Assume that females have pulse rates that are normally distributed with a mean of =74.0 beats per minute and a standard deviation of =12.5 beats per minute. If 1 adult female is randomlyselected, find the probability that her pulse rate is between 67 beats per minute and 81 beats per minute.

An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 130 lb and 171 lb. The new population of pilots has normally distributed weights with a mean of 137lb and a standard deviation of 34.5lb. If a pilot is randomlyselected, find the probability that his weight is between 130 lb and 171 lb.

Before everyflight, 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 37 passengers, and a flight has fuel and baggage that allows for a total passenger load of 6,031 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 6,031lb37=163 lb. What is the probability that the aircraft isoverloaded? Should the pilot take any action to correct for an overloadedaircraft? Assume that weights of men are normally distributed with a mean of 180.2 lb and a standard deviation of 39.1.

The overhead reach distances of adult females are normally distributed with a mean of 200cm and a standard deviation of 8.3cm.

a. Find the probability that an individual distance is greater than 209.30 cm.

b. Find the probability that the mean for 20 randomly selected distances is greater than 198.20cm.

c. Why can the normal distribution be used in part(b), even though the sample size does not exceed30?