Question

A random sample of size 16 is selected from a normal population with a mean of 173 and a standard deviation of 12. What is the probability that the sample mean will exceed 175? Give answer to two decimal places.

Answer 1

Solution :

Given that ,

mean = = 173

standard deviation = = 12

n=16

P(X > 175) = 1 - P(x < 175)

= 1 - P((x - ) / < (175-173 )12 / 16)

= 1 - P(z < 0.67)   Using standard normal table,

= 1 - 0.7486   

= 0.2514

P(x >175 ) = 0.25