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Topic 5 - Core: Statistics and probability

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Topic 5 - Core: Statistics and probability

Description

The aim of this topic is to introduce basic concepts. It may be considered as three parts: manipulation and presentation of statistical data (5.1), the laws of probability (5.2–5.4), and random variables and their probability distributions (5.5–5.7). It is expected that most of the calculations required will be done on a GDC. The emphasis is on understanding and interpreting the results obtained. Statistical tables will no longer be allowed in examinations.

Directly related questions

12M.1.hl.TZ2.11d: The domains of f and g are now restricted to {0, 1, 2, 3, 4} . By considering the values of f...
12M.2.hl.TZ2.10c: The weights of the plums are normally distributed with a mean of 80 grams and a standard...
12M.3sp.hl.TZ0.3a: Calculate the mean and variance of the number of injuries per week.
12N.1.hl.TZ0.5c: Find E(X ) .
12N.2.hl.TZ0.7a: Find the probability that she is successful in all three games.
12N.2.hl.TZ0.11a: If the museum is open 6 hours daily, find the expected number of visitors in 1 day.
08M.2.hl.TZ1.4: A company produces computer microchips, which have a life expectancy that follows a normal...
08M.1.hl.TZ2.7: Let A and B be events such that...
08N.2.hl.TZ0.7: (a) Ahmed is typing Section A of a mathematics examination paper. The number of mistakes that...
11M.2.hl.TZ2.6b: John catches 6 fish. Calculate the probability that at least 4 of the fish weigh more than 1.4 kg.
11M.2.hl.TZ2.12d: To encourage safety the factory pays a bonus of $1000 into a fund for workers if no accidents...
11M.3sp.hl.TZ0.1a: Find the probability that a randomly chosen orange weighs more than 200 grams.
09N.1.hl.TZ0.6: At a nursing college, 80 % of incoming students are female. College records show that 70 % of the...
09N.3sp.hl.TZ0.4: The random variable X has the distribution ${\text{B}}(n{\text{ , }}p)$ . (a) (i) Show...
13M.2.hl.TZ1.10b: It is now decided that the time between crossings, T, will be 10 minutes. The ferry can carry a...
10M.2.hl.TZ1.8: In a factory producing glasses, the weights of glasses are known to have a mean of 160 grams. It...
11N.1.hl.TZ0.10a: Find the value of k.
11N.2.hl.TZ0.11b: In the past year, 80 % of Sia’s throws have been longer than 56.52 metres. If the mean distance...
11N.3sp.hl.TZ0.1b: Find the probability that, of two randomly chosen Megamug tea bags, one contains more than 5.4 g...
08M.2.hl.TZ2.4: A continuous random variable X has probability density...
14M.2.hl.TZ1.11: A random variable $X$ has probability density...
13N.1.hl.TZ0.2: The discrete random variable X has probability distribution: (a) Find the value of...
13N.2.hl.TZ0.11b: A continuous random variable $X$ has probability distribution function $f$ given by ...
15M.2.hl.TZ1.7a: Given that $2{\text{P}}(X = 4) = {\text{P}}(X = 5)$, show that $m = 10$.
15M.2.hl.TZ1.11e: Calculate the mean of $X$.
15M.2.hl.TZ1.11h: Given that $\frac{\pi }{2} \le X \le \frac{{3\pi }}{2}$ find the probability that...
15M.2.hl.TZ2.10a: Farmer Suzie grows turnips and the weights of her turnips are normally distributed with a mean of...
15M.2.hl.TZ2.4a: (i) Find the probability that on a certain day Emma receives more than $7$ texts. (ii) ...
14N.2.hl.TZ0.12d: Find the probability that Ava eventually wins.
14N.3sp.hl.TZ0.1a: Sketch the graph of $y = f(x)$.
14N.3sp.hl.TZ0.5d: If, having done the test, the sample mean is found to lie within the critical region, find the...
15N.2.hl.TZ0.1b: Hence show that the events $A$ and $B$ are independent.
15N.2.hl.TZ0.3b: It is discovered that there is a mistake in the data and that the top scorer, who scored 22...
