Question

A university found that 20% of its students withdraw without completing the introductory statistics course. Assume that 20 students registered for the course. (a) Compute the probability that 2 or fewer will withdraw. If required, round your answer to four decimal places. (b) Compute the probability that exactly 4 will withdraw. If required, round your answer to four decimal places. (c) Compute the probability that more than 3 will withdraw. If required, round your answer to four decimal places. (d) Compute the expected number of withdrawals.

Answer 1

Binomial distribution: P(X) = nCx p^x q^n-x

Sample size, n = 20

P(withdrawal), p = 0.20

q = 1 - p = 0.80

a) P(2 or fewer will withdraw) = P(0) + P(1) + P(2)

= 0.80²⁰ + 20x0.2x0.8¹⁹ + 20C2x0.2²x0.8¹⁸

= 0.0115 + 0.0576 + 0.1369

= 0.2060

b) P(exactly 4 will withdraw) = P(X = 4)

= 20C4 x 0.2⁴ x 0.8¹⁶

= 0.2182

c) P(more than 3 will withdraw) = P(X > 3)

= 1 - P(X 3)

= 1 - P(0) - P(1) - P(2) - P(3)

= 1 - 0.0115 - 0.0576 - 0.0169 - 0.2054

= 0.5886

d) Expected number of withdrawals = np

= 20 x 0.2

= 4