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According to the testing service who offers the GRE, the quantitative GRE score is a whole...

According to the testing service who offers the GRE, the quantitative GRE score is a whole number between 130 and 170. The scores are also normally distributed with a mean of 152.75 points and a standard deviation of 10.25 points. Consider a random sample of 4 students all taking the GRE exam in the same year.

a. What does the Central Limit Theorem tell us about the probability distribution for the average quantitative GRE score for this sample?

b. What does the Central Limit Theorem tell us about the sampling distribution for the mean quantitative GRE score for this sample?

c. What is the probability that the mean quantitative GRE score for this sample is between 150 and 155?

d. What is the probability that the mean quantitative GRE score for this sample is greater than 145?

e. What is the probability that exactly 2 of the 4 students in the sample have a score greater than 145?

Math   Statistics-And-Probability   
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