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Question

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 passagnger was asumed to be 140 lb. All of the passenger are adult men. Assume that weights of men are normally distributed with a mean of 182.9 lb and a standard deviation of 40.8 lb.

a. If one man is randomly selected find the probabilty that he weight less than 174 lb.

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

b. With a load limit of 3500 lb, how many male passengers are allowed if we use new mean weight of 182.9 lb?

Answer 1

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.

(a)

If one man is randomly selected.

Find the probability that he weight less than 174 lb.

Probability of man weighs less than 174 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 .

Therefore .

Solution :

The probability of a man weight less than 174 lb is 0.4136.

Answer 2

(b)

Step 1 :

Passenger load for the water taxi was 3500 lb.

Mean weight of men is 140 lb.

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

Number of passengers are allowed to travel = .

Therefore 25 men are allowed to travel with mean 140 lb.

Solution :

Number of passengers are allowed to travel is 25.

Answer 3

(c)

Step 1 :

Passenger load for the water taxi was 3500 lb.

Mean weight of men is 182.9 lb.

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

Number of passengers are allowed to travel = .

Therefore 19 men are allowed to travel with mean 182.9 lb.

Solution :

Number of passengers are allowed to travel is 19.