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Date May 2017 Marks available 2 Reference code 17M.2.SL.TZ1.S_4
Level Standard Level Paper Paper 2 Time zone Time zone 1
Command term Find and Hence Question number S_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

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

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

eg n p ,   150 × 0.08

k = 12     A1     N2

[2 marks]

a.

P ( X = 12 ) = ( 150 12 ) ( 0.08 ) 12 ( 0.92 ) 138     (A1)

0.119231

probability = 0.119     A1     N2

[2 marks]

b.i.

recognition that X 11     (M1)

0.456800

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 4—Statistics and probability » SL 4.8—Binomial distribution
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Topic 4—Statistics and probability

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