Question

# 11. A boat capsized and sank in a lake. Based on an assumption of a mean...

11. A boat capsized and sank in a lake. Based on an assumption of a mean weight of 147 lb, the boat was rated to carry 70 passengers​ (so the load limit was 10,290 lb). After the boat​ sank, the assumed mean weight for similar boats was changed from 147 lb to 174 lb. Complete parts a and b below

a. Assume that a similar boat is loaded with 70 passengers, and assume that the weights of people are normally distributed with a mean of 179.4 lb and a standard deviation of 36.1 lb. Find the probability that the boat is overloaded because the 70 passengers have a mean weight greater than 147 lb.

The probability is_____

​(Round to four decimal places as​ needed.)

12. An airliner carries 250 passengers and has doors with a height of 72 in. Heights of men are normally distributed with a mean of 69.0 in and a standard deviation of 2.8 in. Complete parts​ (a) through​ (d).

a. If a male passenger is randomly​ selected, find the probability that he can fit through the doorway without bending.

The probability is _____

​(Round to four decimal places as​ needed.)

13. Before every​ flight, the pilot must verify that the total weight of the load is less than the maximum allowable load for the aircraft. The aircraft can carry 40 passengers, and a flight has fuel and baggage that allows for a total passenger load of 6,480 lb. The pilot sees that the plane is full and all passengers are men. The aircraft will be overloaded if the mean weight of the passengers is greater than 6,480 lb/40=162 lb.

What is the probability that the aircraft is​ overloaded?

Should the pilot take any action to correct for an overloaded​ aircraft?

Assume that weights of men are normally distributed with a mean of 181.9 lb and a standard deviation of 36.9.