Question

Five students—the females Ann and Betty and the males Clint, Douglas, and Edward—are rated equally qualified for admission to law school, ahead of other applicants. However, all but two positions have been filled for the entering class. The admissions committee can admit only two more students, so it decides to randomly select two of these five candidates. For this strategy, let of females admitted. Using the first letter of the name to denote a student, the different combinations that could be admitted are (A, B), (A, C), (A, D), (A, E), (B, C), (B, D), (B, E), (C, D), (C, E), and (D, E).

(a)Construct the probability distribution for .
(b)Construct the sampling distribution of the sample proportion of the students selected who are female.

Answer 1

(a) The probability distribution for the number of female students admitted can be calculated as follows:

P(0 female students) = (2C0) × (3C2) / (5C2) = (1) × (3) / (10) = 0.3

P(1 female student) = (2C1) × (3C1) / (5C2) = (2) × (3) / (10) = 0.6

P(2 female students) = (2C2) × (3C0) / (5C2) = (1) × (1) / (10) = 0.1

(b) The sampling distribution of the sample proportion of female students selected can be calculated as follows:

P(p = 0) = 0.3 (for 0 female students)

P(p = 1/2) = 0.6 (for 1 female student)

P(p = 1) = 0.1 (for 2 female students)

Note that the sampling distribution of the sample proportion is a discrete probability distribution with values of 0, 1/2, and 1, and corresponding probabilities 0.3, 0.6, and 0.1, respectively.