Download 11) unit 3 review - Wando High School

Unit 3 Review
CP Probability and Statistics
Name ______________________________
1. The army reports that the distribution of head circumference among male soldiers is
approximately normal with a mean of 22.8 inches and a standard deviation of 1.1
inches. Find the following:
a. What percent of soldiers have head circumferences greater than 23.9 inches?
b. What percent of soldiers have head circumferences between 21.7 inches and 23.9
inches?
2. The length of human pregnancies form conception to birth varies according to a
distribution that is approximately normal with a mean of 266 days and a standard
deviation of 16 days. Find the following:
a. Between what values do the lengths of the middle 95% of all pregnancies fall?
b. What percent of all pregnancies last less than 250 days?
c. What percent of all pregnancies last between 234 days and 266 days?
d. What percent of all pregnancies last less than 250 days or more than 298 days?
Use your calculator to solve each of the following problems.
3. a. P ( z > 2.3)
b. P ( z < -1.5)
c. P ( z < 0)
d. P ( -1.2 < z < 1.15)
e. P ( 1.3 < z < 2.8)
f. P ( -2.7 < z < -1.8)
Use your calculator to solve each of the following problems. Shade in the
appropriate area on the normal curve provided.
4. The distribution of heights of adult American men is approximately normal with a
mean of 69 inches and a standard deviation of 2.5 inches.
a. What percent of men are at least 72 inches tall?
b. What percent of men are between 60 inches and 72 inches?
c. How tall must a man be to be in the tallest 10% of all men?
d. What are the heights of men associated with the middle 50% of all men?
5. Scores on a standard IQ test are approximately normal with a mean of 110 and a
standard deviation of 25.
a. What percent of people have IQ scores above 100?
b. What percent of people have scores between 95 and 120?
c. What scores are associated with the middle 70% of all people?
6. The scores of students on the ACT college entrance exam in a recent year had the
normal distribution with a mean of 18.6 and a standard deviation of 5.9.
a. What is the probability that a single student randomly chosen from all those
taking the test will be 21 or higher?
b. What is the probability that the mean score of these students is lower than 16.2?
7. A bottling company uses a filling machine to fill plastic bottles with cola. The bottles
are supposed to contain 300 milliliters. In fact, the contents vary according to a
normal distribution with mean 296 mL and standard deviation 4 mL.
a. What is the probability that an individual bottle contains less than 292 ml?
b. What is the probability that the mean contents of a bottle are less than 300 mL?
8. On average a test takes 80 minutes to complete with standard deviation of 10 minutes.
a. What is probability the someone will take 90 or more minutes to complete the test.
b. What is the probability that someone will take between 70 and 100 minutes?