.2a: Write down the median value.
11M.1.sl.TZ1.8a(i), (ii) and (iii): (i) Write down the value of s . (ii) Find the value of q . (iii) Write down the value...
11M.1.sl.TZ1.8b(i) and (ii): (i) A student is selected at random. Given that the student takes music, write down the...
11M.1.sl.TZ2.6a: Find the range of the lengths of all 200 fish.
13M.1.sl.TZ2.8c: A girl is selected for the competition if she takes less than $x$ minutes to complete the...
13M.1.sl.TZ2.8d: Girls who are not selected, but took less than $25$ minutes to complete the race, are allowed...
14M.2.sl.TZ1.8a(ii): Find the percentage of rats that weigh 70 grams or less.
14M.2.sl.TZ2.3a(i): Write down the value of $a$ and of $b$.
14M.2.sl.TZ2.4c(ii): Find ${\text{P}}(A \cap B')$.
13N.2.sl.TZ0.6a: A student is selected at random. Find the probability that the student completes the task in less...
14N.1.sl.TZ0.8e: Adam will go to school three times next week. Find the probability that Adam will be late...
14N.2.sl.TZ0.8c: The $2000$ families live in two different types of housing. The following table gives...
14N.2.sl.TZ0.10c: A fishing contest takes place in the lake. Small fish, called tiddlers, are thrown back into the...
15N.2.sl.TZ0.2a: Find the value of $k$.
15N.2.sl.TZ0.5a: Write down an expression for ${\text{P}}(C \cap D)$ in terms of $k$.
10M.1.sl.TZ2.9c: The cost for each day that José catches the bus is 3 euros. José goes to school on Monday and...
09M.1.sl.TZ1.2b: Find ${\rm{P}}(B|A)$ .
09M.2.sl.TZ1.7a: Find the probability that the team wins the game.
10M.2.sl.TZ1.10a: Find the probability that a player weighs more than $82{\text{ kg}}$.
15M.2.sl.TZ1.1a: (i) Find the correlation coefficient. (ii) Write down the value of $a$ and of $b$.
16M.2.sl.TZ1.1b: Write down ${\text{P}}(X \leqslant 25)$, correct to two decimal places.
16M.2.sl.TZ1.8b: (i) A day is chosen at random. Write down the probability that Machine A has no...
17M.1.sl.TZ2.3b: Find ${\text{P}}(100 < X < 107)$.
17M.2.sl.TZ1.1b.i: Find the mean.
17N.2.sl.TZ0.8a: Write down the value of $a$ and of $b$.
18M.1.sl.TZ1.2b: One student sent k text messages, where k > 11 . Given that k is an outlier, find the least...
18M.2.sl.TZ1.5a: Find P(A ∩ B′ ).
18M.2.sl.TZ2.10d.ii: Find the probability that at least 48 bags in this crate contain at most one small apple.
12N.2.sl.TZ0.10a: At a large school, students are required to learn at least one language, Spanish or French. It is...
12M.1.sl.TZ2.4b: Given that ${\rm{E}}(X) = 1.4$ , find the value of p and of q .
08N.2.sl.TZ0.3c: Complete the frequency table below.
12M.1.sl.TZ1.4b(i) and (ii): (i) Show that $r = 0.2$ . (ii) Write down the value of q and of s .
12M.1.sl.TZ1.4c(i) and (ii): (i) Write down ${\rm{P}}(B')$ . (ii) Find ${\rm{P}}(A|B')$ .
12M.2.sl.TZ1.8b: A child is selected at random. Find the probability that the child takes less than 95 seconds to...
09N.1.sl.TZ0.3a: On the diagram below, shade the region representing ${\rm{P}}(X > 105)$ .
09N.1.sl.TZ0.3c: Given that ${\rm{P}}(X > 105) = 0.16$ (correct to two significant figures), find...
09N.1.sl.TZ0.8c: Let A be the event that a boy plays football and B be the event that a boy plays rugby. Explain...
09M.2.sl.TZ2.1a: Write down the median value.
SPNone.2.sl.TZ0.3a: Represent all this information on the following diagram.
11N.2.sl.TZ0.9c(i) and (ii): The heights of the bottles are normally distributed with a mean of $22{\text{ cm}}$ and a...
11M.2.sl.TZ1.5a: Find the expected number of brown eggs in the box.
11M.2.sl.TZ1.5c: Find the probability that there are at least 10 brown eggs in the box.
11M.2.sl.TZ2.6a: Find ${\rm{P}}(X > 27)$ .
11M.2.sl.TZ2.9a: List the pairs of scores that give a sum of 6.
13M.1.sl.TZ1.9a: Find the probability that (i) none of the marbles are green; (ii) exactly one...
