A university found that 18% of its students withdraw without completing the introductory statistics course. Assume that 20 students registered for the course. If required, round your answer to four decimal places. (a) Compute the probability that 2 or fewer will withdraw.

(b) Compute the probability that exactly 4 will withdraw.

(c) Compute the probability that more than 3 will withdraw.

(d) Compute the expected number of withdrawals.

(a)0.2748 (b) 0.2125 (c) 0.4974 (d) 3.6

Explanation:

Solution

Given that:

By applying binomial probability formula we have the following:

P(X = x) = (ₙ Cₓ) * p^x * (1 - p)^n - x

Thus

(a) P(X ≤ 2)

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

= (20 C₀) * 0.18^0 * (0.82)^20 + (20 C₁) * 0.18\^1 * (0.82)^19 + (20 C₂) * 0.18^2 * (0.82)^18

Probability = 0.2748

(b) P(X = 4) = 0.2125

(c) P(X > 3) = 0.4974

(d)The expected number of withdrawals = n * p = 20 * 0.18

= 3.6

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