The lengths of pregnancies are normally distributed with a mean of 266 days and a standard deviation of 15 days. a. Find the probability of a pregnancy lasting 307 days or longer. b. If the length of pregnancy is in the lowest 3 %, then the baby is premature. Find the length that separates premature babies from those who are not premature.

a. The probability that a pregnancy will last 307 days or longer is

b.

Use a standard normal distribution table to find the z-score that corresponds to the lowest

3%.

Start by looking in the body of the table and finding the value closest to

0.03.

Find the x-value use the fact that

x=+(z).

2. A survey found that women's heights are normally distributed with mean 63.7 in and standard deviation 2.3 in. A branch of the military requires women's heights to be between 58 in and 80 in.

a. Find the percentage of women meeting the height requirement. Are many women being denied the opportunity to join this branch of the military because they are too short or too tall?

b. If this branch of the military changes the height requirements so that all women are eligible except the shortest 1% and the tallest 2%, what are the new height requirements?

a. The percentage of women who meet the height requirement is____________

.b. For the new height requirements, this branch of the military requires women's heights to be at least ________in and at most__________

in.(Round to one decimal place as needed.)

3.Assume that human body temperatures are normally distributed with a mean of 98.19F and a standard deviation of 0.63F.

a. A hospital uses 100.6F as the lowest temperature considered to be a fever. What percentage of normal and healthy persons would be considered to have a fever? Does this percentage suggest that a cutoff of 100.6F is appropriate?

b. Physicians want to select a minimum temperature for requiring further medical tests. What should that temperature be, if we want only 5.0% of healthy people to exceed it? (Such a result is a false positive, meaning that the test result is positive, but the subject is not really sick.)

4.A survey found that women's heights are normally distributed with mean

63.8 in. and standard deviation 3.8 in. The survey also found that men's heights are normally distributed with mean 69.3 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.

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 amusement park?The percentage of men who meet the height requirement is

b. If the height requirements are changed to exclude only the tallest 50% of men and the shortest 5% of men, what are the new height requirements?

5.Assume that adults have IQ scores that are normally distributed with a mean of 102.7 and a standard deviation 23.1.

Find the first quartile

Q1,

which is the IQ score separating the bottom 25% from the top 75%.

The first quartile is___________