1. In a recent report released by Consumer Reports, it was reported that 7 in 10 auto...

1. In a recent report released by Consumer Reports, it was reported that 7 in 10 auto accidents involve a single vehicle (thus, 3 out of 10 involve multiple vehicles). Suppose 15 accidents are randomly selected. Let x = the number of accidents involving a single vehicle.

a. What is the probability that less than 14 accidents involve a single vehicle?

b. What is the mean number of single vehicle accidents? What is the standard deviation?

c. What is the probability at least 2 accidents are multiple vehicle accidents?

Solutions

Expert Solution

Answer a)

We have to find P(X < 14) = 1 - P(X ≥ 14)

P(X ≥ 14) = 0.0353

P(X < 14) = 1 - 0.0353

P(X < 14) = 0.9647

The probability that less than 14 accidents involve a single vehicle is 0.9647

Answer b)

The population proportion of success is p = 0.7

Answer c)

We have to find P(X ≥ 2) = 1 - P(X ≤ 1)

P(X ≤ 1) = 0.0353

P(X ≥ 2) = 1 - 0.0353

P(X ≥ 2) = 0.9647

The probability at least 2 accidents are multiple vehicle accidents is 0.9647

orchestra answered 1 year ago

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