Question

In 2019, the average high school GPA for incoming University of Maryland freshman was 4.32 with a standard deviation of 0.285. Suppose UMD freshman are randomly assigned into groups of 25.

Note that this scenario is talking about a sampling distribution since the students are put into groups of size 25. Therefore, you will need to calculate the standard deviation using a formula before using the normalcdf and invNorm commands.



a) What is the mean of the sampling distribution of all samples like this:



b) What is the standard deviation of the sampling distribution of all samples like this:

Give the formula with values that you entered in your calculator as a way of showing your work:

Give your final answer rounded to 3 decimal places:



c) What is the probability of a group having an average high school GPA below 4.1?

Give the command and values you used as a way of showing your work:

Give your final answer rounded to 6 decimal places or write your final answer in scientific notation rounded to one decimal place:

Answer 1

a) The mean of the sampling distribution of all samples is 4.32. b) The standard deviation of the sampling distribution of all samples is 0.057. c) The probability of a group having an average high school GPA below 4.1 is 0.0412.

Step-by-step explanation:

a) The mean of the sampling distribution of all samples is equal to the population mean, which is 4.32.

b) To calculate the standard deviation of the sampling distribution of all samples, we use the formula:

Standard Deviation of Sampling Distribution = Standard Deviation of Population / Square Root of Sample Size

Plugging in the values, we get:

Standard Deviation of Sampling Distribution = 0.285 / √25 = 0.057

c) To find the probability of a group having an average high school GPA below 4.1, we can use the normalcdf command on the calculator with the mean and standard deviation of the sampling distribution:

normalcdf(−10^99, 4.1, 4.32, 0.057)

After evaluating this command, we get a probability of approximately 0.0412.