15N.2.hl.TZ0.6: Josie has three ways of getting to school. $30\% $ of the time she travels by car, $20\% $ of...
17M.1.hl.TZ1.10b.iii: By considering the graph of f write down the mode of $X$.
17M.1.hl.TZ1.10c.i: Show that $P(0 \leqslant X \leqslant 2) = \frac{1}{4}$.
17M.2.hl.TZ1.9b: Calculate ${T_1}$.
17M.2.hl.TZ2.3c: Calculate the new value of $\sigma $.
17M.2.hl.TZ2.10b: Find ${\text{E}}(X)$.
17N.1.hl.TZ0.10b.i: Determine the mean of X.
16N.1.hl.TZ0.2a: Complete the probability distribution table for $X$.
18M.1.hl.TZ1.3b: Find the expected value of T.
18M.2.hl.TZ1.4b: Eight wolves are independently selected at random and their ages recorded. Find the probability...
18M.2.hl.TZ2.3a: Sketch the probability density function for X, and shade the region representing P(μ − 2σ < X...
12M.2.hl.TZ1.3a: In how many ways can the team be selected?
12M.2.hl.TZ1.7: A fisherman notices that in any hour of fishing, he is equally likely to catch exactly two fish,...
12M.2.hl.TZ1.12c: It is found that 20 % of skiers having accidents are at least 25 years of age and 40 % are under...
12M.1.hl.TZ2.11e: Using this probability distribution, calculate the mean of X .
12M.2.hl.TZ2.2a: the value of p ;
12M.2.hl.TZ2.10b: The weights of the pears are normally distributed with a mean of ∝ grams and a standard deviation...
12M.3sp.hl.TZ0.5a: show that ${m^2} = k(k + 1)$;
12N.2.hl.TZ0.11b: Find the probability that the number of visitors arriving during an hour exceeds 100.
08M.1.hl.TZ2.1: The probability distribution of a discrete random variable X is defined...
11M.1.hl.TZ2.9a: What is the probability that there are exactly 3 defective DVD players in the first 8 DVD players...
11M.2.hl.TZ2.12c: Find the length of time, in complete months, for which the probability that at least 1 accident...
09M.1.hl.TZ2.3: A random variable has a probability density function given...
SPNone.2.hl.TZ0.12a: Given that 70 % of the birds weigh more than 2.1 kg and 25 % of the birds weigh more than 2.5 kg,...
13M.1.hl.TZ1.13c: The following day Alfred and Beatrice play the 6 games again. Assume that the probability that...
10M.2.hl.TZ1.12: Casualties arrive at an accident unit with a mean rate of one every 10 minutes. Assume that the...
10M.2.hl.TZ2.6: The random variable X follows a Poisson distribution with mean $\lambda $. (a) Find...
11N.2.hl.TZ0.5b: find the minimum number of work days for which the probability of the 08:00 train being delayed...
11N.2.hl.TZ0.11c: This year, Sia’s throws have a mean of 59.50 metres and a standard deviation of 3.00 metres. The...
11M.1.hl.TZ1.1b: Given that ${\text{P}}(A \cup B) = 0.6$ , find ${\text{P}}(A|B)$ .
11M.1.hl.TZ1.6b: Given that the rabbit tests positive for the disease, show that the probability that the rabbit...
11M.2.hl.TZ1.7b: Hence find (i) the mean of $X$ ; (ii) the median of $X$ .
14M.2.hl.TZ1.9b: On Monday there were more than 10 birds seen on the power line. Show that the probability of...
14M.2.hl.TZ2.6: Six customers wait in a queue in a supermarket. A customer can choose to pay with cash or a...
14M.2.hl.TZ2.11: The probability density function of a random variable X is defined...
15M.1.hl.TZ1.2b: Write down the median score.
15M.2.hl.TZ1.3b: Write down the mean of $W$.
15M.2.hl.TZ1.11a: Sketch the graph $y = f(x)$.
15M.2.hl.TZ2.9a: she travels to Nashville;
15N.2.hl.TZ0.11e: The arrival of the elevators at the ground floor between $08:00$ and $09:00$ can be modelled...
17M.1.hl.TZ1.10a: Find the value of $k$.
17M.2.hl.TZ2.1a: One of the players is chosen at random. Find the probability that this player’s score was 5 or more.
17M.2.hl.TZ2.5b: Find the probability that the 3rd July is calm.
17M.2.hl.TZ2.10e: Find ${\text{E}}(Y)$.
16N.1.hl.TZ0.2b: Find the expected value of $X$.
16N.2.hl.TZ0.8b: Find ${\text{P}}\left( {\left| {X - \mu } \right| < 1.2\sigma } \right)$.
