1.A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of 185 lb and a standard deviation of 39 lb. The gondola has a stated capacity of 25 passengers, and the gondola is rated for a load limit of 3500 lb.

Given that the gondola is rated for a load limit of 3500 lb, what is the maximum mean weight of the passengers if the gondola is filled to the stated capacity of 25 passengers?

The maximum mean weight is lb.(Type an integer or a decimal. Do notround.)

2.Suppose that an airline uses a seat width of 16.5 in. Assume men have hip breadths that are normally distributed with a mean of 14.1 in. and a standard deviation of 1 in.

Find the probability that if an individual man is randomlyselected, his hip breadth will be greater than 16.5 in.

The probability is

(Round to four decimal places asneeded.)

3.An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 140 lb and 191 lb. The new population of pilots has normally distributed weights with a mean of 149lb and a standard deviation of 29.2lb.

If a pilot is randomlyselected, find the probability that his weight is between 140 lb and 191 lb.

The probability is approximately

(Round to four decimal places asneeded.)

4.An airliner carries 400 passengers and has doors with a height of 74 in. Heights of men are normally distributed with a mean of 69.0 in and a standard deviation of 2.8 in.

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

The probability is

(Round to four decimal places asneeded.)