1.Assume that military aircraft use ejection seats designed for men weighing between 135.7 lb and 214 lb. Ifwomen's weights are normally distributed with a mean of 162.8 lb and a standard deviation of 49.3 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

%.

(Round to two decimal places asneeded.)

Are many women excluded with thosespecifications?

A.

No, the percentage of women who areexcluded, which is equal to the probability foundpreviously, shows that very few women are excluded.

B.

Yes, the percentage of women who areexcluded, which is equal to the probability foundpreviously, shows that about half of women are excluded.

C.

Yes, the percentage of women who areexcluded, which is the complement of the probability foundpreviously, shows that about half of women are excluded.

D.

No, the percentage of women who areexcluded, which is the complement of the probability foundpreviously, shows that very few women are excluded.

2.Assume that adults have IQ scores that are normally distributed with a mean of 102 and a standard deviation 16.4. Find the first quartile Q1, which is the IQ score separating the bottom25% from the top75%.

The first quartile is

(Type an integer or decimal rounded to one decimal place asneeded.)

3.Find the indicated IQ score. The graph to the right depicts IQ scores ofadults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.

x

0.2317

A symmetric bell-shaped curve is plotted over a horizontal scale. A vertical line runs from the scale to the curve at labeled coordinate x, which is to the right of the curve's center and peak. The area under the curve to the right of the vertical line is shaded and labeled 0.2317.

The indicated IQ score is

(Round to the nearest whole number asneeded.)

4.A common design requirement is that an environment must fit the range of people who fall between the 5th percentile for women and the 95th percentile for men. In designing an assembly worktable, the sitting knee height must beconsidered, which is the distance from the bottom of the feet to the top of the knee. Males have sitting knee heights that are normally distributed with a mean of 21.5 in. and a standard deviation of 1.1 in. Females have sitting knee heights that are normally distributed with a mean of 19.2 in. and a standard deviation of 1.0 in. Use this information to answer the following questions.

a.What is the minimum table clearance required to satisfy the requirement of fitting95% ofmen?

. (Round to one decimal place asneeded.)

b.Determine if the following statement is true or false. If there is clearance for95% ofmales, there will certainly be clearance for all women in the bottom5%.

A.

The statement is true because some women will have sitting knee heights that are outliers.

B.

The statement is false because the 95th percentile for men is greater than the 5th percentile for women.

C.

The statement is true because the 95th percentile for men is greater than the 5th percentile for women.

D.

The statement is false because some women will have sitting knee heights that are outliers.

c.The author is writing this exercise at a table with a clearance of 23.6 in. above the floor. What percentage of men fit thistable

% (Round to two decimal places asneeded.)

d.What percentage of women fit thistable?

% (Round to two decimal places asneeded.)

e.Does the table appear to be made to fit almosteveryone? Choose the correct answer below.

A.

The table will fit only 3% of men.

B.

The table will only fit1% of women.

C.

The table will fit almost everyone except about 3% of men with the largest sitting knee heights.

D.

Not enough information to determine if the table appears to be made to fit almost everyone.