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Analyzing Normal Distribution: Key Concepts and Exercises

Explore key concepts of the normal distribution including z-values, areas under the curve, probabilities, and real-world applications. Practice exercises included.

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Analyzing Normal Distribution: Key Concepts and Exercises

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  1. Chapter 6 The Normal Distribution Section 6-3 The Standard Normal Distribution

  2. Chapter 6 The Normal Distribution Section 6-3 Exercise #7

  3. 0 0.75 Find the area under the normal distribution curve.

  4. Chapter 6 The Normal Distribution Section 6-3 Exercise #15

  5. 0 0.79 1.28

  6. Chapter 6 The Normal Distribution Section 6-3 Exercise #31

  7. 0 2.83

  8. Chapter 6 The Normal Distribution Section 6-3 Exercise #45

  9. Find the z value that corresponds to the given area. 0.8962 z 0 0.8962 – 0.5 = 0.3962

  10. 0.8962 z 0 Find the z value that corresponds to the given area.

  11. Chapter 6 The Normal Distribution Section 6 - 4 Exercise #3

  12. a. Greater than 700,000. b. Between 500,000 and 600,000.

  13. 0 1.63 a. Greater than 700,000

  14. b. Between 500,000 and 600,000.

  15. – 2 .36 – 0.36 b. Between 500,000 and 600,000.

  16. Chapter 6 The Normal Distribution Section 6-4 Exercise #11

  17. The average credit card debt for college seniors is $3262. If the debt is normally distributed with a standard deviation of $1100, find these probabilities. • That the senior owes at least $1000 • That the senior owes more than $4000 • That the senior owes between • $3000 and $4000

  18. a. That the senior owes at least $1000

  19. – 2.06 a. That the senior owes at least $1000

  20. b. That the senior owes more than $4000

  21. 0.67 b. That the senior owes more than $4000

  22. c. That the senior owes between $3000 and $4000.

  23. 0.67 – 0.24 c. That the senior owes between $3000 and $4000.

  24. Chapter 6 The Normal Distribution Section 6-4 Exercise #27

  25. 0.18 0.32 $18,840.48 $24,596 The bottom 18% means that 32% of the area is between z and 0. The corresponding z score will be .

  26. Chapter 6 The Normal Distribution Section 6-5 Exercise #13

  27. $2.02 $2.00

  28. Chapter 6 The Normal Distribution Section 6-5 Exercise #21

  29. The average time it takes a group of adults to complete a certain achievement test is 46.2 minutes. The standard deviation is 8 minutes. Assume the variable is normally distributed.

  30. Average time = 46.2 minutes, Standard deviation = 8 minutes, variable is normally distributed.

  31. Average time = 46.2 minutes, Standard deviation = 8 minutes, variable is normally distributed.

  32. Average time = 46.2 minutes, Standard deviation = 8 minutes, variable is normally distributed.

  33. 43 46.2 Average time = 46.2 minutes, Standard deviation = 8 minutes, variable is normally distributed.

  34. Average time = 46.2 minutes, Standard deviation = 8 minutes, variable is normally distributed.

  35. 43 46.2 Average time = 46.2 minutes, Standard deviation = 8 minutes, variable is normally distributed.

  36. Average time = 46.2 minutes, Standard deviation = 8 minutes, variable is normally distributed. Yes, since it is within one standard deviation of the mean.

  37. Average time = 46.2 minutes, Standard deviation = 8 minutes, variable is normally distributed. It is very unlikely, since the probability would be less than 1%.

  38. Chapter 6 The Normal Distribution Section 6-5 Exercise #23

  39. The average cholesterol of a certain brand of eggs is 215 milligrams, and the standard deviation is 15 milligrams. Assume the variable is normally distributed.

  40. The average cholesterol of a certain brand of eggs is 215 milligrams, and the standard deviation is 15 milligrams. Assume the variable is normally distributed.

  41. 215 220 The average cholesterol of a certain brand of eggs is 215 milligrams, and the standard deviation is 15 milligrams. Assume the variable is normally distributed.

  42. The average cholesterol of a certain brand of eggs is 215 milligrams, and the standard deviation is 15 milligrams. Assume the variable is normally distributed.

  43. 215 220 The average cholesterol of a certain brand of eggs is 215 milligrams, and the standard deviation is 15 milligrams. Assume the variable is normally distributed.

  44. Chapter 6 The Normal Distribution Section 6-6 Exercise #5

  45. Two out of five adult smokers acquired the habit by age 14. If 400 smokers are randomly selected, find the probability that 170 or more acquired the habit by age 14.

  46. 160 169.5 Two out of five adult smokers acquired the habit by age 14. If 400 smokers are randomly selected, find the probability that 170 or more acquired the habit by age 14.

  47. Chapter 6 The Normal Distribution Section 6-6 Exercise #7

  48. The percentage of Americans 25 years or older who have at least some college education is 50.9%. In a random sample of 300 Americans 25 years and older, what is the probability that more than 175 have at least some college education?

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