Water Taxi SafetyWhen a water taxi sank in Baltimore’s Inner Harbor, an investigation revealed that the safe passenger load for the water taxi was 3500 lb. It was also noted that the mean weight of a passenger was assumed to be 140 lb. Assume a “worst-case” scenario in which all of

the passengers are adult men. Assume that weights of men are normally distributed with a mean of 188.6 lb and a standard deviation of 38.9 lb (based on Data Set 1 “Body Data” in Appendix B).

a. If one man is randomly selected, find the probability that he weighs less than 174 lb (the new value suggested by the National Transportation and Safety Board).

b. With a load limit of 3500 lb, how many male passengers are allowed if we assume a mean weight of 140 lb?

c. With a load limit of 3500 lb, how many male passengers are allowed if we assume the updated mean weight of 188.6 lb?

d. Why is it necessary to periodically review and revise the number of passengers that are allowed to board?

Theweights of men are normally distributed.

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

The mean weight is $\mu =188.6$lb.

The standard deviation of the weight is$\sigma =38.9$ 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.

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

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.

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

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.