Chapter 11.5, Problem 19PPS

(a)

To determine

To find: The ranges of rates you would expect the middle $68\%$ of the population to pay annually.

Answer to Problem 19PPS

The range is $\$714<X<\$944$ .

Explanation of Solution

Given:

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

Calculation:

Since the middle $68\%$ represents all data values within one standard deviation, $\sigma$ .

Therefore the range is calculated as:

  $\begin{array}{c}\$829-\$115<X<\$829+\$115\\ \$714<X<\$944\end{array}$

The range is $\$714<X<\$944$ .

(b)

To determine

To find: The expected number of people would be to pay more than $\$1000$ annually.

Answer to Problem 19PPS

The answer is given below.

Explanation of Solution

Given:

  $900$ People were sampled.

The $z$ - value is calculated as:

  $\begin{array}{c}z=\frac{X-\mu }{\sigma }\\ =\frac{1000-829}{115}\\ \approx 1.487\end{array}$

Using graphing calculator, find

  $normalcdf\left(1.487,4\right)$

  

The probability is about $6.8\%$ .

Therefore, we expect $0.068\left(900\right)\approx 62$ people to pay more than $\$1000$ annually.

(c)

To determine

To find: The place on the distribution would you expect a person with several traffic citations to lie.

Answer to Problem 19PPS

The explanation is given below.

Explanation of Solution

We can expect people with several traffic citations to lie on the far right of the distribution where the insurance costs are higher because the insurance companies would charge them more.

Therefore the place on the distribution that would we expect a person with several traffic citations to lie is on the far right of the distribution.

(d)

To determine

To find: The way that the auto insurance companies use each factor to calculate an individual’s insurance rate.

Answer to Problem 19PPS

The explanation is given below.

Explanation of Solution

Because as the probability of an accident occurring increases, the more an auto insurance company is going to charge.

Therefore possible answers are:

Age: Young or inexperienced drivers are going to be charged more.

Car Driven: Experience car owners are going to be charged more.

Driving Record: People with more tickets & accidents or bad history in driving are going to be charged more.

The explanation is given above.