The College Student Journal (December 1992)investigated differences in traditional and nontraditional students,where nontraditional students are defined as 25 years or older and working.Based on the study results,we can assume the population mean and standard deviation for the GPA of nontraditional students is µ = 3.5 and $\sigma$ = 0.5.Suppose a random sample of 100 nontraditional students is selected and each student's GPA is calculated.What is the probability that the random sample of 100 nontraditional students have a mean GPA greater than 3.42?
A).0548
B).4364
C).9452
D).5636

Question

The College Student Journal (December 1992)investigated differences in traditional and nontraditional students,where nontraditional students are defined as 25 years or older and working.Based on the study results,we can assume the population mean and standard deviation for the GPA of nontraditional students is µ = 3.5 and  $\sigma$ = 0.5.Suppose a random sample of 100 nontraditional students is selected and each student's GPA is calculated.What is the probability that the random sample of 100 nontraditional students have a mean GPA greater than 3.42?
A).0548
B).4364
C).9452
D).5636

Quizplus · Accepted Answer

We can use the central limit theorem since the sample size is greater than 30 (n=100). The sample mean can be approximated by a normal distribution with a mean of mu and a standard deviation of sigma/sqrt(n). Thus, the z-score can be calculated as (3.42-3.5)/(0.5/sqrt(100))=-1.60. Looking at a z-table or using a calculator, the probability of getting a z-score greater than -1.60 is 0.9452. Therefore, the probability that the random sample of 100 nontraditional students have a mean GPA greater than 3.42 is 0.9452 or 94.52%.

The College Student Journal (December 1992)investigated Differences in Traditional and Nontraditional