Chapter 12.5, Problem 14PPS

(a)

To determine

To Find: The range of the rates it is expected 68% of the population to pay annually.

Answer to Problem 14PPS

The 68% data values lies within the interval $\left(714,944\right)$ .

Explanation of Solution

Given:

The mean annual cost per person is $829 and the standard deviation is $115.

Calculation:

Consider that for the 68% value falls within 1 standard deviation of mean 95% of values fall with in 2 standard deviation of the mean and 97.7% of the values fall within 3 standard deviation of the mean.

Consider the X is the random variable that show the annual cost per person and x is the normal distribution that has the parameters $\mu =829$ and $\sigma =115$ .

Then, the interval that corresponds to one standard deviation of the mean is,

  $\begin{array}{c}\mu \pm \sigma =829\pm 115\\ =\left(714,944\right)\end{array}$

Thus, the 68% data values lies within the interval $\left(714,944\right)$ .

(b)

To determine

To Find: The expected number to pay more than $1059 annually.

Answer to Problem 14PPS

The expected number of people is $22.5$ .

Explanation of Solution

Calculation:

Consider the equation is,

  $\begin{array}{c}\mu +2\sigma =829+2\cdot 115\\ =1059\end{array}$

Then, the area to the right is,

  $1-\left(0.50+0.475\right)=0.025$

Then, the number of people is,

  $900\cdot 0.025=22.5$

Thus, the expected number of people is $22.5$ .

(c)

To determine

To Find: The point on the distribution where it is expected for a person with several traffic citations to lie and explain the reason for it.

Answer to Problem 14PPS

The required interval is

  $\left(599,1059\right)$ .

Explanation of Solution

Given:

The number of people sampled is 900. Then, find the number that are expected to pay more than $1059 annually.

Calculation:

Consider that 95% of traffic citation lies within 2 standard deviation of the mean then the interval is,

  $\begin{array}{c}\mu \pm \sigma =829\pm 2\cdot 115\\ =\left(599,1059\right)\end{array}$

(d)

To determine

To Find: The way in which the insurance companies use the factor to calculate the risk.

Answer to Problem 14PPS

The insurance company will compile the data based on each of the factor and determine the rate of accidents for each of the categories and then use the price and calculate the risk.

Explanation of Solution

Calculation:

The insurance company will compile the data based on each of the factor and determine the rate of accidents for each of the categories and then use the price and calculate the risk.