16M.2.hl.TZ1.13b.i: the total of the three numbers is 5;
16M.2.hl.TZ1.13c: Ten balls are taken from the bag. Find the probability that less than four of the balls are...
16M.2.hl.TZ1.6: The heights of students in a single year group in a large school can be modelled by a normal...
16M.2.hl.TZ2.10e: Find the probability that $T$ lies between the mean and the mode.
16M.2.hl.TZ2.6a: Find the probability that a randomly chosen glass sheet contains at least one flaw.
18M.1.hl.TZ2.3b.ii: Find P(X > μ).
18M.2.hl.TZ2.8a: Find the least possible value of n.
18M.2.hl.TZ2.9a.i: Find the probability that exactly 4 taxis arrive during T.
18M.1.hl.TZ2.3a: Find the value of p.
18M.1.hl.TZ2.3b.i: Find μ, the expected value of X.
12M.1.hl.TZ2.3c: Given that the “Tigers” soccer team won, what is the probability that it rained on that day?
12M.2.hl.TZ2.2b: ${\text{P}}(X = 10)$ ;
12M.3sp.hl.TZ0.5b: hence show that the mode of X is k .
08M.2.hl.TZ2.7: Over a one month period, Ava and Sven play a total of n games of tennis. The probability that...
11M.1.hl.TZ2.9b: What is the probability that the ${9^{{\text{th}}}}$ DVD player examined is the...
11M.2.hl.TZ2.6c: Determine the probability that a fish which is caught weighs less than 1 kg, given that it weighs...
SPNone.1.hl.TZ0.3a: Calculate the probability that no head is obtained.
SPNone.1.hl.TZ0.3b: Given that no head is obtained, find the probability that he tossed two coins.
SPNone.3sp.hl.TZ0.5a: Determine ${\text{E}}(X)$ and show that ${\text{Var}}(X) = 6\theta - 16{\theta ^2}$.
13M.1.hl.TZ1.4: The probability density function of the random variable X is defined...
13M.2.hl.TZ1.3b: Find the probability she is late at least once during the next week (Monday to Friday).
13M.1.hl.TZ2.4b: Find the probability that Tim and Caz eat the same type of chocolate.
13M.2.hl.TZ2.7c: Find ${\text{P}}(X < 0.6)$.
13M.2.hl.TZ2.7a: Show that a = 9.6.
08M.2.hl.TZ2.11a: The distance travelled by students to attend Gauss College is modelled by a normal distribution...
11M.1.hl.TZ1.6a: Find the probability that the rabbit tests positive for the disease.
11M.2.hl.TZ1.12c: Maelis had not arrived by 08:30. Find the probability that she arrived late.
09N.2.hl.TZ0.5: The annual weather-related loss of an insurance company is modelled by a random variable $X$...
14M.2.hl.TZ1.9a: Find the probability that during a certain seven-day week, more than 40 birds have been seen on...
14M.1.hl.TZ2.11b: In a pack of seven transistors, three are found to be defective. Three transistors are selected...
13N.2.hl.TZ0.4: The duration of direct flights from London to Singapore in a particular year followed a normal...
15M.1.hl.TZ1.2a: Find the mean score for the class.
15M.2.hl.TZ1.7b: Given that $X \le 11$, find the probability that $X = 6$.
15M.2.hl.TZ2.4b: Find the probability that Emma receives fewer than $30$ texts during a week.
15M.3sp.hl.TZ0.5c: Two independent random variables ${X_1}$ and ${X_2}$ are such that...
14N.2.hl.TZ0.12c: Find the probability that Ava wins in one of her first three turns.
14N.3sp.hl.TZ0.4d: Could either $S$ or $T$ model a Poisson distribution? Justify your answer.
15N.1.hl.TZ0.6b: The game is now changed so that the ball chosen is replaced after each turn. Darren still plays...
15N.2.hl.TZ0.8c: Find the value ${\text{P}}(X \le 3|X \ge 2)$.
15N.2.hl.TZ0.11c: There are elevators in the office building that take the office workers to their offices. Given...
17M.1.hl.TZ1.10c.ii: Hence state the interquartile range of $X$.
17M.2.hl.TZ1.9a: Find the probability that a runner selected at random will complete the marathon in less than 3...
17M.2.hl.TZ2.3b: Calculate the new value of $\mu $ giving your answer correct to two decimal places.
17N.2.hl.TZ0.6a: Find the probability that Lucca eats at least one banana in a particular day.
