Question

In: Math

The probability is0.45 that a traffic fatality involves an intoxicated or​ alcohol-impaired driver or nonoccupant. In...

The probability is0.45 that a traffic fatality involves an intoxicated or​ alcohol-impaired driver or nonoccupant. In

seven traffic​ fatalities, find the probability that the​ number, Y, which involve an intoxicated or​ alcohol-impaired driver or nonoccupant is

a. exactly​ three; at least​ three; at most three.

b. between two and four​, inclusive.

c. Find and interpret the mean of the random variable Y.

d. Obtain the standard deviation of Y.

Solutions

Expert Solution

Here Y has binomial distribution with following parameters as follow:

n = 7 and p=0.45

The pdf of Y is

(a)

The probability that exactly​ three involve an intoxicated or​ alcohol-impaired driver or non occupant is

----------------------

The probability that at least ​ three involve an intoxicated or​ alcohol-impaired driver or non occupant is

----------------------

The probability that at most​ three involve an intoxicated or​ alcohol-impaired driver or non occupant is

(b)

(c)

The mean is

The average number of traffic fatality involves an intoxicated or​ alcohol-impaired driver or non occupant is 3.15.

(d)

The standard deviation is


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