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cnnbc recently reported that the mean annual cost of auto insurance is 1007 dollars. assume the standard deviation is 241 dollars. you take a simple random sample of 99 auto insurance policies. find the probability that a single randomly selected value is less than 971 dollars.

Answer :

Using the normal distribution, the probability that a single randomly selected value is less than 971 dollars is 0.2123.

In the given question,

CNNBC recently reported that the mean annual cost of auto insurance is 1007 dollars.

The standard deviation is 241 dollars.

We take a simple random sample of 99 auto insurance policies.

We have to find the probability that a single randomly selected value is less than 971 dollars.

From the question,

Mean = 1107 dollars

Standard Deviation = 241 dollars

So the probability that a single randomly selected value is less than 971 dollars.

Using the normal distribution

z = (x−mean)/Standard Deviation

P(x<971) = P(z<(973−1107)/241)

Simplifying

P(x<971) = P(z<(−134)/241)

P(x<971) = P(z<−0.56)

P(x<971) = 0.2123

Hence, the probability that a single randomly selected value is less than 971 dollars is 0.2123.

To learn more about normal distribution link is here

https://brainly.com/question/15103234

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