Question

CNNBC recently reported that the mean annual cost of auto insurance is 954 dollars. Assume the standard deviation is 234 dollars. You take a simple random sample of 61 auto insurance policies. Find the probability that a single randomly selected value is at least 960 dollars.

Answer 1

Answer: 0.42

Explanation:

Given: Mean :
`\mu=954\text{ dollars}`

Standard deviation :
`234\text{ dollars}`

Sample size :
`n=61`

The formula to calculate z score is given by :-

`z=(X-\mu)/((\sigma)/(√(n)))`

For X=960

`z=(960 -954)/((234)/(√(61)))=0.200262812203\approx0.2`

The p-value =
`P(X\geq960)=1-P(X<960)=1-P(z<0.2)=1-0.5792597=0.4207403\approx0.42`

Hence, the probability that a single randomly selected value is at least 960 dollars = 0.42