17N.1.SL.TZ0.T_13

pestleMathematicsAASLPaper 117N· sl-4-9-normal-distribution-and-calculationssource ↗

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]

Find the value of $k$ .

[2]

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

[2]

Markscheme / solution

* 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, ${\text{P}}(X > 40)$ , or a correctly shaded normal distribution graph.

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

[2 marks]

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

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

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

[2 marks]

$0.0423433 \ldots \times 400$ (M1)

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

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]

Examiners’ report

[N/A]