I need help with a Statistics question. All explanations and answers will be used to help me learn.

1. The overhead reach distances of adult females are normally distributed with a mean of 195 cm

and a standard deviation of

8.6 cm

.

**a.** Find the probability that an individual distance is greater than 207.50 cm.

**b.** Find the probability that the mean for 20 randomly selected distances is greater than 193.20 cm.

2. An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 150

lb and 201

lb. The new population of pilots has normally distributed weights with a mean of

155 lb and a standard deviation of 31.9 lb.

A . If a pilot is randomly selected, find the probability that his weight is between 150 lb and 201 lb.

The probability is approximately…

B. If 32 different pilots are randomly selected, find the probability that their mean weight is between 150 lb and 201 lb.

The probability is approximately …..