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Date November Example questions Marks available 2 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]
a.

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

[2]
b.

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

[2]
c.

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

[3]
d.

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]
e.

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~Nμ,8.62

PT36.8=0.7        (A1)

states a correct equation, for example, 36.8-μ8.6=0.5244        A1

attempts to solve their equation        (M1)

μ=36.8-0.52448.6  =32.2902        A1

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

 

[4 marks]

a.

let t0.86 be the 86th percentile

attempts to use the inverse normal feature of a GDC to find t0.86       (M1)

t0.86=41.6 (mins)        A1

 

[2 marks]

b.

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

Note: Award M1 for a clearly labelled sketch.

PT>30=0.605         A1

 

[2 marks]

c.

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

X~B6,0.6049         (M1)

for example, PX=5+PX=6 or 1-PX4         (A1)

PX5=0.241         A1

 

[3 marks]

d.

recognizes that PT>30 T25 is required         (M1)

 

Note: Award M1 for recognizing conditional probability.

 

=PT>30T25PT25         (A1)

=PT>30PT25=0.60490.8016         M1

=0.755         A1

 

[4 marks]

e.

Examiners report

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e.

Syllabus sections

Topic 4—Statistics and probability » SL 4.9—Normal distribution and calculations
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Topic 4—Statistics and probability » SL 4.12—Z values, inverse normal to find mean and standard deviation
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