Water Taxi Safety Passengers died when a water taxi sank in Baltimore's Inner Harbor. Men are typically heavier than women and children, so when loading a water taxi, assume a worst-case scenario in which all passengers are men. Assume that weights of men are normally distributed with a mean of 182.9 lb and a standard deviation of 40.8 lb (based on Data Set 1 in Appendix B). The water taxi that sank had a stated capacity of 25 passengers, and the boat was rated for a load limit of 3500 lb.

a. Given that the water taxi that sank was rated for a load limit of 3500 lb, what is the mean weight of the passengers if the boat is filled to the stated capacity of 25 passengers?

b. If the water taxi is filled with 25 randomly selected men, what is the probability that their mean weight exceeds the value from part (a)?

c. After the water taxi sank, the weight assumptions were revised so that the new capacity became 20 passengers. If the water taxi is filled with 20 randomly selected men, what is the probability that their mean weight exceeds 175 lb, which is the maximum mean weight that does not cause the total load to exceed 3500 lb?

d. Is the new capacity of 20 passengers safe?

Problem 15BSC

Answer:

Step1 of 3:

We have Passengers died when a water taxi sank in Baltimore’s Inner Harbor. Men are typically heavier than women and children, so when loading a water taxi, assume a worst-case scenario in which all passengers are men. Assume that weights of men are normally distributed with a mean of 182.9 lb and a standard deviation of 40.8 lb (based on Data Set 1). The water taxi that sank had a stated capacity of 25 passengers, and the boat was rated for a load limit of 3500 lb.

That is182.9 and 40.8

Ste2 of 3:

We need to find,

a. Given that the water taxi that sank was rated for a load limit of 3500 lb, what is the mean weight of the passengers if the boat is filled to the stated capacity of 25 passengers?

b.If the water taxi is filled with 25 randomly selected men, what is the probability that their mean weight exceeds the value from part (a)?

c.After the water taxi sank, the weight assumptions were revised so that the new capacity became 20 passengers. If the water taxi is filled with 20 randomly selected men, what is the probability that their mean weight exceeds 175 lb, which is the maximum mean weight that does not cause the total load to exceed 3500 lb?

d. Is the new capacity of 20 passengers safe?

Step3 of 3:

a).

Given that the water taxi that sank was rated for a load limit of 3500 lb,

The mean weight of passengers is =140.

b).

If the water taxi is filled with 25 randomly selected men,the probability that their mean weight exceeds the value from part (a) is given by

Consider the z statistics when x = 140

P(x = 140) = P(Z = )

= P()

= P()

= P(-5.26)

Probability of -5.26 is calculated by using standard normal table(area under normal curve).In area under normal curve we have to see row -5.2 under column 0.06

P(-5.26) = 0.99999

1

Therefore, the probability that their mean weight exceeds the value from part (a) is 1.

c).

After the water taxi sank, the weight assumptions were revised so that the new capacity became 20 passengers. If the water taxi is filled with 20 randomly selected men, the probability that their mean weight exceeds 175 lb is given by

Consider the z statistics when x = 175

P(x = 175) = P(Z = )

= P()

= P()

= P(-0.870)

Probability of -0.870 is calculated by using standard normal table(area under normal curve).In area under normal curve we have to see row -0.87 under column 0.00

P(-0.870) = 0.8078.

Therefore, the probability that their mean weight exceeds 175 lb is 0.8078.

d).

From Part(c)we have that there is a 0.8078 probability of exceeding the 3500 lb. limit when the water taxi is loaded with 20 random men, the new capacity of 20 passengers does not appear to be safe enough because the probability of overloading is too high.