13M.2.sl.TZ1.10e: In one rotation of the wheel, find the probability that a randomly selected seat is at least...
13M.2.sl.TZ2.9c: Find the probability that at most five of the balls are gold.
14M.2.sl.TZ1.3a(ii): The relationship between the variables is modelled by the regression equation \(y = ax +...
14M.2.sl.TZ2.3b: Use the model to estimate the amount of fuel the car would use if it is driven $110$ km.
14M.2.sl.TZ2.4a: Find ${\text{P}}(A \cap B)$.
13N.2.sl.TZ0.4b: Given that $A$ and $B$ are independent, find ${\text{P}}(B)$.
13N.2.sl.TZ0.10b: Given that Samantha went to school by bus on Monday, find the probability that it was raining.
14N.2.sl.TZ0.8d: A family is chosen at random. (i) Find the probability that this family lives in an...
14N.2.sl.TZ0.10d: A fish is caught at random. Find the probability that it is a tiddler.
14N.2.sl.TZ0.8e: Estimate the mean monthly income for families living in a villa.
15N.2.sl.TZ0.10b: The following table shows the percentages of small, medium and large watermelons grown on the...
15N.2.sl.TZ0.10a: Find the standard deviation of the masses of the watermelons.
15M.1.sl.TZ1.1a: Find $p$.
15M.2.sl.TZ1.9b: The company decides that the probability of a container being underfilled should be reduced to...
16M.1.sl.TZ1.8a: Find the median number of cans collected.
16M.2.sl.TZ2.3b: On the following grid, sketch the graph of $f$, for $ - 4 \leqslant x \leqslant 4$.
16N.1.sl.TZ0.5b: Find ${\text{P}}(A \cup B)$.
16N.2.sl.TZ0.7a: Write down the probability that the first disc selected is red.
16N.2.sl.TZ0.7b: Let $X$ be the number of red discs selected. Find the smallest value of $m$ for which...
16N.2.sl.TZ0.8d: (i) Find the number of students who spent between 25 and 30 hours browsing the...
17M.1.sl.TZ1.10c: Let $y = \frac{1}{{\cos x}}$, for $0 < x < \frac{\pi }{2}$. The graph of $y$between...
17M.1.sl.TZ2.8b.i: Find the amount of money an employee earned for working 40 hours;
17M.2.sl.TZ1.4a: Find $k$.
17M.2.sl.TZ1.9a: Find ${\text{P}}(X < 9)$.
17M.2.sl.TZ1.9b: Find the value of $\mu $.
17M.2.sl.TZ2.10a.ii: Find $p$.
17M.2.sl.TZ2.10b.iii: The bag contains a total of ten marbles of which $w$ are white. Find $w$.
17N.2.sl.TZ0.8b: Use this regression line to estimate the monthly honey production from a hive that has 270 bees.
17N.1.sl.TZ0.1b: Find the probability that exactly one of the selected balls is green.
18M.2.sl.TZ1.2b: Calculate the expected value of the score.
18M.2.sl.TZ1.8c: The relationship between x and y can be modelled using the formula y = kxn, where k ≠ 0 , n ≠ 0 ,...
18M.2.sl.TZ1.9c: To the nearest gram, find the minimum weight of an orange that the grocer will buy.
18M.2.sl.TZ1.9d: Find the probability that the grocer buys more than half the oranges in a box selected at random.
18M.1.sl.TZ2.8a: Copy and complete the following tree diagram.
18M.1.sl.TZ2.8b: Find the probability that Pablo leaves home before 07:00 and is late for work.
12N.1.sl.TZ0.8b(i), (ii), (iii): The box-and-whisker plot below displays the weekly wages of the employees. Write down the...
12N.1.sl.TZ0.8c: Employees are paid $$\ 20$ per hour. Find the median number of hours worked per week.
12N.1.sl.TZ0.8d: Employees are paid $\$ 20$ per hour. Find the number of employees who work more than $25$...
12N.2.sl.TZ0.6: In a large city, the time taken to travel to work is normally distributed with mean $\mu $ and...
12M.1.sl.TZ2.4a: Find the value of r .
12M.1.sl.TZ2.9c: Bag A contains three white balls and four red balls. Two balls are chosen at random without...
08M.2.sl.TZ1.6b: Find the probability that there are exactly six defective switches in the sample.
08M.1.sl.TZ2.6b: Two students are selected at random. Calculate the probability that neither student plays football.
08M.2.sl.TZ2.5a: Complete the following diagram to represent this information.
08M.2.sl.TZ2.6a: Write down the expected number of times that Paula goes to work on a red bus in one week.
10N.1.sl.TZ0.4b: Find ${\rm{P}}(B)$ .
10N.1.sl.TZ0.4c: Find ${\rm{P}}(A'|B)$ .
