Standard Deviation Quiz

 

Assume that a population is normally distributed with a mean of 100 and a standard deviation of 15. Would it be unusual for the mean of a sample of 3 to be 115 or more? Why or why not?

Answer:

For standard deviation;

 

Where n is the sample size

this simply implies that;

 

= 15/(√3)

= 8.6602

Although the term “unusual” may be interpreted differently, it is an indication that the given set of data lies more or less on 1.96 standard deviations from the mean.

This implies that the subsequent value for z=1.96 is as shown below:

100 + (8.6602)*(1.96)

= 169116.974

However, 115 lies within the middle 95%. Hence, it will not be seen to be unusual.