Chapter PIV, Problem 10RE

(a)

To determine

To find: the mean and standard deviation of the number of people who might have accidents due to fault.

Answer to Problem 10RE

Mean = 7

Standard Deviation = 2.596

Explanation of Solution

Given:

  $\begin{array}{c}n=1355\\ p=0.005\end{array}$

Formula used:

  $\begin{array}{c}\mu =np\\ \sigma =\sqrt{npq}\end{array}$

Calculation:

Let X be the number of drivers in a given year with a fault crash.

The probability of drivers being covered is 1355.

The probability of a driver causing an accident at fault is 0.005.

X is a binom (1355, 0.005)

Mean number is

  $\begin{array}{c}\mu =np\\ =1355\left(0.005\right)\\ =6.775\\ =7\end{array}$

Standard deviation is,

  $\begin{array}{c}\sigma =\sqrt{npq}\\ =\sqrt{1355\left(0.005\right)\left(0.995\right)}\\ =\sqrt{6.741}\\ =2.596\end{array}$

Mean and standard deviation is mention by 6.8 and 2.596 respectively.

(b)

To determine

To explain: the distribution of a normal model of these accidents.

Explanation of Solution

A normal model cannot explain the distribution of these incidents. Because, because,

  $\begin{array}{c}np=6.8\\ <10\end{array}$

  $\begin{array}{c}nq=\left(1355\right)\left(0.995\right)\\ =1348.2\\ \ge 10\end{array}$

There is required both $np\ge 10\text{and}nq\ge \text{10}$