Chapter 7.3, Problem 62E

a.

To determine

To explain: Whether the exact distribution of the provided count is normal or not.

Answer to Problem 62E

No

Explanation of Solution

Given:

  $\begin{array}{l}\text{Population mean }\left(\mu \right)=1.5\\ \text{Population standard deviation}\left(\sigma \right)=0.75\end{array}$

It is known that the normal distribution is allowed to take any real number. Here, count is taking only values that are positive integer. Thus, the distribution of count is not normal.

b.

To determine

To find: The probability that more than 1075 people would be carried out by the 700 cars.

Answer to Problem 62E

The probability is 1.038.

Explanation of Solution

Calculation:

There are total 700 passengers. The average number of passengers can be calculated as:

  $\begin{array}{c}\overline{x}=\frac{1075}{700}\\ =1.536\end{array}$

The probability that more than 1075 people would be carried out by the 700 cars is calculated as follows:

  $\begin{array}{c}P\left(\overline{X}>21.536\right)=P\left(\frac{\overline{x}-\mu }{\frac{\sigma }{\sqrt{n}}}>\frac{1.536-\mu }{\frac{\sigma }{\sqrt{n}}}\right)\\ =P\left(Z>\frac{1.536-1.5}{\frac{0.75}{\sqrt{700}}}\right)\\ =P\left(Z>1.26\right)\left(\text{From standard normal table}\right)\\ =0.1038\end{array}$

Thus, the required probability is 0.1038.