Question

Water Taxi Safety When 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?

Answer 1

Answer:

a: 0.3594

b: 25 passengers

c:  18 passengers

d:  Read below

Step-by-step explanation:

We have:

µ = 140

x = 188.6

s = 38.9

For a:  Probability of choosing 1 male passenger that weights less than 174 lbs, first find the z-score, then look up that score on the z-score chart

z = (174 - 188.6)/38.9 = -0.36

P(z < -0.36) = 0.3594

For b:  Divide 3500 by 140 to determine the amount of passengers

3500/140 = 25 passengers

For c:  Divide 3500 by 188.6 to determine the amount of passengers

3500/188.6 = 18.56.  We have to round down so we don't go over the limit, so 18 passengers

For d:  For safety reasons, so they don't overload the ship.  Also for financial reasons, so they can sell as many tickets as possible to make as much money as possible

Answer 2

Using the normal distribution and proportions, it is found that:

a) 0.352 = 35.2% probability that he weighs less than 174 lb.

b) 25 male passengers are allowed.

c) 18 male passengers are allowed.

d) It is important because the weight of the passengers change, and also because the structures get older, thus resisting less weight.

In a normal distribution with mean $\mu$ and standard deviation $\sigma$, the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

• It measures how many standard deviations the measure is from the mean.
• After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

Item a:

• Mean of 188.6 lb, thus $\mu = 188.6$
• Standard deviation of 38.9 lb, thus $\sigma = 38.9$.

The probability is the p-value of Z when X = 174, thus:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{174 - 188.6}{38.9}$

$Z = -0.38$

$Z = -0.38$ has a p-value of 0.352.

0.352 = 35.2% probability that he weighs less than 174 lb.

Item b:

Applying the proportion, dividing 3500 by 140, we get that:

$\frac{3500}{140} = 25$

25 male passengers are allowed.

Item c:

$\frac{3500}{188.6} = 18.5$

18 male passengers are allowed, as rounding to 19 would result in the load limit being exceeded.

Item d:

It is important because the weight of the passengers change, and also because the structures get older, thus resisting less weight.

A similar problem is given at https://brainly.com/question/15181104