Answer Each of the Following Questions

Stat 2820

Section 3.1 Lab Assignment

Name_________________________

Date_____________ Section_______

Answer each of the following questions.

1. The US Army requires women’s heights to be between 59 and 80 inches tall. Assume that it is known that the heights of women in the US are normally distributed with a mean of 63.6 in and a standard deviation of 2.5 inches.

a. What percent of women could serve in the US army? What percent could not serve?

b. Would it be unusual to find a woman that was too tall to be in the US Army? How do you know?

c. Would it be unusual to find a woman that was too short to be in the US Army? How do you know?

2. The standard casket has an inside length of 68 inches tall. Assuming that the same distribution for women’s heights applies as in question 1:

a. What is the probability that a randomly selected dead female would not fit in this casket?

b. If the length of the casket were changed to 70 inches, what is the probability that a randomly selected dead female would not fit?

c. Assume that the casket manufacturer wants to save money on production costs. They decide that if they make a casket that would fit 95% of all women, they could save several hundred dollars per casket. What length is required to fit these specifications?

3. Birth weights in Sweden are normally distributed with a mean of 3420 g and a standard deviation of 495 g.

a. What is the probability that a randomly selected Swedish baby weighs less than 3000g?

b. What is the probability that a randomly selected Swedish baby weighs more than 4000g?

c. What is the probability that a randomly selected Swedish baby weighs between 3145g and 3672g?

d. If a hospital plans to set up special observation conditions for the lightest 2% of babies, what weight is used for the cut-off separating the lightest 2% from the others?

5. Scores by women on the SAT-1 test are normally distributed with a mean of 998 and a standard deviation of 202. Scores by women on the ACT test are normally distributed with a mean of 20.9 and a standard deviation of 4.6. Assume that the two tests use different scales to measure the same aptitude.

a. If a woman gets a SAT score that is the 67th percentile, find her actual SAT score.

b. Using part a, find her equivalent ACT score if she scored in the 67th percentile on the SAT test.

c. If a woman gets a SAT score of 1220, find her equivalent ACT score.