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Date May Specimen paper Marks available 6 Reference code SPM.1.AHL.TZ0.10
Level Additional Higher Level Paper Paper 1 Time zone Time zone 0
Command term Find Question number 10 Adapted from N/A

Question

In a coffee shop, the time it takes to serve a customer can be modelled by a normal distribution with a mean of 1.5 minutes and a standard deviation of 0.4 minutes.

Two customers enter the shop together. They are served one at a time.

Find the probability that the total time taken to serve both customers will be less than 4 minutes.

Clearly state any assumptions you have made.

Markscheme

let T be the time to serve both customers and Ti the time to serve the ith customer

assuming independence of T1 and T2      R1

T is normally distributed and T=T1+T2       (M1)

E(T)=1.5+1.5=3     A1

Var(T)=0.42+0.42=0.32      M1A1

P(T<4)=0.961       A1

[6 marks]

Examiners report

[N/A]

Syllabus sections

Topic 4—Statistics and probability » AHL 4.15—Central limit theorem
Topic 4—Statistics and probability

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