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Question

For all answers, use a TI-84 cacluator, not the table in the back of the textbook

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 scenaireo 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. The water taxi that sank had a stated capacity of 25 passengers and the boast was rated for a load limit of 3500 ln.

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

b. If the water taxi is filled with 25 randonmly selected men, what is the probabilty that their mean wieght exceeds the value of 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 randonmly selected men, what is the probabilit that their mean weigh exceeds 175 lb, which is the maximum mean weight that does not cause the total load to exceed 3500lb

d. Is the new capacity of 20 passengers safe?

Answer 1

Step 1 :

(a)

Passenger load for the water taxi was 3500 lb.

Number of passengers in water taxi is 25.

Find the mean weight of passengers allowed to travel.

Number of passengers are allowed to travel = .

Mean weight of passengers = .

Therefore mean weight of passengers allowed is 140 lb.

Solutions:

Mean weight of passengers allowed is 140 lb.

Answer 2

Step 1 :

(b)

Let the random variable  be the passenger load allowed.

Passenger load for the water taxi was 3500 lb.

Mean weight of men is 182.9 lb.

Standard deviation of men is 40.8 lb.

25 men are randomly selected.

Find the probability that the weight should exceeds 140 lb.     (From (a))

Probability of men weights exceeds 140 lb is .

Standardize x to z using z - Score formula.

z - Score formula is ,

where is the passenger load allowed,

is the mean and

is the standard deviation.

From z - score table the probability is .

Therefore .

Solution:

.

Note:

Using TI-84 calculator,

You need to type in your calculator as shown below.

normalcdf(-1.05,100)

Then you will get .

Answer 3

Step 1 :

Passenger load for the water taxi was 3500 lb.

Mean weight of men is 182.9 lb.

Standard deviation of men is 40.8 lb.

(c)

20 men are randomly selected.

Find the probability that he weight should not exceed 175 lb.

Probability of men weight exceeds 175 lb is .

Standardize x to z using z - Score formula.

z - Score formula is .

Where σ is standard deviation,

         μ is the mean.

From z - score table the probability is .

Thus, .

Solution :

.

Note :

Using TI-84,

You need to type in your calculator as shown below.

normalcdf(-0.193, 100)

Then you will get .

Answer 4

Step 1 :

(d)

Passenger load for the water taxi was 3500 lb.

Mean weight of men is 175 lb.

Find the number of passengers are allowed to travel with specifications.

Number of passengers are allowed to travel = .

Thus, the number of passengers are allowed to travel is 20.

Since the number of passengers are allowed to travel is 20, the new capacity of 20 passengers is safe.

Solution :

The new capacity of 20 passengers is safe.