DP Mathematics SL Questionbank

• Syllabus

5.9

Sub sections and their related questions

Normal distributions and curves.

• 12N.2.sl.TZ0.6: In a large city, the time taken to travel to work is normally distributed with mean \(\mu \) and...
• 08N.2.sl.TZ0.7a: Find the standard deviation of the scores.
• 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.TZ1.8a(i) and (ii): One biscuit is chosen at random from the box. Find the probability that this biscuit (i)    ...
• 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...
• 08M.2.sl.TZ1.8c: The weights of biscuits in another box are normally distributed with mean \(\mu \) and standard...
• 08M.2.sl.TZ2.5a: Complete the following diagram to represent this information.
• 08M.2.sl.TZ2.5b: Given that the mean height is \(6.84{\text{ cm}}\) and the standard deviation...
• 12M.2.sl.TZ1.8a(i) and (ii): (i)     Write down the value of p and of q . (ii)    Write down the median class.
• 12M.2.sl.TZ1.8b: A child is selected at random. Find the probability that the child takes less than 95 seconds to...
• 12M.2.sl.TZ1.8c(i) and (ii): Consider the class interval \(45 \le T < 55\) . (i)     Write down the interval...
• 12M.2.sl.TZ1.8d(i) and (ii): Hence find an estimate for the (i)     mean; (ii)    standard deviation.
• 12M.2.sl.TZ1.8e: John assumes that T is normally distributed and uses this to estimate the probability that a...
• 09N.1.sl.TZ0.3a: On the diagram below, shade the region representing \({\rm{P}}(X > 105)\) .
• 09N.1.sl.TZ0.3b: Given that \({\rm{P}}(X < d) = {\rm{P}}(X > 105)\) , find the value of \(d\) .
• 09N.1.sl.TZ0.3c: Given that \({\rm{P}}(X > 105) = 0.16\) (correct to two significant figures), find...
• 09M.2.sl.TZ1.4a: Find \({\rm{P}}(X \le 475)\) .
• 09M.2.sl.TZ1.4b: Given that \({\rm{P}}(X > a) = 0.27\) , find \(a\).
• 09M.2.sl.TZ2.9a: For Route A, find the probability that the journey takes more than \(60\) minutes.
• 09M.2.sl.TZ2.9b: For Route B, the probability that the journey takes less than \(60\) minutes is \(0.85\). Find...
• 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.TZ1.10a: Find the probability that a player weighs more than \(82{\text{ kg}}\).
• 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.TZ1.10d: Of the players in the league, \(25\% \) are women. Of the women, \(70\% \) take part in the...
• SPNone.2.sl.TZ0.3a: Represent all this information on the following diagram.
• SPNone.2.sl.TZ0.3b: Given that the standard deviation is 20, find a . Give your answer correct to the nearest whole...
• 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.TZ1.4a: 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.2.sl.TZ2.6a: Find \({\rm{P}}(X > 27)\) .
• 11M.2.sl.TZ2.6b: Find the standard deviation of X .
• 13M.2.sl.TZ1.7: A random variable \(X\) is normally distributed with \(\mu  = 150\) and \(\sigma  = 10\) . Find...
• 13M.2.sl.TZ2.2a: Find \({\rm{P}}(X \le 22.9)\) .
• 13M.2.sl.TZ2.2b: Given that \({\rm{P}}(X < k) = 0.55\) , find the value of \(k\) .
• 14M.2.sl.TZ1.8d: Assume that the weights of these rats are normally distributed with the mean and standard...
• 14M.2.sl.TZ2.10a(i): A tree is selected at random from the forest. Find the probability that this tree is a giant.
• 14M.2.sl.TZ2.10a(ii): A tree is selected at random from the forest. Given that this tree is a giant, find the...
• 13N.2.sl.TZ0.6a: A student is selected at random. Find the probability that the student completes the task in less...
• 13N.2.sl.TZ0.6b: The probability that a student takes between \(k\) and \(21.8\) minutes is \(0.3\). Find the...
• 14N.2.sl.TZ0.10b: (i)     Write down the standardized value for \(815\) g. (ii)     Hence or otherwise, find...
• 14N.2.sl.TZ0.10c: A fishing contest takes place in the lake. Small fish, called tiddlers, are thrown back into the...
• 14N.2.sl.TZ0.10d: A fish is caught at random. Find the probability that it is a tiddler.
• 15M.2.sl.TZ1.9a: A container is chosen at random. Find the probability that it is underfilled.
• 15N.2.sl.TZ0.10a: Find the standard deviation of the masses of the watermelons.
• 15N.2.sl.TZ0.10b: The following table shows the percentages of small, medium and large watermelons grown on the...
• 16M.2.sl.TZ1.1a: On the following diagram, shade the region representing \({\text{P}}(X \leqslant 25)\).
• 16M.2.sl.TZ1.1b: Write down \({\text{P}}(X \leqslant 25)\), correct to two decimal places.
• 16M.2.sl.TZ1.1c: Let \({\text{P}}(X \leqslant c) = 0.7\). Write down the value of \(c\).
• 16M.2.sl.TZ2.6a: A contestant is chosen at random. Find the probability that their \(S\) score is less than 50.
• 16M.2.sl.TZ2.6b: Given that 1% of the contestants are disqualified, find the value of \(x\).
• 17N.2.sl.TZ0.7: The heights of adult males in a country are normally distributed with a mean of 180 cm and a...
• 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.

