q 1.

A survey found thatwomen's heights are normally distributed with mean 62.9 in. and standard deviation 2.1 in. The survey also found thatmen's heights are normally distributed with mean 69.7 in. and standard deviation 3.9 in. Most of the live characters employed at an amusement park have height requirements of a minimum of 56 in. and a maximum of 64 in. Complete parts(a) and(b) below.

a. Find the percentage of men meeting the height requirement. What does the result suggest about the genders of the people who are employed as characters at the amusementpark?

The percentage of men who meet the height requirement is

nothing

??%.

B. If the height requirements are a minimum of ???? in. and a maximum of ??? in.

q2.

Assume that military aircraft use ejection seats designed for men weighing between 146.4 lb and 204 lb. Ifwomen's weights are normally distributed with a mean of 163.7 lb and a standard deviation of 40.5 lb, what percentage of women have weights that are within thoselimits? Are many women excluded with thosespecifications?

The percentage of women that have weights between those limits is

nothing

??%

q3

The weights of a certain brand of candies are normally distributed with a mean weight of 0.8625 g and a standard deviation of 0.0514 g. A sample of these candies came from a package containing 460 candies, and the package label stated that the net weight is 393.0 g.(If every package has 460 candies, the mean weight of the candies must exceed 393.0/460=0.8543 g for the net contents to weigh at least 393.0 g.)

a. If 1 candy is randomlyselected, find the probability that it weighs more than 0.8543 g.

The probability is ??

B. If 460 candies are randomly selected, find the probability that their mean weight is at least 0.8543g.

The probability that a sample of 460 candies will have a mean of 0.8543 or greater is ???

q4

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 25.7lb.

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

The probability is approximately 0.5858

b. If 33 different pilots are randomlyselected, find the probability that their mean weight is between 140 lb and 191 lb.

The probability is approximately ??

.