Question

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 1

Solution :

Given that ,

mean = = 100

standard deviation = = 15

n = 3

= 100

= / n = 15 / 3

P( 115 ) = 1 - P( 115 )

= 1 - P(( - ) /   < (115 - 100) / 15 / 3)

= 1 - P(z < 1.73)   Using standard normal table,

= 1 - 0.9582

= 0.0418

P( 115 ) = 0.0418

Probability = 0.0418

Here probability < 0.05

If probability is 0.05 then event is unusual .

Yes it be unusual .