Question

If it is assumed that the heights of men are normally distributed with a standard deviation of 2.5 inches, how large a sample should be taken to be fairly sure (probability 0.95) that the sample mean does not differ from the true mean (population mean) by more than 0.10? (Give your answer as a whole number.)

n ≥

Answer 1

Solution :

Given that,

Population standard deviation = = 2.5

Margin of error = E = 0.10

At 95% confidence level the z is,

= 1 - 95%

= 1 - 0.95 = 0.05

/2 = 0.025

Z/2 = Z0.025 = 1.96  

sample size = n = [Z/2* / E] 2

n = [1.96 * 2.5 / 0.10]2

Sample size = n   2401