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 = 0.05. 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

Answer: 0.0548

Explanation:

Given, 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 = 0.05.

Let
`\overline{X}` represents the sample mean GPA for each student.

Then, the probability that the random sample of 100 male students has a mean GPA greater than 3.42:

`P(\overline{X}>3.42)=P(\frac{\overline{X}-\mu}{(\sigma)/(√(n))}>(3.42-3.5)/((0.5)/(√(100))))\\\\=P(Z>(-0.08)/((0.5)/(10)))\ \ \ [Z=\frac{\overline{X}-\mu}{(\sigma)/(√(n))}]\\\\=P(Z>1.6)\\\\=1-P(Z<1.6)\\\\=1-0.9452=0.0548`

hence, the required probability is 0.0548.