Normal Probability

1. For any continuous random variable, the probability that the random variable takes on exactly a specific value is
a. 1.00
b. 0.50
c. any value between 0 to 1
d. zero

2. A normal probability distribution
a. is a continuous probability distribution
b. is a discrete probability distribution
c. can be either continuous or discrete
d. must have a standard deviation of 1

3. If the mean of a normal distribution is negative,
a. the standard deviation must also be negative
b. the variance must also be negative
c. a mistake has been made in the computations, because the mean of a normal distribution can not be negative
d None of these alternatives is correct.

4. The highest point of a normal curve occurs at
a. one standard deviation to the right of the mean
b. two standard deviations to the right of the mean
c. approximately three standard deviations to the right of the mean
d. the mean

5. The ages of students at a university are normally distributed with a mean of 21. What percentage of the student body is at least 21 years old?
a. It could be any value, depending on the magnitude of the standard deviation
b. 50%
c. 21%
d. 1.96%

6. Larger values of the standard deviation result in a normal curve that is
a. shifted to the right
b. shifted to the left
c. narrower and more peaked
d. wider and flatter

The Standard Normal Probability Distribution

7. A standard normal distribution is a normal distribution
a. with a mean of 1 and a standard deviation of 0
b. with a mean of 0 and a standard deviation of 1
c. with any mean and a standard deviation of 1
d. with any mean and any standard deviation

8. In a standard normal distribution, practically the entire range of values of z is from
a. -2 to 2
b. -1 to 1
c. 0 to 1
d. -3.09 to 3.09

9. What value of Z is the mean of the SND? ___________

10. What is the area under the curve of the standard normal distribution? ___________

11. What does this represent?

12. What is the area under the right half of the standard normal distribution?_______________

13. What is the area between +1 and -1 Z? ________

14. +2 and -2? ________
`
15. +3 and -3? ________

16. For a normal distribution, a negative value of z indicates
a. a mistake has been made in computations, because z is always positive
b. the area corresponding to the z is negative
c. the z is to the left of the mean
d. the z is to the right of the mean

Z to Probability

17. Z is a standard normal random variable. The P (1.20 ≤ Z ≤ 1.85) equals
a. 0.4678
b. 0.3849
c. 0.8527
d. 0.0829

18. Z is a standard normal random variable. The P(Z > 2.11) equals
a. 0.4821
b. 0.9821
c. 0.5
d. 0.0174

19. For a standard normal distribution, the probability of obtaining a z value of less than 1.6 is
a. 0.1600
b. 0.0160
c. 0.0016
d. 0.9452

Probability to Z

20. Z is a standard normal random variable. What is the value of Z if the area to the right of Z is 0.1112?
a. 0.3888
b. 1.22
c. 2.22
d. 3.22

21. Z is a standard normal random variable. What is the value of Z if the area to the right of Z is 0.9803?
a. -2.06
b. 0.4803
c. 0.0997
d. 3.06

22. Z is a standard normal random variable. What is the value of Z if the area between -Z and Z is 0.754?
a. 0.377
b. 0.123
c. 2.16
d. 1.16

X to Probability

23. X is a normally distributed random variable with a mean of 12 and a standard deviation of 3. The probability that X equals 19.62 is
a. 0.000
b. 0.0055
c. 0.4945
d. 0.9945

24. X is a normally distributed random variable with a mean of 8 and a standard deviation of 4. The probability that X is between 1.48 and 15.56 is
a. 0.0222
b. 0.4190
c. 0.5222
d. 0.9190

25. X is a normally distributed random variable with a mean of 5 and a variance of 4. The probability that X is greater than 10.52 is
a. 0.0029
b. 0.0838
c. 0.4971
d. 0.9971

Problems (Use the template. No work = No credit)

1. The price of personal computers manufactured by MNM Company are normally distributed with a mean of $1,200 and a standard deviation of $220.

a. What is the probability that a randomly selected computer will have a price of at least $1,530?

b. If 513 of the MNM computers were priced at or below $647.80, how many computers were produced by MNM?

2. A professor at a local university noted that the grades of her students were normally distributed with a mean of 73 and a standard deviation of 11.

a. The professor has informed us that 7.93 percent of her students received grades of A. What is the minimum score needed to receive a grade of A?

b. Students who made 57.93 or lower on the exam failed the course. What percent of students failed the course?

3. The starting salaries of this year's MBA students are normally distributed with a mean of $35,000 and a standard deviation of $5,000. What are the minimum and the maximum starting salaries of the middle 95% of MBA graduates?

4. "DRUGS R US" is a large manufacturer of various kinds of liquid vitamins. The quality control department has noted that the bottles of vitamins marked 6 ounces vary in content with a standard deviation of 0.3 ounces. Assume the contents of the bottles are normally distributed.

a. What percentage of all bottles produced contains less than 5.415 ounces?

b. Ninety-five percent of the bottles will contain at least how many ounces?