Question

A research study investigated differences between male and female students. Based on the study results, we can assume the population mean and standard deviation for the GPA of male students are µ = 3.5 and σ = 0.6. Suppose a random sample of 100 male students is selected and the GPA for each student is calculated. What is the probability that the random sample of 100 male students has a mean GPA greater than 3.42?

Answer 1

Solution :

Given that ,

mean = = 3.5

standard deviation = = 0.6

n = 100

=   = 3.5

= / n = 0.6 / 100 = 0.06

P( > 3.42 ) = 1 - P( < 3.42 )

= 1 - P[( - ) / < ( 3.42 - 3.5 ) / 0.06 ]

= 1 - P(z < - 1.33 )

Using z table

= 1 - 0.0918

= 0.9082.

The probability is = 0.9082