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Date	November Example questions	Marks available	3	Reference code	EXN.2.SL.TZ0.8
Level	Standard Level	Paper	Paper 2	Time zone	Time zone 0
Command term	Find	Question number	8	Adapted from	N/A

Question

The time, $T$ minutes, taken to complete a jigsaw puzzle can be modelled by a normal distribution with mean $μ$ and standard deviation $8.6$ .

It is found that $30 %$ of times taken to complete the jigsaw puzzle are longer than $36.8$ minutes.

Use $μ = 32.29$ in the remainder of the question.

Six randomly chosen people complete the jigsaw puzzle.

By stating and solving an appropriate equation, show, correct to two decimal places, that $μ = 32.29$ .

[4]

Find the $86$ th percentile time to complete the jigsaw puzzle.

[2]

Find the probability that a randomly chosen person will take more than $30$ minutes to complete the jigsaw puzzle.

[2]

Find the probability that at least five of them will take more than $30$ minutes to complete the jigsaw puzzle.

[3]

Having spent $25$ minutes attempting the jigsaw puzzle, a randomly chosen person had not yet completed the puzzle.

Find the probability that this person will take more than $30$ minutes to complete the jigsaw puzzle.

[4]

Markscheme

* This sample question was produced by experienced DP mathematics senior examiners to aid teachers in preparing for external assessment in the new MAA course. There may be minor differences in formatting compared to formal exam papers.

$T ~ N (μ, 8 . 6^{2})$

$P (T \leq 36.8) = 0.7$ (A1)

states a correct equation, for example, $\frac{36.8 - μ}{8.6} = 0.5244 \dots$ A1

attempts to solve their equation (M1)

$μ = 36.8 - (0.5244 \dots) (8.6) (= 32.2902 \dots)$ A1

the solution to the equation is $μ = 32.29$ , correct to two decimal places AG

[4 marks]

let $t_{0.86}$ be the $86$ th percentile

attempts to use the inverse normal feature of a GDC to find $t_{0.86}$ (M1)

$t_{0.86} = 41.6$ (mins) A1

[2 marks]

evidence of identifying the correct area under the normal curve (M1)

Note: Award M1 for a clearly labelled sketch.

$P (T > 30) = 0.605$ A1

[2 marks]

let $X$ represent the number of people out of the six who take more than $30$ minutes to complete the jigsaw puzzle

$X ~ B (6, 0.6049 \dots)$ (M1)

for example, $P (X = 5) + P (X = 6)$ or $1 - P (X \leq 4)$ (A1)

$P (X \geq 5) = 0.241$ A1

[3 marks]

recognizes that $P (T > 30 T \geq 25)$ is required (M1)

Note: Award M1 for recognizing conditional probability.

$= \frac{P (T > 30 \cap T \geq 25)}{P (T \geq 25)}$ (A1)

$= \frac{P (T > 30)}{P (T \geq 25)} = \frac{0.6049 \dots}{0.8016 \dots}$ M1

$= 0.755$ A1

[4 marks]

Examiners report

[N/A]

Syllabus sections

Topic 4—Statistics and probability » SL 4.8—Binomial distribution

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Topic 4—Statistics and probability

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