Question

Problem 1 A university found that in an introductory statistics course, about 40% of the enrolled students will pass the course with A or B grades, 30% will pass with a C and i 0% will obtained D or F grades. 20% of the students withdraw without completing the course. Assume that 20 students are registered for the course a Computethe probaill withdraw b. Compute the probability that exactly 4 will withdraw Compute the probability that more than 3 will withdraw Compute the expected number of students who will withdraw from the class. c. d.

Answer 1

P(withdraw) = 0.2

n = 20

P(X = x) = 20Cx * 0.2^x * (1 - 0.2)^20-x

a) P(X < 2) = P(X = 0) + P(X = 1) + P(X = 2)

                   = 20C0 * 0.2⁰ * 0.8²⁰ + 20C1 * 0.2¹ * 0.8¹⁹ + 20C2 * 0.2² * 0.8¹⁸

                   = 0.2061

b) P(X = 4) = 20C4 * 0.2⁴ * 0.8¹⁶ = 0.2182

c) P(X > 3) = 1 - P(X < 3)

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

                  = 1 - (20C0 * 0.2⁰ * 0.8²⁰ + 20C1 * 0.2¹ * 0.8¹⁹ + 20C2 * 0.2² * 0.8¹⁸ + 20C3 * 0.2³ * 0.8¹⁷)

                  = 1 - 0.4114

                  = 0.5886

d) Expected number = 20 * 0.2 = 4