Tabansi

2021-03-02

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.

Write your answers as numbers accurate to 4 decimal places.

Corben Pittman

Skilled2021-03-03Added 83 answers

The Z-score of a random variable X is defined as follows:

$Z=\frac{X-\mu}{\sigma}$

Here, $\mu {\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}\sigma$ 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 is

$P\left(X<969\right)=P\left(\frac{(X-\mu )}{\sigma}<\frac{969-954}{271}\right)$

$=P\left(Z<0.06\right)=0.5221$

(Using standard normal table: $P\left(Z<0.06\right)=0.5221$)

Thus, there is a 0.5221 percent chance that a single randomly chosen value will be less than 969 dollars.

Jeffrey Jordon

Expert2021-11-14Added 2605 answers

Answer is given below (on video)

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