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Mice21 [21]
3 years ago
6

A research study investigated differences between male and female students. Based on the study results, we can assume the popula

tion 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?
Mathematics
1 answer:
oksian1 [2.3K]3 years ago
6 0

Answer: 0.0548

Step-by-step 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(\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}>\dfrac{3.42-3.5}{\dfrac{0.5}{\sqrt{100}}})\\\\=P(Z>\dfrac{-0.08}{\dfrac{0.5}{10}})\ \ \ [Z=\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=P(Z>1.6)\\\\=1-P(Z

hence, the required probability is 0.0548.

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