16M.2.hl.TZ1.13b.ii: the median of the three numbers is 1.
16M.2.hl.TZ1.10: Students sign up at a desk for an activity during the course of an afternoon. The arrival of each...
16M.2.hl.TZ2.10b: Use your sketch to find the mode of $T$.
16M.2.hl.TZ2.10d: Find the variance of $T$.
18M.2.hl.TZ1.10b: Find ${\text{P}}\left( {X < 1} \right)$.
18M.2.hl.TZ1.4a: Find the probability that a wolf selected at random is at least 5 years old.
18M.2.hl.TZ1.8: Each of the 25 students in a class are asked how many pets they own. Two students own three pets...
18M.2.hl.TZ1.6: The mean number of squirrels in a certain area is known to be 3.2 squirrels per hectare of...
12M.2.hl.TZ1.5b: State, with reasons, the maximum possible number and minimum possible number of students who...
12M.2.hl.TZ1.12a(i)(ii): Find the probability that in a certain week (Monday to Friday only) (i) there are fewer than...
12M.2.hl.TZ2.5a: the value of m ;
12M.3sp.hl.TZ0.3b: Explain why these values provide supporting evidence for using a Poisson distribution model.
12M.3sp.hl.TZ0.4b: (i) Determine E(X ). (ii) Determine ${\text{E}}({X^2})$.
12N.2.hl.TZ0.11d: The ages of the visitors to the museum can be modelled by a normal distribution with mean...
12N.2.hl.TZ0.11e: The ages of the visitors to the museum can be modelled by a normal distribution with mean...
12N.2.hl.TZ0.7b: Assuming that she is successful in the first game, find the probability that she is successful in...
12N.2.hl.TZ0.11c: Find the probability that the number of visitors in each of the 6 hours the museum is open...
08M.1.hl.TZ1.9: The random variable T has the probability density...
08M.2.hl.TZ1.11: The lifts in the office buildings of a small city have occasional breakdowns. The breakdowns at...
08M.2.hl.TZ2.11c: The number of telephone calls, T, received by Euler College each minute can be modelled by a...
08N.2.hl.TZ0.11Part A: (a) A box of biscuits is considered to be underweight if it weighs less than 228 grams. It is...
SPNone.1.hl.TZ0.4b: Determine the mode of X .
SPNone.3sp.hl.TZ0.2a: Write down the value of ${\text{P}}(X = 1)$ and show that ${\text{P}}(X = 2) = \frac{1}{6}$.
13M.1.hl.TZ1.13a: Show that the probability that Alfred wins exactly 4 of the games is $\frac{{80}}{{243}}$.
13M.1.hl.TZ1.13d: Alfred and Beatrice play n games. Let A denote the number of games Alfred wins. The expected...
10M.1.hl.TZ1.10: The ten numbers ${x_1},{\text{ }}{x_2},{\text{ }} \ldots ,{\text{ }}{x_{10}}$ have a mean of 10...
13M.2.hl.TZ2.11c: The random variable $X \sim B(n,{\text{ }}p)$ has mean 4 and variance 3. (i) Determine n...
11N.1.hl.TZ0.10c: Find the median of X.
11M.2.hl.TZ1.12e: At 15:00 it is the end of the school day and it is assumed that the departure of the students...
09M.2.hl.TZ2.11: (a) Show that the probability that a randomly selected bottle filled by Machine A contains...
14M.2.hl.TZ2.2: The weights, in kg, of one-year-old bear cubs are modelled by a normal distribution with mean...
13N.2.hl.TZ0.5a: Find the probability that they watch a French movie.
15M.2.hl.TZ1.11f: Calculate the variance of $X$.
15M.2.hl.TZ1.11d: Write down the median of $X$.
15M.2.hl.TZ1.11b: Find ${\text{P}}(X \le \pi )$.
14N.1.hl.TZ0.4b: Determine the range of possible values of ${\text{P}}\left( {A|B} \right)$.
14N.2.hl.TZ0.2b: In a field experiment, a research team studies a large sample of these birds. The wingspans of...
14N.2.hl.TZ0.11a: On a randomly chosen day, find the probability that (i) there are no complaints; (ii) ...
14N.2.hl.TZ0.11c: On a randomly chosen day, find the most likely number of complaints received. Justify your answer.
15N.1.hl.TZ0.6a: Darren plays first, find the probability that he wins.
15N.2.hl.TZ0.11b: Find the probability that an office worker weighs more than $100$ kg.
