A university found that 26% 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. |
n = 20
p = 0.26
It is a binomial distribution
P(X = x) = nCx * px * (1 - p)n - x
a) P(X < 2) = P(X = 0) + P(X = 1) + P(X = 2)
= 20C0 * (0.26)^0 * (0.74)^20 + 20C1 * (0.26)^1 * (0.74)^19 + 20C2 * (0.26)^2 * (0.74)^18 = 0.0763
b) P(X = 4) = 20C4 * (0.26)^4 * (0.74)^16 = 0.1790
c) P(X > 3) = 1 - P(X < 3)
= 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3))
= 1 - (20C0 * (0.26)^0 * (0.74)^20 + 20C1 * (0.26)^1 * (0.74)^19 + 20C2 * (0.26)^2 * (0.74)^18 + 20C3 * (0.26)^3 * (0.74)^17)
= 1 - 0.1962 = 0.8038
d) Expected no of withdrawals = n * p = 20 * 0.26 = 5.2 = 5
A university found that 26% of its students withdraw without completing the introductory statistics course. Assume...
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