Question

The College of UCLA 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

Solution: We are given:

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

Answer:

Proof:

We have to find

To find this probability, we need to find the z score value first.

  

  

Therefore we have to find

Using the standard normal table, we have:

Therefore the probability that the random sample of 49 nontraditional students have a mean GPA less than 2.57 is .

b. Fifty-four percent of the samples of n = 49 students drawn from this population will have a sample mean GPA of at least .

Answer:

Proof:

We need to find the z value corresponding to probability 0.44 using standard normal table.

We have:

  

Fifty-four percent of the samples of n = 49 students drawn from this population will have a sample mean GPA of at least