17M.1.hl.TZ1.10d: Calculate $P(X \leqslant 4|X \geqslant 3)$.
17M.1.hl.TZ2.7b: The random variable $Y$ has the Poisson distribution ${\text{Po}}(2m)$. Find...
17M.2.hl.TZ1.5b: Find the probability that exactly seven rooms will have fewer than three faults in the carpet.
17M.2.hl.TZ2.1b: Calculate the mean score.
17N.2.hl.TZ0.2c: Hence show that events $A’$ and $B$ are independent.
17N.2.hl.TZ0.4: It is given that one in five cups of coffee contain more than 120 mg of caffeine.It is also known...
16N.1.hl.TZ0.10a: Show that ${\text{P}}(A \cup B) = {\text{P}}(A) + {\text{P}}(A' \cap B)$.
16N.2.hl.TZ0.3b: Given that ${\text{P}}(X = 2) = 0.241667$ and ${\text{P}}(X = 3) = 0.112777$, use part (a) to...
16N.2.hl.TZ0.8a: Find $\mu $ and $\sigma $.
16M.1.hl.TZ2.5a: Find, in terms of $p$, an expression for ${\text{P}}(X = 4)$.
16M.1.hl.TZ2.7a: Show that ${\text{P}}(A \cup B) = 2p - {p^2}$.
16M.2.hl.TZ2.10a: Sketch the graph of $y = f(t)$.
16M.2.hl.TZ2.10c: Find the mean of $T$.
16M.2.hl.TZ2.6c: Find the probability that it contains no flaws.
16M.2.hl.TZ2.6b: Find the expected profit, $P$ dollars, per glass sheet.
18M.2.hl.TZ2.9b: During quiet periods of the day, taxis arrive at a mean rate of 1.3 taxis every 10 minutes. Find...
12M.2.hl.TZ1.12b(i)(ii): Due to the increased usage, it is found that the probability of more than 3 accidents in a day at...
12M.2.hl.TZ2.2c: ${\text{P}}(X \geqslant 15)$ .
12M.2.hl.TZ2.5b: P (X > 2) .
12M.2.hl.TZ2.7b: Find the mean of X .
12M.2.hl.TZ2.10a: The weights of the apples are normally distributed with a mean of 200 grams and a standard...
12N.1.hl.TZ0.5b: Determine the value of a .
12N.3sp.hl.TZ0.1f: Find P(B = 5) .
08M.2.hl.TZ2.1: Consider the data set...
08N.2.hl.TZ0.11Part B: There are six boys and five girls in a school tennis club. A team of two boys and two girls will...
11M.2.hl.TZ2.6a: Determine the probability that a fish which is caught weighs less than 1.4 kg.
13M.2.hl.TZ1.3a: Find the probability she is late next Monday.
10N.2.hl.TZ0.3: The weight loss, in kilograms, of people using the slimming regime SLIM3M for a period of three...
10N.2.hl.TZ0.11: Tim throws two identical fair dice simultaneously. Each die has six faces: two faces numbered 1,...
13M.2.hl.TZ2.3a: Calculate the range of lifespans of Manx cats whose lifespans are within one standard deviation...
13M.2.hl.TZ2.9b: Over a weekend of two days, it is given that a total of three requests are received. Find the...
11N.2.hl.TZ0.11a: In the past year, 80 % of Jan’s throws have been longer than x metres. Find x correct to two...
11M.2.hl.TZ1.7a: Find the value of $k$ .
11M.2.hl.TZ1.12d: At 15:00 it is the end of the school day and it is assumed that the departure of the students...
09M.2.hl.TZ1.4: (a) the probability that he catches at least one fish in the first hour; (b) the probability...
14M.1.hl.TZ2.1: Events $A$ and $B$ are such that...
14M.1.hl.TZ2.11a: Mobile phone batteries are produced by two machines. Machine A produces 60% of the daily output...
14M.2.hl.TZ2.8: The random variable $X$ has a Poisson distribution with mean $\mu $. Given that...
15M.3sp.hl.TZ0.1a: A large can is selected at random. Find the probability that the can contains at least $4995$...
14N.1.hl.TZ0.4a: Determine the value of ${\text{P}}(A \cup B)$ when (i) $A$ and $B$ are mutually...
14N.1.hl.TZ0.9b: Find the interquartile range of $T$.
15N.2.hl.TZ0.8b: Find the mode of $X$.
15N.2.hl.TZ0.11a: (i) Determine two simultaneous linear equations satisfied by $\mu $ and $\sigma $. (ii)...
15N.2.hl.TZ0.11f: An elevator can take a maximum of $10$ workers. Given that $400$ workers arrive in a half...
17M.1.hl.TZ2.7a: The random variable $X$ has the Poisson distribution ${\text{Po}}(m)$. Given that...
17M.2.hl.TZ1.9c: Find the standard deviation of the times taken by female runners.
