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Date November 2017 Marks available 2 Reference code 17N.1.SL.TZ0.T_13
Level Standard Level Paper Paper 1 Time zone Time zone 0
Command term Find Question number T_13 Adapted from N/A

Question

Applicants for a job had to complete a mathematics test. The time they took to complete the test is normally distributed with a mean of 53 minutes and a standard deviation of 16.3. One of the applicants is chosen at random.

For 11% of the applicants it took longer than k minutes to complete the test.

There were 400 applicants for the job.

Find the probability that this applicant took at least 40 minutes to complete the test.

[2]
a.

Find the value of k .

[2]
b.

Estimate the number of applicants who completed the test in less than 25 minutes.

[2]
c.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

0.787 (0.787433…, 78.7%)     (M1)(A1)     (C2)

 

Note:     Award (M1) for a correct probability statement, P ( X > 40 ) , or a correctly shaded normal distribution graph.

 

N17/5/MATSD/SP1/ENG/TZ0/13.a/M

[2 marks]

a.

73.0 (minutes) (72.9924…)     (M1)(A1)     (C2)

 

Note:     Award (M1) for a correct probability statement, P ( X > k ) = 0.11 , or a correctly shaded normal distribution graph.

 

N17/5/MATSD/SP1/ENG/TZ0/13.b/M

[2 marks]

b.

0.0423433 × 400     (M1)

 

Note:     Award (M1) for multiplying a probability by 400. Do not award (M1) for 0.11 × 400 .

Use of a lower bound less than zero gives a probability of 0.0429172….

= 16     (A1)     (C2)

 

Notes:     Accept a final answer of 17. Do not accept a final answer of 18. Accept a non-integer final answer either 16.9 (16.9373…) from use of lower bound zero or 17.2 (17.1669…) from use of the default lower bound of 10 99 .

 

[2 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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