91影视

Theweights of men are normally distributed.

The safe passenger load for the water taxi is 3500 lb.

The mean weight is $渭=188.6$lb.

The standard deviation of the weight is$蟽=38.9$ lb.

Let x represent the weight of a man.

a.

The probabilitythat he weighs less than 174 lb is computed using the standard normal table as follows.

$$\begin{gathered} P\left(x<174\right)=P\left(\frac{x-渭}{蟽}<\frac{174-188.6}{38.9}\right) \\ =P\left(Z<-0.38\right) \\ =0.352 \end{gathered}$$.

Therefore, the probabilitythat he weighs less than 174 lb is 0.352.

b.

The number of male passengers that are allowed if we assume a mean weight of 140 lb is computed as follows.

$$\begin{gathered} \text{Number}\text{of}\text{passengers}=\frac{\text{Total}\text{load}\text{limit}}{\text{Mean}\text{weight}\text{of}\text{passengers}} \\ =\frac{3500}{140} \\ =25 \end{gathered}$$

Therefore, the number of male passengers that are allowed if we assume a mean weight of 140 lb is 25.

c.

The number of male passengers that are allowed if we assume the updated mean weight of 188.6 lb is computed as follows.

$$\begin{gathered} \text{Number}\text{of}\text{passengers}=\frac{\text{Total}\text{load}\text{limit}}{\text{Updated}\text{mean}\text{weight}\text{of}\text{passengers}} \\ =\frac{3500}{188.6} \\ =18.557 \\ 鈮�19 \end{gathered}$$

Therefore, the number of male passengers that are allowed if we assume the updated mean weight of 188.6 lb is 19.

d.

It is important to periodically review and revise the number of passengers that are allowed to board because the weights of the passengers tend to change over time.