Posted: March 9th, 2017

# For a standard normal distribution, what is the value of the standard deviation and the mean? 4. What is the area under a standard normal curve between z = 2:21 and z = 1:27?

. True or False? The normal distribution is the most important discrete probability distribution.
2. True or False? Every normal distribution can be transformed to a standard normal
distribution.
3. For a standard normal distribution, what is the value of the standard deviation and the mean?
4. What is the area under a standard normal curve between z = 2:21 and z = 1:27?
5. What is the area under a standard normal curve to the left of z = 1:95?
6. What is the area under a standard normal curve between z = 2 and z = 2?
7. The probability that z lies between a and b is denoted P(a < z < b). Using a standard normal
curve, what is P(1:09 < z < 2:35)?
8. SAT Math Scores: Suppose the population of SAT math scores follows a normal distribution.
Suppose = 574 and = 156. What is P(600 < x < 685)?
Use the Information below to answer questions 9-11.
Beagles: The weights of a group of adult male beagles are normally distributed, with a mean
of 22:5 pounds and a standard deviation of 3:7 pounds. A beagle is randomly selected.
9. Find the probability that the beagle’s weight is less than 20 pounds.
10. Find the probability that the beagle’s weight is between 18 and 23 pounds.
11. Find the probability that the beagle’s weight is more than 25 pounds.
The following directions apply to problems 12 and 13.
Use the Standard Normal Distribution Table to find the z-score that corresponds to the
given cumulative area. If the area is not in the table, use the entry closest to the area.
If the area is halfway between two entries, use the z-score halfway between the corresponding z-scores.
12. Area = 0:9678
13. Area = 0:1220
14. Find the z-score that has 69:5% of the distribution’s area to its right.
Use the following information to answer questions 15 and 16.
A population with n = 744 has a mean = 279 and a standard deviation = 53.
15. Find the mean of the sampling distribution of the sample means.
16. Find the standard deviation of the sampling distribution of the sample means.
17. True or False? As the standard deviation increases, the standard deviation of the distribution
of sample means increases.
Use the following information to answer questions 18 and 19.
Finding Probabilities For a sample with n = 49, = 132 and = 35.
18. What is P(x < 125)?
19. Would it be considered unusual if x < 125?
20. Salaries: The population mean annual salary for employees at a software ?rm is \$77; 000. A
random sample of 45 employees is selected from this population. What is the probability that
the mean annual salary of the sample is greater than \$79; 000. Assume = \$6300.
21. Would it be unusual for a randomly selected employee to have a salary greater than \$79,000?
Use the following information to answer question 1 – 4.
Lengths of Fish You are performing a study about the lengths of ?sh in a mountain lake. A previous
study found the lengths to be normally distributed, with a mean of 20 inches and a standard deviation
of 4.0 inches. You randomly sample 30 ?sh and ?nd their lengths (in inches) are as follows.
19 17 23 20 20 13 17 19 22 18
14 18 19 15 23 21 26 19 16 19
21 16 10 13 25 25 12 21 24 28
1. Draw a frequency histogram to display the data using 7 classes
2. Is it reasonable to assume the heights are normally distributed? Why?
3. Find the mean and standard deviation of your sample.
4. Compare the mean and standard deviation of your sample with those in the previous study.
5. Using the standard normal distribution, ?nd the probability. P(z > 1:05).
6. Using the standard normal distribution, ?nd the probability. P(1:45 < z < 1:17).
Section 5.2
above.
Health Club Schedule The time per workout an athlete uses a stair climber is normally distributed, with a mean of 25 minutes and a standard deviation of 6 minutes. An athlete is
randomly selected.
7. Find the probability that the athlete uses a stair climber for less than 17 minutes.
8. Find the probability that the athlete uses a stair climber between 20 and 28 minutes.
9. Find the probability that the athlete uses a stair climber for more than 30 minutes.
Use the following information to answer questions 10-11.
Utility Bills Utility are normally distributed with a mean equal to \$130 and a standard deviation of \$15.
10. What percent of the utility bills are more than \$140?
11. If 300 utility bills are randomly selected, about how many would you expect to be less than
\$115?
Use the following information to answer questions 12-13.
Peanuts: Assume the mean annual consumption of peanuts is normally distributed, with a
mean of 4.8 pounds per person and a standard deviation of 1.6 pounds per person.
12. What percent of people annually consume less than 3.5 pounds of peanuts person?
13. Would it be unusual for a person to consume less than 3.5 pounds of peanuts in a year?
Explain.
14. Find the z-score for which 94% of the standard normal distribution’s area lies between z and
z.
Use the following information to answer questions 15-16.
Heights of Men: In a study of men at a college (ages 20-29), the mean height was 70.9 inches
with a standard deviation of 3.5 inches.
15. What height represents the 90th percentile? (Note: Percentiles were discussed in the text in
the same section as quartiles.)
16. What height represents the third quartile?
Use the following information to answer questions 17-19.
Brake Pads: A brake pad manufacturer claims its brake pads will last for an average of 40,000
miles. You work for a consumer protection agency and you are testing the manufacturer’s
brake pads. Assume the life spans of the brake pads are normally distributed. You randomly
select 50 brake pads. In your tests, the mean life for the brake pads is 38,850 miles. Assume
= 900 miles.
17. Assuming the manufacturer’s claim is correct, what is the probability the mean of the sample
is 38,850 or less?