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: