Question

Experience with workmen in a certain industry indicates that the time required for a randomly selected workman to complete a certain job is approximately normally distributed with a standard deviation of 10 minutes. How large a sample would one need to take if one wished to estimate the unknown population mean to within 2 minutes with 95% confidence

Answer 1

Solution:

Given ,

= 10 ..Population SD

E = 2 Margin of error

c = 95% = 0.95 ...confidence level

Find sample size required.

c = 0.95

= 1- c = 1- 0.95 = 0.05

  /2 = 0.025

Using Z table ,

= 1.96

Now, sample size (n) is given by,

=  {(1.96* 10)/ 2}²

=  96.04

= 97 ..(round to the next whole number)

Answer : 97