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Date May 2017 Marks available 2 Reference code 17M.2.sl.TZ1.4
Level SL only Paper 2 Time zone TZ1
Command term Find Question number 4 Adapted from N/A

Question

In a large university the probability that a student is left handed is 0.08. A sample of 150 students is randomly selected from the university. Let k be the expected number of left-handed students in this sample.

Find k.

[2]
a.

Hence, find the probability that exactly k students are left handed;

[2]
b.i.

Hence, find the probability that fewer than k students are left handed.

[2]
b.ii.

Markscheme

evidence of binomial distribution (may be seen in part (b))     (M1)

egnp, 150×0.08

k=12     A1     N2

[2 marks]

a.

P(X=12)=(15012)(0.08)12(0.92)138    (A1)

0.119231

probability =0.119     A1     N2

[2 marks]

b.i.

recognition that X     (M1)

0.456800

{\text{P}}(X < 12) = 0.457     A1     N2

[2 marks]

b.ii.

Examiners report

[N/A]
a.
[N/A]
b.i.
[N/A]
b.ii.

Syllabus sections

Topic 5 - Statistics and probability » 5.7 » Expected value (mean), {\text{E}}(X) for discrete data.
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