The probability is 0.4 that a traffic fatality involves an intoxicated or alcohol-impaired driver or nonoccupant. In 7 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.

a.

b.

c. mean=2.8

d . standard deviation=1.2961

Step-by-step explanation:

We determine that the accident rates follow a binomial distribution. The rate of success p=0.4 and sample n=7:

#the probability of exactly three;

#At least(more than 2)

#At most 3;

b. Between 2 and 4:

Using the binomial expression, this probability is calculated as:

Hence,the probability of between 2 and four is 0.7451

c. From a above, we have the values of n=7 and p=0.4.

-We substitute this values in the formula below to calculate the mean:

-The mean of a binomial distribution is calculated as the product of the probability of success by the sample size, mean=np:

Hence, the standard deviation of the sample is 2.8

d. From a above, we have the values of n=7 and p=0.4

--We substitute this values in the formula below to calculate the standard deviation

-The standard deviation a binomial distribution is given as:

Hence, the standard deviation of the sample is 1.2961