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Date November 2020 Marks available 2 Reference code 20N.2.SL.TZ0.S_9
Level Standard Level Paper Paper 2 Time zone Time zone 0
Command term Calculate Question number S_9 Adapted from N/A

Question

Fiona walks from her house to a bus stop where she gets a bus to school. Her time, W minutes, to walk to the bus stop is normally distributed with W~N12, 32.

Fiona always leaves her house at 07:15. The first bus that she can get departs at 07:30.

The length of time, B minutes, of the bus journey to Fiona’s school is normally distributed with B~N50, σ2. The probability that the bus journey takes less than 60 minutes is 0.941.

If Fiona misses the first bus, there is a second bus which departs at 07:45. She must arrive at school by 08:30 to be on time. Fiona will not arrive on time if she misses both buses. The variables W and B are independent.

Find the probability that it will take Fiona between 15 minutes and 30 minutes to walk to the bus stop.

[2]
a.

Find σ.

[3]
b.

Find the probability that the bus journey takes less than 45 minutes.

[2]
c.

Find the probability that Fiona will arrive on time.

[5]
d.

This year, Fiona will go to school on 183 days.

Calculate the number of days Fiona is expected to arrive on time.

[2]
e.

Markscheme

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

0.158655

P15<W<30=0.159    A2   N2

[2 marks]

a.

finding standardized value for 60       (A1)

eg       z=1.56322

correct substitution using their z-value       (A1)

eg       60-50σ=1.56322, 60-501.56322=σ

6.39703

σ=6.40    A1   N3

[3 marks]

b.

0.217221

PB<45=0.217    A2   N2

[2 marks]

c.

valid attempt to find one possible way of being on time (do not penalize incorrect use of strict inequality signs)       (M1)

eg       W15 and B<6015<W30 and B<45

correct calculation for PW15 and B<60 (seen anywhere)       (A1)

eg       0.841×0.941, 0.7917

correct calculation for P15<W30 and B<45 (seen anywhere)       (A1)

eg       0.159×0.217, 0.03446

correct working       (A1)

eg       0.841×0.941+0.159×0.217, 0.7917+0.03446

0.826168

P (on time) =0.826    A1   N2

[5 marks]

d.

recognizing binomial with n=183, p=0.826168       (M1)

eg       X~B183, 0.826

151.188   (151.158 from 3 sf )

151    A1   N2

[2 marks]

e.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.
[N/A]
d.
[N/A]
e.

Syllabus sections

Topic 4—Statistics and probability » SL 4.3—Mean, median, mode. Mean of grouped data, standard deviation. Quartiles, IQR
Show 159 related questions
Topic 4—Statistics and probability » SL 4.5—Probability concepts, expected numbers
Topic 4—Statistics and probability » SL 4.6—Combined, mutually exclusive, conditional, independence, prob diagrams
Topic 4—Statistics and probability » SL 4.12—Z values, inverse normal to find mean and standard deviation
Topic 4—Statistics and probability

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