Question

A university found that 40% of its students withdraw without completing the introductory statistics course. Assume that 20 students registered for the course.

a. Compute the probability that two or fewer will withdraw.

b. Compute the probability that exactly four will withdraw.

c. Compute the probability that more than three will withdraw.

d. Compute the expected number of withdrawals.

Answer 1

a)

Here, n = 20, p = 0.4, (1 - p) = 0.6 and x = 2
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X <= 2).
P(X <= 2) = (20C0 * 0.4^0 * 0.6^20) + (20C1 * 0.4^1 * 0.6^19) + (20C2 * 0.4^2 * 0.6^18)
P(X <= 2) = 0 + 0.0005 + 0.0031
P(X <= 2) = 0.0036

b)

Here, n = 20, p = 0.4, (1 - p) = 0.6 and x = 4
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 4)
P(X = 4) = 20C4 * 0.4^4 * 0.6^16
P(X = 4) = 0.035

c)

Here, n = 20, p = 0.4, (1 - p) = 0.6 and x = 3
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X > 3).
P(X > 3) = 1 - P(X <= 3)
P(X >3) =1 - 0.016 = 0.984

d)

Expected number = np
= 20 * 0.40 = 8