At a small high school, 5 students took Mrs. Jones's AP Statistics class last year. The student's names are Ashley, Brayden, Carmen, Dale, and Eve. Ashley, Brayden, and Carmen each got a 5 on the AP Statistics exam. Mrs. Jones would like to use the results of these 5 students to demonstrate how to create a sampling distribution of the sample proportion for simple random samples of size n = 2 for her current students.

a) What is the value of p, the population proportion of students in Mrs. Jones's AP Statistics class who got a 5 on the AP Statistics exam? Explain.

b) Using the table provided, list all 10 possible simple random samples of size n = 2, and for each sample calculate p = the sample proportion of students who got a 5 on the AP Statistics exam. The first one is completed for you.

c) Using the number line provided, create a dotplot to display the sampling distribution of p.

d) Is the sample proportion an unbiased estimator of the population proportion? Explain.

The distribution of the number of children per family in the United States is strongly skewed right with a mean of 2.5 children per family and a standard deviation of 1.3 children per family.

a) Without doing any calculations, which event is more likely? Explain. Event A: Randomly selecting a family from the United States that has 3 or more children. Event B: Randomly selecting 40 families from the United States and finding an average of 3 or more children.

b) The probability of one of the two events listed in part (a) can be calculated even though the distribution of the population is strongly skewed right. For which event can the probability be calculated? Explain.

c) Calculate the probability of the event that you selected in part (b).