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Date May 2022 Marks available 2 Reference code 22M.1.SL.TZ2.5
Level Standard Level Paper Paper 1 Time zone Time zone 2
Command term Calculate Question number 5 Adapted from N/A

Question

A polygraph test is used to determine whether people are telling the truth or not, but it is not completely accurate. When a person tells the truth, they have a 20% chance of failing the test. Each test outcome is independent of any previous test outcome.

10 people take a polygraph test and all 10 tell the truth.

Calculate the expected number of people who will pass this polygraph test.

[2]
a.

Calculate the probability that exactly 4 people will fail this polygraph test.

[2]
b.

Determine the probability that fewer than 7 people will pass this polygraph test.

[3]
c.

Markscheme

EX= 10×0.8          (M1)

8 (people)           A1

 

[2 marks]

a.

recognition of binomial probability          (M1)

0.0881   0.0880803            A1

 

[2 marks]

b.

0.8 and 6 seen   OR   0.2 and 3 seen           (A1)

attempt to use binomial probability           (M1)

0.121   0.120873            A1

 

[3 marks]

c.

Examiners report

Calculating expected value was well done, with some finding the probability of passing first and then multiplying by 10, while others calculated the expected number who would fail and then subtracted from 10.

a.

There were some candidates who did not recognize binomial probability, and attempted to calculate probability using other methods. For the candidates who did recognize binomial probability, part (b) was well done with most selecting correct calculator entries for the probability. In part (c), there was some confusion as to what value to use in their binomial cumulative distribution function for “less than 7”, with the most common error being the use of 7 rather than 6 as the parameter in the calculation.

b.
[N/A]
c.

Syllabus sections

Topic 4—Statistics and probability » SL 4.5—Probability concepts, expected numbers
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Topic 4—Statistics and probability » SL 4.8—Binomial distribution
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