Question

Suppose the average GPA of all chemical engineering majors is normally distributed with  μ = 3.47 and σ  = 0.24. What is the probability that the sample mean from a random sample of the GPAs of 16 chemical engineering majors would be greater than 3.5444?

Answer 1

Solution :

Given that,

mean = = 3.47

standard deviation = = 0.24

n=16

= =3.47

= / n = 0.24/ 16= 0.06

P( > 3.5444 ) = 1 - P( < 3.5444 )

= 1 - P[( - ) / < ( 3.5444 -3.47) / 0.06]

= 1 - P(z < 1.24)

Using z table

= 1 -0.8925

= 0.1075

probability=0.1075