(MASTERY Problem) Chapter 4 Review Practice Problems, Problem 36: A programmer m
ID: 3339048 • Letter: #
Question
(MASTERY Problem) Chapter 4 Review Practice Problems, Problem 36: A programmer makes two wrong entries every hour, on the average. Find the probability that during the next five hours she will make: (a) Fewer than eight wrong entries. (b) At least four wrong entries (c) Between three to five (inclusive) wrong entries. (d) More than one wrong entry What type of distribution should be used? a) What is the probability of fewer than eight wrong entries, PN b) What is the probability of at least four wrong entries, PX 24)? c) What is the probability of between three to five (inclusive) wrong entries, P(3 s Xs 5)? d) What is the probability of more than one wrong entry, P(X> 1)? LExplanation / Answer
The type of distribution should be poisson.
= 2 per hour = 10 per 5 hours
P(X = x) = e- * x / x!
a) P(X < 8) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 7)
= e-10 * 100 / 0! + e-10 * 101 / 1! + e-10 * 102 / 2! + ... + e-10 * 107 / 7!
= 0.2202
b) P(X > 4) = 1 - [P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)]
= 1 - [e-10 * 100 / 0! + e-10 * 101 / 1! + e-10 * 102 / 2! + e-10 * 103 / 3!]
= 1 - 0.0103
= 0.9897
c) P(3 < X < 5) = P(X = 3) + P(X = 4) + P(X = 5)
= e-10 * 103 / 3! + e-10 * 104 / 4! + e-10 * 105 / 5!
= 0.0076 + 0.0189 + 0.0378
= 0.0643
d) P(X > 1) = 1 - [P(X = 0) + P(X = 1)]
= 1 - [e-10 * 100 / 0! + e-10 * 101 / 1!]
= 1 - 0.0005
= 0.9995
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