Module 6: Normal Distribution
Section Exercises
Barbara Illowsky & OpenStax et al.
The Standard Normal Distribution
1. A bottle of water contains 12.05 fluid ounces with a standard deviation of 0.01 ounces. Define the random variable X in words. X = ____________.
2. A normal distribution has a mean of 61 and a standard deviation of 15. What is the median?
3. X ~ N(1, 2)
σ = _______
4. A company manufactures rubber balls. The mean diameter of a ball is 12 cm with a standard deviation of 0.2 cm. Define the random variable X in words. X = ______________.
5. X ~ N(–4, 1)
What is the median?
σ = _______
7. X ~ N(–2, 1)
μ = _______
8. What does a z-score measure?
9. What does standardizing a normal distribution do to the mean?
10. Is X ~ N(0, 1) a standardized normal distribution? Why or why not?
11. What is the z-score of x = 12, if it is two standard deviations to the right of the mean?
12. What is the z-score of x = 9, if it is 1.5 standard deviations to the left of the mean?
13. What is the z-score of x = –2, if it is 2.78 standard deviations to the right of the mean?
14. What is the z-score of x = 7, if it is 0.133 standard deviations to the left of the mean?
15. Suppose X ~ N(2, 6). What value of x has a z-score of three?
16. Suppose X ~ N(8, 1). What value of x has a z-score of –2.25?
17. Suppose X ~ N(9, 5). What value of x has a z-score of –0.5?
18. Suppose X ~ N(2, 3). What value of x has a z-score of –0.67?
19. Suppose X ~ N(4, 2). What value of x is 1.5 standard deviations to the left of the mean?
20. Suppose X ~ N(4, 2). What value of x is two standard deviations to the right of the mean?
21. Suppose X ~ N(8, 9). What value of x is 0.67 standard deviations to the left of the mean?
22. Suppose X ~ N(–1, 2). What is the z-score of x = 2?
23. Suppose X ~ N(12, 6). What is the z-score of x = 2?
24. Suppose X ~ N(9, 3). What is the z-score of x = 9?
25. Suppose a normal distribution has a mean of six and a standard deviation of 1.5. What is the z-score of x = 5.5?
26. In a normal distribution, x = 5 and z = –1.25. This tells you that x = 5 is ____ standard deviations to the ____ (right or left) of the mean.
27. In a normal distribution, x = 3 and z = 0.67. This tells you that x = 3 is ____ standard deviations to the ____ (right or left) of the mean.
28. In a normal distribution, x = –2 and z = 6. This tells you that x = –2 is ____ standard deviations to the ____ (right or left) of the mean.
29. In a normal distribution, x = –5 and z = –3.14. This tells you that x = –5 is ____ standard deviations to the ____ (right or left) of the mean.
30. In a normal distribution, x = 6 and z = –1.7. This tells you that x = 6 is ____ standard deviations to the ____ (right or left) of the mean.
31. About what percent of x values from a normal distribution lie within one standard deviation (left and right) of the mean of that distribution?
32. About what percent of the x values from a normal distribution lie within two standard deviations (left and right) of the