17M.2.hl.TZ2.10f: Find ${\text{P}}(Y \geqslant 3)$.
17N.1.hl.TZ0.10b.ii: Determine the variance of X.
17N.2.hl.TZ0.6b: Find the expected number of weeks in the year in which Lucca eats no bananas.
259339: This is an example question for the example test. You can delete this question.
16N.1.hl.TZ0.1: Find the coordinates of the point of intersection of the planes defined by the equations...
16N.2.hl.TZ0.11a: Show that ${\text{P}}(X = 3) = 0.001$ and ${\text{P}}(X = 4) = 0.0027$.
16M.2.hl.TZ1.13a: A single ball is taken from the bag. Let $X$ denote the value shown on the ball. Find...
16M.2.hl.TZ2.10f: (i) Find $\int_0^\pi {f(t){\text{d}}t} $ where \(0 \leqslant T \leqslant \frac{\pi...
16M.2.hl.TZ2.2a: Find ${\text{P}}(0 \leqslant X \leqslant 2)$.
18M.2.hl.TZ1.10a: Show that $a = \frac{2}{3}$.
18M.1.hl.TZ1.3a: Find the value of a and the value of b.
18M.2.hl.TZ2.8b: It is further given that P(X ≤ 1) = 0.09478 correct to 4 significant figures. Determine the...
12M.2.hl.TZ1.3b: In how many of these selections is exactly one girl in the team?
12M.1.hl.TZ2.3b: What is the probability that the “Tigers” soccer team wins?
08M.2.hl.TZ1.8: Only two international airlines fly daily into an airport. UN Air has 70 flights a day and IS Air...
08N.1.hl.TZ0.8: John removes the labels from three cans of tomato soup and two cans of chicken soup in order to...
08N.2.hl.TZ0.3: A continuous random variable X has a probability density function given...
11M.2.hl.TZ2.12b: Find the probability that no accidents occur in a given 6 month period.
SPNone.1.hl.TZ0.4a: Determine ${\text{E}}(X)$ .
SPNone.2.hl.TZ0.12c: The number of eggs, Y , laid by female birds of this species during the nesting season is...
13M.2.hl.TZ1.1: The marks obtained by a group of students in a class test are shown below. Given the...
13M.2.hl.TZ1.10a: Find T, to the nearest minute, if ${\text{P}}(X \leqslant 3) = 0.6$.
10M.1.hl.TZ2.1: A continuous random variable X has the probability density function f given...
10M.2.hl.TZ2.2: A discrete random variable X has a probability distribution given in the following...
13M.1.hl.TZ2.4a: Draw a tree diagram representing the possible outcomes, clearly labelling each branch with the...
13M.2.hl.TZ2.7b: Sketch the graph of the distribution.
13M.2.hl.TZ2.9a: Find the probability that on a particular weekend, three requests are received on Saturday and...
11N.1.hl.TZ0.3: In a particular city 20 % of the inhabitants have been immunized against a certain disease. The...
11N.1.hl.TZ0.10b: Find ${\text{E}}(X)$.
11M.2.hl.TZ1.12a: Find the mean and standard deviation of $X$.
11M.2.hl.TZ1.12b: The school has 1200 students and classes start at 09:00. Estimate the number of students who will...
09N.2.hl.TZ0.6: (a) Tim says he will leave if he is not seated at a table within $25$ minutes of arriving...
09N.2.hl.TZ0.13: (a) The first game consists of one round. If Ying obtains more heads than Mario, she receives...
15M.1.hl.TZ1.10: A football team, Melchester Rovers are playing a tournament of five matches. The probabilities...
15M.1.hl.TZ2.1a: Find ${\text{P}}(A \cap B)$.
15M.1.hl.TZ2.1b: Determine whether events $A$ and $B$ are independent.
15M.2.hl.TZ1.2a: Find the probability that a runner finishes the race in under three hours.
15M.2.hl.TZ1.2b: The fastest $90\% $ of the finishers receive a certificate. Find the time, below which a...
15M.3sp.hl.TZ0.5a: Determine the probability generating function for $X \sim {\text{B}}(1,{\text{ }}p)$.
14N.2.hl.TZ0.11b: In a randomly chosen five-day week, find the probability that there are no complaints.
14N.2.hl.TZ0.11d: The department store introduces a new policy to improve customer service. The number of...
15N.2.hl.TZ0.8a: Find the value of $A$ to three decimal places.
