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Date November 2019 Marks available 3 Reference code 19N.1.SL.TZ0.T_12
Level Standard Level Paper Paper 1 Time zone Time zone 0
Command term Find Question number T_12 Adapted from N/A

Question

The Malthouse Charity Run is a 5 kilometre race. The time taken for each runner to complete the race was recorded. The data was found to be normally distributed with a mean time of 28 minutes and a standard deviation of 5 minutes.

A runner who completed the race is chosen at random.

Write down the probability that the runner completed the race in more than 28 minutes.

[1]
a.

Calculate the probability that the runner completed the race in less than 26 minutes.

[2]
b.

It is known that 20% of the runners took more than 28 minutes and less than k minutes to complete the race.

Find the value of k.

[3]
c.

Markscheme

0.5 12, 50%       (A1) (C1)

[1 mark]

a.

PX26       (M1)

 

Note: Award (M1) for a correct mathematical statement.

OR
Award (M1) for a diagram that shows the value 26 labelled to the left of the mean and the correct shaded region.

 

3.45 0.344578, 34.5%       (A1) (C2)

[2 marks]

b.

0.7 OR 0.3 (seen)     (A1)

Note: Award (A1) for 0.7 or 0.3 seen.

 

Ptime<7=0.7  OR  Ptime>k=0.3     (M1)

Note: Award (M1) for a correct mathematical statement.
OR
Award (M1) for a diagram that shows k greater than the mean and shading in the region below k, above k, or between k and the mean.

k= 30.6 30.6220 (minutes)     (A1)   (C3)

Note: Accept “30 minutes and 37 seconds” or (from 3 sf k value) “30 minutes and 36 seconds”.

[3 marks]

c.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.

Syllabus sections

Topic 4—Statistics and probability » SL 4.9—Normal distribution and calculations
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Topic 4—Statistics and probability

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