DP Mathematics SL Questionbank

• Syllabus

5.8

Sub sections and their related questions

Binomial distribution.

• 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.TZ0.5a: Find the probability of obtaining exactly two heads.
• 08N.2.sl.TZ0.5b: Find the probability of obtaining at least two heads.
• 08M.2.sl.TZ1.6a: Find the mean number of defective switches in the sample.
• 08M.2.sl.TZ1.6b: Find the probability that there are exactly six defective switches in the sample.
• 08M.2.sl.TZ1.6c: Find the probability that there is at least one defective switch in the sample.
• 08M.2.sl.TZ2.6a: Write down the expected number of times that Paula goes to work on a red bus in one week.
• 08M.2.sl.TZ2.6b: In one week, find the probability that she goes to work on a red bus on exactly two days.
• 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.TZ1.7a: The probability of obtaining “tails” when a biased coin is tossed is \(0.57\). The coin is tossed...
• 12M.2.sl.TZ1.7b: The probability of obtaining “tails” when a biased coin is tossed is 0.57. The coin is tossed ten...
• 09N.2.sl.TZ0.3a: Find the expected number of questions Jose answers correctly.
• 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.2.sl.TZ2.9d: On five consecutive days the van sets out at 06:00 and takes Route B. Find the probability...
• 10N.2.sl.TZ0.9a(i) and (ii): (i)     Find E(X ) . (ii)    Find the probability that Mark passes the test.
• 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.TZ1.7a: Find the probability that he wins exactly four games.
• 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.TZ1.7c: Hence, find the values of p such that the probability that he wins exactly four games is 0.15.
• 10M.2.sl.TZ2.3a: Jan tosses the two dice once. Find the probability that she wins a prize.
• 10M.2.sl.TZ2.3b: Jan tosses the two dice 8 times. Find the probability that she wins 3 prizes.
• SPNone.2.sl.TZ0.5a(i) and (ii): (i)     Write down the mean number of heads. (ii)    Find the standard deviation of the number...
• SPNone.2.sl.TZ0.5b: Find the probability that the number of heads obtained is less than one standard deviation away...
• 11N.2.sl.TZ0.9a: Find the probability that exactly one cap in the sample will be defective.
• 11N.2.sl.TZ0.9b: The sample of caps passes inspection if at most one cap is defective. Find the probability that...
• 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...
• 11N.2.sl.TZ0.9d(i) and (ii): (i)     A bottle is accepted if its height lies between \(21.37{\text{ cm}}\) and...
• 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.TZ1.5a: Find the expected number of brown eggs in the box.
• 11M.2.sl.TZ1.5b: Find the probability that there are 15 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.TZ2.9a: List the pairs of scores that give a sum of 6.
• 11M.2.sl.TZ2.9b: The probability distribution for the sum of the scores on the two dice is shown below. Find...
• 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.TZ2.9c: Find the probability that at most five of the balls are gold.
• 14M.2.sl.TZ1.8e: Assume that the weights of these rats are normally distributed with the mean and standard...
• 14M.2.sl.TZ2.10c(i): \(100\) trees are selected at random. Find the expected number of these trees that are giants.
• 14M.2.sl.TZ2.10c(ii): \(100\) trees are selected at random. Find the probability that at least \(25\) of these trees...
• 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.1.sl.TZ0.8e: Adam will go to school three times next week. Find the probability that Adam will be late...
• 15M.2.sl.TZ1.9d: A sample of \(50\) containers is chosen at random. Find the probability that \(48\) or more of...
• 16M.2.sl.TZ1.8a: Find \(k\).
• 16M.2.sl.TZ1.8b: (i)     A day is chosen at random. Write down the probability that Machine A has no...
• 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...
• 17N.2.sl.TZ0.8a: Write down the value of \(a\) and of \(b\).
• 17N.2.sl.TZ0.8b: Use this regression line to estimate the monthly honey production from a hive that has 270 bees.
• 17N.2.sl.TZ0.8c: Write down the number of low production hives.
• 17N.2.sl.TZ0.8d.i: Find the value of \(k\);
• 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...
• 259340: This is an example question for the example test. You can delete this question.
• 18M.2.sl.TZ1.9a: Find the probability that an orange weighs between 289 g and 310 g.
• 18M.2.sl.TZ1.9b.i: Find the standardized value for 289 g.
• 18M.2.sl.TZ1.9b.ii: Hence, find the value of σ.
• 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.2.sl.TZ1.9e: The grocer selects two boxes at random. Find the probability that the grocer buys more than half...
• 18M.2.sl.TZ2.10a.i: Write down the value of k.
• 18M.2.sl.TZ2.10a.ii: Show that μ = 106.
• 18M.2.sl.TZ2.10b: Find P(M < 95) .
• 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.TZ2.10d.ii: Find the probability that at least 48 bags in this crate contain at most one small apple.

Mean and variance of the binomial distribution.

• 08M.2.sl.TZ1.6a: Find the mean number of defective switches in the sample.
• 08M.2.sl.TZ1.6b: Find the probability that there are exactly six defective switches in the sample.
• 08M.2.sl.TZ1.6c: Find the probability that there is at least one defective switch in the sample.
• 08M.2.sl.TZ2.6a: Write down the expected number of times that Paula goes to work on a red bus in one week.
• 08M.2.sl.TZ2.6b: In one week, find the probability that she goes to work on a red bus on exactly two days.
• 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.
• 10N.2.sl.TZ0.9a(i) and (ii): (i)     Find E(X ) . (ii)    Find the probability that Mark passes the test.
• 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.
• SPNone.2.sl.TZ0.5a(i) and (ii): (i)     Write down the mean number of heads. (ii)    Find the standard deviation of the number...
• SPNone.2.sl.TZ0.5b: Find the probability that the number of heads obtained is less than one standard deviation away...
• 11M.2.sl.TZ1.5a: Find the expected number of brown eggs in the box.
• 11M.2.sl.TZ1.5b: Find the probability that there are 15 brown eggs in the box.
• 11M.2.sl.TZ1.5c: Find the probability that there are at least 10 brown eggs in the box.
• 14M.2.sl.TZ2.10c(i): \(100\) trees are selected at random. Find the expected number of these trees that are giants.
• 16M.2.sl.TZ1.8a: Find \(k\).
• 16M.2.sl.TZ1.8b: (i)     A day is chosen at random. Write down the probability that Machine A has no...
• 18M.2.sl.TZ1.9a: Find the probability that an orange weighs between 289 g and 310 g.
• 18M.2.sl.TZ1.9b.i: Find the standardized value for 289 g.
• 18M.2.sl.TZ1.9b.ii: Hence, find the value of σ.
• 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.2.sl.TZ1.9e: The grocer selects two boxes at random. Find the probability that the grocer buys more than half...