15N.2.hl.TZ0.11d: Given that there are $10$ workers in an elevator and at least one weighs more than $100$...
17M.2.hl.TZ2.5c: Find the probability that the 1st July was calm given that the 3rd July is windy.
17M.2.hl.TZ2.10a: Show that $a = 32$ and $b = \frac{1}{{12}}$.
17M.2.hl.TZ2.10d: Find the median of $X$.
17N.2.hl.TZ0.2b: Find ${\text{P}}(A)$.
16N.1.hl.TZ0.10b: (i) show that ${\text{P}}(A) = \frac{1}{3}$; (ii) hence find ${\text{P}}(B)$.
16N.2.hl.TZ0.1a: Determine the value of ${\text{E}}({X^2})$.
16M.1.hl.TZ1.4a: On the Venn diagram shade the region $A' \cap B'$.
16M.2.hl.TZ1.13d: Find the least number of balls that must be taken from the bag for the probability of taking out...
16M.1.hl.TZ2.5b: (i) Determine the value of $p$ for which ${\text{P}}(X = 4)$ is a maximum. (ii) For...
16M.2.hl.TZ2.2c: If ${\text{P}}(X > c) = 0.44$, find the value of $c$.
16M.2.hl.TZ2.2b: Find ${\text{P}}(\left| X \right| > 1)$.
18M.2.hl.TZ1.10c: Given that...
18M.2.hl.TZ2.3b: Find the value of P(μ − 2σ < X < μ + σ).
18M.2.hl.TZ2.9a.ii: Find the most likely number of taxis that would arrive during T.
18M.2.hl.TZ2.9a.iii: Given that more than 5 taxis arrive during T, find the probability that exactly 7 taxis arrive...
12M.2.hl.TZ1.3c: If the selection of the team is made at random, find the probability that exactly one girl is in...
12M.2.hl.TZ1.5a: How many students obtained a grade of more than 4?
11M.1.hl.TZ2.3b: Find the value of k .
SPNone.2.hl.TZ0.12b: A random sample of ten of these birds is obtained. Let X denote the number of birds in the sample...
10M.3sp.hl.TZ0.3a: The random variable X is assumed to have probability density function f,...
13M.2.hl.TZ2.3b: Estimate the number of Manx cats in a population of 10 000 that will have a lifespan of less than...
11N.2.hl.TZ0.3a: Find the probability that no vehicles pass in a given minute.
11N.2.hl.TZ0.3b: Find the expected number of vehicles which pass in a given two minute period.
11N.3sp.hl.TZ0.1a: Find the probability that a randomly chosen Supermug tea bag contains more than 3.9 g of tea.
09M.2.hl.TZ2.1: (a) Illustrate this information on a Venn diagram. (b) Find the probability that a...
09M.2.hl.TZ2.5: (a) Find the percentage of the population that has been vaccinated. (b) A randomly...
14M.3sp.hl.TZ0.1a: (i) Find ${\text{P}}(X = 6)$. (ii) Find ${\text{P}}(X = 6|5 \leqslant X \leqslant 8)$.
14M.2.hl.TZ1.2: A student sits a national test and is told that the marks follow a normal distribution with mean...
14M.2.hl.TZ1.8b: Mina and Norbert each have a fair cubical die with faces labelled 1, 2, 3, 4, 5 and 6; they...
13N.3sp.hl.TZ0.1a: Using the data in the table, (i) show that an estimate of the mean speed of the sample is...
15M.1.hl.TZ1.2c: Write down the number of students who scored (i) above the mean score; (ii) below the...
15M.2.hl.TZ1.3a: State the distribution of $W$, including the values of any parameters.
15M.2.hl.TZ1.11g: Find ${\text{P}}\left( {\frac{\pi }{2} \le X \le \frac{{3\pi }}{2}} \right)$.
15M.2.hl.TZ2.10b: Farmer Ray also grows turnips and the weights of his turnips are normally distributed with a mean...
14N.2.hl.TZ0.3: Consider the data set...
14N.2.hl.TZ0.12b: Find the probability that Barry wins on his first turn.
15N.2.hl.TZ0.1a: Find ${\text{P}}(A \cap B)$.
17M.1.hl.TZ1.10b.i: By considering the graph of f write down the mean of $X$;
17M.2.hl.TZ1.1b: Find ${\text{P}}(A' \cap B)$.
17M.2.hl.TZ2.3a: Given that $\mu = 253$ and $\sigma = 1.5$ find the probability that a randomly chosen packet...
17N.2.hl.TZ0.2a: Find ${\text{P}}(B)$.
16N.2.hl.TZ0.11e: Determine the minimum value of $x$ such that the probability Kati receives at least one free...
16M.1.hl.TZ2.7b: Find ${\text{P}}(A|A \cup B)$ in simplest form.
12M.2.hl.TZ1.2: The probability density function of the continuous random variable X is given by...
