I have chosen a sample of 50 students from 5000 students to

I have chosen a sample of 50 students from 5000 students to study the GPA distribution across campus.

1. Can I assume the sample average has a Normal distribution?

2. If I am estimating standard deviation should I use a correction factory?

3. If in this sample GPA average is 2.25 and if the standard deviation of population GPA is 1.5 and population mean is 2.5 then what is the Normal distribution for population mean?

4.Please identify the area which includes population mean with 90 percent possibility.

Confidence Level

/2

Area

z _/2

90%

.10

.05

.95

1.645

95%

.05

.025

.975

1.960

99%

.01

.005

.995

2.576

Solution

I have chosen a sample of 50 students from 5000 students to study the GPA distribution across campus.

1.Yes, the sample average has a normal distribution with same mean as population mean.

2.Estimating standard deviation divide population standard deviation by square root of sample size.

4.The area which includes population mean with 90 percent possibility is 1.645.