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Date May 2013 Marks available 2 Reference code 13M.2.hl.TZ1.3
Level HL only Paper 2 Time zone TZ1
Command term Find Question number 3 Adapted from N/A

Question

Emily walks to school every day. The length of time this takes can be modelled by a normal distribution with a mean of 11 minutes and a standard deviation of 3 minutes. She is late if her journey takes more than 15 minutes.

Find the probability she is late next Monday.

[2]
a.

Find the probability she is late at least once during the next week (Monday to Friday).

[3]
b.

Markscheme

Let X represent the length of time a journey takes on a particular day.

\(P(X > 15) = 0.0912112819 \ldots  = 0.0912\)     (M1)A1

a.

Use of correct Binomial distribution     (M1)

\(N \sim B(5,0.091 \ldots )\)

\(1 - 0.0912112819 \ldots  = 0.9087887181 \ldots \)

\(1 - {(0.9087887181 \ldots )^5} = 0.380109935 \ldots  = 0.380\)     (M1)A1

Note: Allow answers to be given as percentages.

[5 marks]

b.

Examiners report

There were many good answers to this question. Some students lost accuracy marks by early rounding. Some students struggled with the Binomial distribution.

a.

There were many good answers to this question. Some students lost accuracy marks by early rounding. Some students struggled with the Binomial distribution.

b.

Syllabus sections

Topic 5 - Core: Statistics and probability » 5.7 » Normal distribution.
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