91影视

It is given in the question that, the mean annual loss, $渭=250$

the standard deviation of the loss, $蟽=300$

follow the four-step process.

The central limit theorem states that if the sample size of a sampling distribution is $300$or more, then the sample mean is approximately normal whose mean is $渭$and the standard deviation is $\frac{蟽}{\sqrt{n}}$.

The $z$value of a distribution can be found by dividing the difference between the population mean and sample mean by the standard deviation that is, $z=\frac{x鈭�渭}{\frac{s^r}{\sqrt{n}}}.$

Since the sample size of $10,000$policies is at least $30$; so we can apply the central limit theorem.

Find the $z$value by using the formula$z=\frac{x鈭�渭}{\frac{s^r}{\sqrt{n}}}.$

Substitute $275$for $x$,$250for渭,300for蟽,and10,000forn$the above formula and simplify.

$z=\frac{275鈭�250}{\frac{300}{\sqrt{10000}}}$

$=\frac{25}{\frac{306}{100}}$

$=8.33$

Thus, the corresponding probability is:

$P(\stackrel{炉}{x}>275)=P(z>8.33)=P(Z<鈭�8.33)=0.0001$

Thus, the company can safely assume that the average loss will be no greater than $275$because the probability is almost zero.

Accordingly, the company can safely base its rates on the assumption that its average loss will be no greater than $275$it sells $10,000$policies.