Standardization of normal variables (\(z\)-values, \(z\)-scores).

• 12N.2.sl.TZ0.6: In a large city, the time taken to travel to work is normally distributed with mean \(\mu \) and...
• 09M.2.sl.TZ1.4b: Given that \({\rm{P}}(X > a) = 0.27\) , find \(a\).
• 09M.2.sl.TZ2.9b: For Route B, the probability that the journey takes less than \(60\) minutes is \(0.85\). Find...
• SPNone.2.sl.TZ0.3b: Given that the standard deviation is 20, find a . Give your answer correct to the nearest whole...
• 13M.2.sl.TZ1.7: A random variable \(X\) is normally distributed with \(\mu  = 150\) and \(\sigma  = 10\) . Find...
• 13M.2.sl.TZ2.2b: Given that \({\rm{P}}(X < k) = 0.55\) , find the value of \(k\) .
• 14N.2.sl.TZ0.10b: (i)     Write down the standardized value for \(815\) g. (ii)     Hence or otherwise, find...
• 14N.2.sl.TZ0.10c: A fishing contest takes place in the lake. Small fish, called tiddlers, are thrown back into the...
• 15M.2.sl.TZ1.9b: The company decides that the probability of a container being underfilled should be reduced to...
• 15N.2.sl.TZ0.10a: Find the standard deviation of the masses of the watermelons.
• 15N.2.sl.TZ0.10b: The following table shows the percentages of small, medium and large watermelons grown on the...
• 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.

Properties of the normal distribution.

• 12M.2.sl.TZ2.4a: The heights of a group of seven-year-old children are normally distributed with mean...
• 12M.2.sl.TZ2.4b: The heights of a group of seven-year-old children are normally distributed with mean...
• 09N.1.sl.TZ0.3b: Given that \({\rm{P}}(X < d) = {\rm{P}}(X > 105)\) , find the value of \(d\) .
• 09N.1.sl.TZ0.3c: Given that \({\rm{P}}(X > 105) = 0.16\) (correct to two significant figures), find...
• 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.TZ1.10a: Find the probability that a player weighs more than \(82{\text{ kg}}\).
• 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.TZ1.10d: Of the players in the league, \(25\% \) are women. Of the women, \(70\% \) take part in the...
• 15N.2.sl.TZ0.10b: The following table shows the percentages of small, medium and large watermelons grown on the...