Homework 5.4 The Department of Public safety reports that sixty percent of vehic
ID: 2936522 • Letter: H
Question
Homework 5.4 The Department of Public safety reports that sixty percent of vehicle accidents are caused by speeding. (Express answers to 4 decimals) a. What is the probability that among five accidents reported, four are caused by speeding? b. What is the probability that among five accidents reported, three are not caused by speeding? c. What is the probability that among five accidents reported, at least one is caused by speeding? d. Find the mean and standard deviation of the number of accidents caused by speeding among forty accidents reported. e. Find the mean and standard deviation of the number of accidents not caused by speeding among fifty accidents reported.Explanation / Answer
p = 0.6
n = 5
P(X = x) = 5Cx * 0.6x * (1 - 0.6)5-x
a) P(X = 4) = 5C4 * 0.64 * 0.41 = 0.2592
b) P(three not cuased by speeding) = P(2 caused by speeding)
= P(X = 2)
= 5C2 * 0.62 * 0.43
= 0.2304
c) P(X > 1) = 1 - P(X = 0)
= 1 - 5C0 * 0.60 * 0.45
= 1 - 0.0102
= 0.9898
d) p = 0.6
n = 40
mean = n * p = 40 * 0.6 = 24
Standard deviation = sqrt(n * p * (1 - p)) = sqrt(40 * 0.6 * 0.4) = 3.10
e) p = 0.4
n = 50
mean = n * p = 50 * 0.4 = 20
Standard deviation = sqrt(n * p * (1 - p)) = sqrt(50 * 0.4 * 0.6) = 3.46
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