Question

The Office of Student Life at Cleveland State University investigated differences in traditional and nontraditional students, where nontraditional students are defined as 25 years or older and working. Based on the study results, it was assumed that the population mean and standard deviation for the GPA of nontraditional students is µ = 2.75 and ? = 0.56.

a. Suppose a random sample of 49 nontraditional students is selected and each student's GPA is calculated. The probability that the random sample of 49 nontraditional students have a mean GPA less than 2.57 is . Use only the appropriate formula and/or statistical table in your textbook to answer this question. Report your answer to 4 decimal places, using conventional rounding rules.

b. Fifty-four percent of the samples of n = 49 students drawn from this population will have a sample mean GPA of at least . Use only the appropriate formula and/or statistical table in your textbook to answer this question. Report your answer to 4 decimal places, using conventional rounding rules.

Answer 1

a). The probability of random sample of 49 nontraditional students have a mean GPA less than 2.57=

b) Find x, the sample mean

And, the z score for 0.46 is = -0.10

So, this population will have a sample mean GPA of at least 2.742.