10M.1.sl.TZ1.5b: Find the value of ${\rm{P}}(A|B')$ .
10M.1.sl.TZ1.5c: Hence, or otherwise, show that the events A and B are not independent.
09M.1.sl.TZ2.9a: Copy and complete the table below to show all nine equally likely outcomes.
09M.2.sl.TZ2.1b: Find the value of (i) $a$ ; (ii) $b$ .
09M.2.sl.TZ2.9d: On five consecutive days the van sets out at 06:00 and takes Route B. Find the probability...
10M.2.sl.TZ1.4a: Find the value of x.
10M.2.sl.TZ1.7a: Find the probability that he wins exactly four games.
10M.2.sl.TZ2.1c: Write down the standard deviation.
SPNone.1.sl.TZ0.2a: Write down the possible minimum and maximum values of r .
SPNone.1.sl.TZ0.9b: Elena plays a game where she tosses two dice. If the sum is 6, she wins 3 points. If the sum is...
11N.2.sl.TZ0.9d(i) and (ii): (i) A bottle is accepted if its height lies between $21.37{\text{ cm}}$ and...
11M.2.sl.TZ1.5b: Find the probability that there are 15 brown eggs in the box.
11M.1.sl.TZ2.6b: Four cumulative frequency graphs are shown below. Which graph is the best representation of...
13M.2.sl.TZ2.2b: Given that ${\rm{P}}(X < k) = 0.55$ , find the value of $k$ .
14M.1.sl.TZ1.5: Celeste wishes to hire a taxicab from a company which has a large number of taxicabs. The...
14M.1.sl.TZ1.9c: Find the probability that Bill wins at least one game.
14M.2.sl.TZ1.8b(i): The same data is presented in the following table. Weights...
13N.1.sl.TZ0.3b: Find the number of students who took between 35 and 45 minutes to complete the task.
13N.2.sl.TZ0.10a: On a randomly selected school day, find the probability that Samantha goes to school by bus.
14N.1.sl.TZ0.3a: Find the probability that the dart does not hit the board.
14N.2.sl.TZ0.8a: Find the median monthly income.
14N.2.sl.TZ0.2c: Rita scored a total of $26$ in her IB Diploma. Use your regression line to estimate Rita’s...
15N.2.sl.TZ0.2b: Find ${\text{E}}(X)$.
15N.2.sl.TZ0.10c: All the medium and large watermelons are delivered to a grocer. The grocer selects a watermelon...
09M.2.sl.TZ1.8b: A cumulative frequency diagram is given below for the lengths of the fish. Use the graph to...
15M.1.sl.TZ1.10a: Find the probability that Ann wins on her first roll.
15M.2.sl.TZ1.9a: A container is chosen at random. Find the probability that it is underfilled.
15M.2.sl.TZ1.9c: The company changes to the new standard deviation, $\sigma $, and leaves the mean unchanged. A...
16M.2.sl.TZ1.8a: Find $k$.
16M.1.sl.TZ2.8a: (i) Write down the value of $p$. (ii) Find the value of $q$. (iii) Write down...
16M.2.sl.TZ2.8c: Calculate the price of Lina’s car after 6 years.
17M.1.sl.TZ1.1a.i: Find the value of $p$;
17M.1.sl.TZ1.1b: A girl is selected at random. Find the probability that she takes economics but not history.
17M.1.sl.TZ1.10a: Show that $\cos \theta = \frac{3}{4}$.
17M.1.sl.TZ1.10b: Given that $\tan \theta > 0$, find $\tan \theta $.
17M.1.sl.TZ2.8a.i: Find the median number of hours worked by the employees.
17M.1.sl.TZ2.8b.ii: Find the amount of money an employee earned for working 43 hours.
17M.2.sl.TZ1.1a.i: Write down the mode.
17M.2.sl.TZ1.9d: Given that $Y > 9$, find ${\text{P}}(Y < 13)$.
17M.2.sl.TZ2.2b: Use the regression equation to estimate the number of visitors on a day when the maximum...
17N.2.sl.TZ0.4b: Write down ${\text{P}}(X = 2)$.
17N.2.sl.TZ0.8c: Write down the number of low production hives.
17N.2.sl.TZ0.8d.ii: Find the number of hives that have a high production.
17N.2.sl.TZ0.8e: Adam decides to increase the number of bees in each low production hive. Research suggests that...
18M.1.sl.TZ1.2a: Find the value of the interquartile range.
18M.2.sl.TZ1.2a: Find the value of k.
18M.1.sl.TZ2.8c: Find the probability that Pablo is late for work.
18M.1.sl.TZ2.8d: Given that Pablo is late for work, find the probability that he left home before 07:00.

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DP Mathematics SL Questionbank

Topic 5 - Statistics and probability

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