12M.1.hl.TZ2.3a: Draw a tree diagram to represent these events and their outcomes.
12M.2.hl.TZ2.7a: Find the value of a .
12M.3sp.hl.TZ0.4a: Sketch the function f and show that the lower quartile is 0.5.
12N.1.hl.TZ0.5a: State the mode of X .
12N.2.hl.TZ0.4: A set of 15 observations has mean 11.5 and variance 9.3. One observation of 22.1 is considered...
12N.3sp.hl.TZ0.1d: State the distribution of B .
12N.3sp.hl.TZ0.1e: Find P(B = 3) .
08M.2.hl.TZ2.11b: At Euler College, the distance travelled by students to attend their school is modelled by a...
11M.2.hl.TZ2.12a: Find the probability that no accidents occur in a given month.
13M.1.hl.TZ1.9: Two events A and B are such that ${\text{P}}(A \cup B) = 0.7$ and \({\text{P}}(A|B') =...
10M.1.hl.TZ1.7: Two players, A and B, alternately throw a fair six-sided dice, with A starting, until one of them...
10M.1.hl.TZ1.12: A continuous random variable X has probability density...
10M.1.hl.TZ2.4: A biased coin is weighted such that the probability of obtaining a head is $\frac{4}{7}$. The...
10M.2.hl.TZ2.3: After being sprayed with a weedkiller, the survival time of weeds in a field is normally...
10N.1.hl.TZ0.4: Jenny goes to school by bus every day. When it is not raining, the probability that the bus is...
10N.2.hl.TZ0.7: The random variable X follows a Poisson distribution with mean m and...
11N.2.hl.TZ0.5a: find the probability that the 08:00 train is delayed exactly twice during any period of five work...
11N.2.hl.TZ0.3c: Find the probability that more than this expected number actually pass in a given two minute period.
11M.1.hl.TZ1.1a: Find the value of ${\text{P}}(A \cup B)$ when(i) $A$ and $B$ are mutually...
09M.2.hl.TZ1.1: Bob measured the heights of 63 students. After analysis, he conjectured that the height, $H$ ,...
14M.1.hl.TZ1.2: Four numbers are such that their mean is 13, their median is 14 and their mode is 15. Find the...
13N.2.hl.TZ0.5b: Given that last week they watched a French movie, find the probability that it was on a Saturday...
13N.2.hl.TZ0.11a: The number of cats visiting Helena’s garden each week follows a Poisson distribution with mean...
15M.2.hl.TZ1.11c: Show that $a = \frac{1}{{{\pi ^2}}}$.
15M.2.hl.TZ1.3c: Find ${\text{P}}(W > 89)$.
15M.2.hl.TZ2.9b: she is on her way to Nashville, given that she is flying.
15M.3sp.hl.TZ0.5b: Explain why the probability generating function for ${\text{B}}(n,{\text{ }}p)$ is a polynomial...
14N.2.hl.TZ0.2a: Find the value of $x$.
14N.2.hl.TZ0.12a: Find the probability that Ava wins on her first turn.
15N.2.hl.TZ0.3a: Given that the mean number of goals scored per player is $1.95$ , find the value of $k$.
17M.1.hl.TZ1.10b.ii: By considering the graph of f write down the median of $X$;
17M.2.hl.TZ1.1a: Calculate $k$;
17M.2.hl.TZ1.5a: Find the probability that the carpet laid in the first room has fewer than three faults.
17M.2.hl.TZ2.5a: Draw a tree diagram to represent this information for the first three days of July.
17M.2.hl.TZ2.10c: Find ${\text{Var}}(X)$.
16N.2.hl.TZ0.1b: Find the value of ${\text{Var}}(X)$.
16N.2.hl.TZ0.11d: (i) Hence show that $X$ has two modes ${m_1}$ and ${m_2}$. (ii) State the values...
16N.2.hl.TZ0.3a: Show that...
16M.1.hl.TZ1.2: At a skiing competition the mean time of the first three skiers is 34.1 seconds. The time for the...
16M.1.hl.TZ1.4b: Find ${\text{P}}(A'|B')$.
16M.2.hl.TZ1.13e: Another bag also contains balls numbered 1 , 2 or 3. Eight balls are to be taken from this bag...
18M.2.hl.TZ2.3c: Find the value of k for which P(μ − kσ < X < μ + kσ) = 0.5.

Sub sections and their related questions

DP Mathematics HL Questionbank

Topic 5 - Core: Statistics and probability

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Directly related questions

Sub sections and their related questions

5.1

5.2

5.3

5.4

5.5

5.6

5.7