Question

A population has a mean of 37.6 and a standard deviation of 14.8. A sample of 75 will be taken. Find the probability that the sample mean will be greater than 42.0.

a) Calculate the z score. (Round your answer to 2 decimals.)

b) Find the probability that the sample mean will be greater than 42.0. (Round your answer to 4 decimals.)

Answer 1

Solution :

Given that,

mean = = 37.6

standard deviation = = 14.8

n=75

= =37.6

= / n = 14.8 / 75 = 1.71

a

z score = ( - ) / = (42-37.6) / 1.71 =2.57

b

P( >42 ) = 1 - P( < 42)

= 1 - P[( - ) / < (42-37.6) / 1.71]

= 1 - P(z < 2.57)

Using z table

= 1 - 0.9949

= 0.0051

probability= 0.0051