Question

Twenty-three percent of automobiles are not covered by insurance (CNN, February 23,2006). On a particular weekend, 35 automobiles are involved in traffic accidents.a. What is the expected number of these automobiles that are not covered by insurance?b. What are the variance and standard deviation?

Answer 1

Explanation:

Given that twenty-three percent of automobiles are not covered by insurance (CNN, February 23,2006).

considering the total number of vehicles, probability for a randomly drawn vehicle not covered by insurance = 0.23

Each vehicle can be treated as independent of the other

Hence X no of vehicles not covered by insurance is Binom with n = 35 and p - 0.23

a) the expected number of these automobiles that are not covered by insurance=E(x) =

`np = 35(0.23)\\= 8.05`

b) the variance

=
`npq = 8.05(0.77) \\=6.1985`

Std dev = square root of variance = 2.4897