Question

A sample average of size 14 is drawn from a normally distributed population and has a mean of 77 and a standard deviation of 14. Find the lower end, if 95% of all possible sample averages?

Answer 1

= 77

= 14

n = 14

SE = /

= 14/ = 3.7417

Lower end of 95% corresponds to area= 0.95 - 050 = 0.45 from mid value to Z on LHS.

Table of Area Under Standard Normal Curve gives Z = - 1.645

So,

Z = - 1.645 = ( - 77)/3.7417

So,

= 77 - (1.645 X 3.7417) = 70.8450

So,

Answer is:

70.8450