User interface language: English | Español

Date May 2017 Marks available 2 Reference code 17M.2.AHL.TZ1.H_9
Level Additional Higher Level Paper Paper 2 Time zone Time zone 1
Command term Find Question number H_9 Adapted from N/A

Question

The times taken for male runners to complete a marathon can be modelled by a normal distribution with a mean 196 minutes and a standard deviation 24 minutes.

It is found that 5% of the male runners complete the marathon in less than T 1 minutes.

The times taken for female runners to complete the marathon can be modelled by a normal distribution with a mean 210 minutes. It is found that 58% of female runners complete the marathon between 185 and 235 minutes.

Find the probability that a runner selected at random will complete the marathon in less than 3 hours.

[2]
a.

Calculate T 1 .

[2]
b.

Find the standard deviation of the times taken by female runners.

[4]
c.

Markscheme

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

T N ( 196 ,   24 2 )

P ( T < 180 ) = 0.252      (M1)A1

[2 marks]

a.

P ( T < T 1 ) = 0.05      (M1)

T 1 = 157      A1

[2 marks]

b.

F N ( 210 ,   σ 2 )

P ( F < 235 ) = 0.79      (M1)

235 210 σ = 0.806421 or equivalent     (M1)(A1)

σ = 31.0      A1

[4 marks]

c.

Examiners report

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

Syllabus sections

Topic 4—Statistics and probability » SL 4.9—Normal distribution and calculations
Show 130 related questions
Topic 4—Statistics and probability » SL 4.12—Z values, inverse normal to find mean and standard deviation
Topic 4—Statistics and probability

View options