CHAPTER 6: Z-SCORES
Exercise 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 =____________.
Solution ounces of water in a bottle
Exercise 2. A normal distribution has a mean of 61 and a standard deviation of 15. What is the
median?
Solution 61
Exercise 3. X ~ N(1,2)
σ =_______
Solution 2
Exercise 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
=______________.
Solution diameter of a rubber ball
Exercise 5. X ~ N(-4,1).
What is the median?
Solution -4
Exercise 6. X ~ N(3,5).
σ =_______
,Solution 5
Exercise 7. X ~ N(-2,1)
μ =______
Solution –2
Exercise 8. What does a z-score measure?
Solution the number of standard deviations a value is from the mean
Exercise 9. What does standardizing a normal distribution do to the mean?
Solution The mean becomes zero.
Exercise 10. Is X ~ N(0,1) a standardized normal distribution? Why or why not?
Solution Yes, because the mean is zero and the standard deviation is one.
Exercise 11. What is the z-score of x = 12, if it is two standard deviations to the right of the
mean?
Solution z=2
Exercise 12. What is the z-score of x = 9, if it is 1.5 standard deviations to the left of the mean?
Solution z = -1.5
Exercise 13. What is the z-score of x = -2, if it is 2.78 standard deviations to the right of the
mean?
Solution z = 2.78
, Exercise 14. What is the z-score of x = 7, if it is 0.133 standard deviations to the left of the mean?
Solution z = -0.133
Exercise 15. Suppose X ~ N(2, 6). What value of x has a z-score of three?
Solution x = 20
Exercise 16. Suppose X ~ N(8, 1). What value of x has a z-score of -2.25?
Solution x = 5.75
Exercise 17. Suppose X ~ N(9, 5). What value of x has a z-score of -0.5?
Solution x = 6.5
Exercise 18. Suppose X ~ N(2, 3). What value of x has a z-score of -0.67 ?
Solution x = -0.01
Exercise 19. Suppose X ~ N(4, 2). What value of x is 1.5 standard deviations to the left of the
mean?
Solution x=1
Exercise 20. Suppose X ~ N(4, 2). What value of x is two standard deviations to the right of the
mean?
Solution x=8
Exercise 21. Suppose X ~ N(8, 9). What value of x is 0.67 standard deviations to the left of the
mean?
Solution x = 1.97
Exercise 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 =____________.
Solution ounces of water in a bottle
Exercise 2. A normal distribution has a mean of 61 and a standard deviation of 15. What is the
median?
Solution 61
Exercise 3. X ~ N(1,2)
σ =_______
Solution 2
Exercise 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
=______________.
Solution diameter of a rubber ball
Exercise 5. X ~ N(-4,1).
What is the median?
Solution -4
Exercise 6. X ~ N(3,5).
σ =_______
,Solution 5
Exercise 7. X ~ N(-2,1)
μ =______
Solution –2
Exercise 8. What does a z-score measure?
Solution the number of standard deviations a value is from the mean
Exercise 9. What does standardizing a normal distribution do to the mean?
Solution The mean becomes zero.
Exercise 10. Is X ~ N(0,1) a standardized normal distribution? Why or why not?
Solution Yes, because the mean is zero and the standard deviation is one.
Exercise 11. What is the z-score of x = 12, if it is two standard deviations to the right of the
mean?
Solution z=2
Exercise 12. What is the z-score of x = 9, if it is 1.5 standard deviations to the left of the mean?
Solution z = -1.5
Exercise 13. What is the z-score of x = -2, if it is 2.78 standard deviations to the right of the
mean?
Solution z = 2.78
, Exercise 14. What is the z-score of x = 7, if it is 0.133 standard deviations to the left of the mean?
Solution z = -0.133
Exercise 15. Suppose X ~ N(2, 6). What value of x has a z-score of three?
Solution x = 20
Exercise 16. Suppose X ~ N(8, 1). What value of x has a z-score of -2.25?
Solution x = 5.75
Exercise 17. Suppose X ~ N(9, 5). What value of x has a z-score of -0.5?
Solution x = 6.5
Exercise 18. Suppose X ~ N(2, 3). What value of x has a z-score of -0.67 ?
Solution x = -0.01
Exercise 19. Suppose X ~ N(4, 2). What value of x is 1.5 standard deviations to the left of the
mean?
Solution x=1
Exercise 20. Suppose X ~ N(4, 2). What value of x is two standard deviations to the right of the
mean?
Solution x=8
Exercise 21. Suppose X ~ N(8, 9). What value of x is 0.67 standard deviations to the left of the
mean?
Solution x = 1.97
