CNNBC recently reported that the mean annual cost of auto insurance is 954 dollars. Assume the standard deviation is 271 dollars. You take a simple random sample of 96 auto insurance policies. Find the probability that a single randomly selected value is less than 969 dollars. P(x&lt;969)=P(x&lt;969)=? Write your answers as numbers accurate to 4 decimal places.

Question

CNNBC recently reported that the mean annual cost of auto insurance is 954 dollars. Assume the standard deviation is 271 dollars. You take a simple random sample of 96 auto insurance policies. Find the probability that a single randomly selected value is less than 969 dollars. P(x&amp;lt;969)=P(x&amp;lt;969)=?  Write your answers as numbers accurate to 4 decimal places.

Corben Pittman · Accepted Answer

The Z-score of a random variable X is defined as follows:Z=X−μσHere,&amp;nbsp;μ&amp;nbsp;and&amp;nbsp;σ&amp;nbsp;are the mean and standard deviation of X, respectively.Take into account the X random variable, which represents the annual cost of car insurance.The information provided indicates that X has a normal distribution, with a mean of 954 and a standard deviation of 271. The sample size, n is 96.The likelihood that any given value chosen at random is less than 969 dollars isP(X&amp;lt;969)=P((X−μ)σ&amp;lt;969−954271)=P(Z&amp;lt;0.06)=0.5221(Using standard normal table:&amp;nbsp;P(Z&amp;lt;0.06)=0.5221)Thus, there is a 0.5221 percent chance that a single randomly chosen value will be less than 969 dollars.

Jeffrey Jordon · Accepted Answer

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CNNBC recently reported that the mean annual cost of auto insurance is 954 dollars. Assume the standard deviation is 271 dollars.

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