Chapter 7.3, Problem 61E

a.

To determine

To explain: The reason of not calculating the probability that the weight of passenger more than 200 pounds.

Answer to Problem 61E

Population is not normally distributed.

Explanation of Solution

Given:

  $\begin{array}{l}\text{Population mean }\left(\mu \right)=190\\ \text{Population standard deviation}\left(\sigma \right)=35\\ \text{Sample size}\left(n\right)=30\end{array}$

To compute the probability the population must be normally distributed. Here, it has been provided that the distribution of the population is not normally distributed. Thus, the required probability cannot be computed here.

b.

To determine

To find: The probability that total weight of the passengers in the flight is above 6000 pounds.

Answer to Problem 61E

The probability is 0.0594.

Explanation of Solution

Calculation:

There are total 30 passengers. The average weight of the passenger can be calculated as:

  $\begin{array}{c}\overline{x}=\frac{6000}{30}\\ =200\end{array}$

The probability that total weight of the passengers in the flight is above 6000 pounds is calculated as follows:

  $\begin{array}{c}P\left(\overline{X}>200\right)=P\left(\frac{\overline{x}-\mu }{\frac{\sigma }{\sqrt{n}}}>\frac{200-\mu }{\frac{\sigma }{\sqrt{n}}}\right)\\ =P\left(Z>\frac{200-190}{\frac{35}{\sqrt{30}}}\right)\\ =P\left(Z>1.56\right)\left(\text{From standard normal table}\right)\\ =0.0594\end{array}$

Thus, the required probability is 0.0594.