Normal Distribution Review WS

AP Statistics Name______Normal Distribution Review WS

1. Weights of newborn babies in the United States are normally distributed with a mean of 3420 g and a standard deviation of 495 g. A newborn weighing less than 2200 g is considered to be at risk, because the mortality rate for this group is at least 1%.

a. What percentage of newborn babies are in the “at-risk” category?

b. If Wilkes Regional Medical Center has 900 births in a year, how many of the babies can they expect to be in the “at-risk” category.

2. One classic use of the normal distribution is inspired by a letter to “Dear Abby” in which a wife claimed to gave given birth 308 days after a brief visit from her husband, who was serving the Navy. The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. Given this information, find the probability of a pregnancy lasting 308 days or longer. What does the result suggest?

3. Using the information about length of pregnancies in #2, answer the following question.

If we stipulate a baby is premature if the length of the pregnancy is in the lowest 4%, find the length that separates premature babies from those that are not premature. 4. Scores on the biology portion of the Medical College Admissions Test were normally distributed with a mean of 9.1 and a standard deviation of 2.1 in 2005. a. What percentage of scores were above 8.5 in 2005, the minimum score required for admission to the Providence School of Medicine?

b. What percentage of the scores were between 7.5 and 9.0 in 2005?

c. What score was at the D2 in 2005? Be sure to write a sentence to interpret this answer.

d. Suppose that in 2007, 10% of all scores on this test were below 2.65 and 15% of scores were above 9.85. Show how you can use this information to find the mean and standard deviation. Assume the scores were roughly symmetric and unimodal.

e. In 2008, the mean score on this test was 8.85 and D4 was 8.43. Find the standard deviation of the scores and write a sentence to interpret the meaning of the standard deviation in the context of the problem.