Loading [MathJax]/jax/output/CommonHTML/fonts/TeX/fontdata.js

User interface language: English | Español

Date November 2015 Marks available 4 Reference code 15N.3sp.hl.TZ0.1
Level HL only Paper Paper 3 Statistics and probability Time zone TZ0
Command term Find Question number 1 Adapted from N/A

Question

It is known that the standard deviation of the heights of men in a certain country is 15.0 cm.

One hundred men from that country, selected at random, had their heights measured.

The mean of this sample was 185 cm. Calculate a 95% confidence interval for the mean height of the population.

[3]
a.

A second random sample of size n is taken from the same population. Find the minimum value of n needed for the width of a 95% confidence interval to be less than 3 cm.

[4]
b.

Markscheme

valid attempt to use ˉx±zσn     (M1)

[182, 188]     A1A1

 

Note:     Accept answers that round to the correct 3 sf.

[3 marks]

a.

1.96×15.0n<1.5     M1A1

n>(15.01.5×1.96)2     (M1)

 

Note:     Award M1 for attempting to solve the inequality.

 

Note:     Allow the use of =.

 

minimum value n=385     A1

[4 marks]

Total [7 marks]

b.

Examiners report

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

Syllabus sections

Topic 7 - Option: Statistics and probability » 7.5 » Confidence intervals for the mean of a normal population.

View options