Exercises

Review Exercises

    1. Scores on a certain standardized test have a mean of 500, and a standard deviation of 100. How common is a score between 600 and 700?
    2. Considering a full-grown show-quality male Siberian Husky has a mean weight of 52.5 lbs, with SD of 7.5 lbs, how common are male huskies in the 37.5–45 lbs range?
    3. A population µ = 125, and σ = 25, how common are values in the 100 – 150 range?
    4. Population µ = 0.0025 and σ = 0.0005, how common are values between 0.0025 and 0.0030?
    5. A 12 oz can of soda has a mean volume of 12 oz, with a standard deviation of .25 oz. How common are cans with between 11 and 11.5 oz of soda?
    6. µ = 0.0025 and σ = 0.0005, how common are values between 0.0045 and 0.005?
    7. If a population µ = 1130 and σ = 5, how common are values between 0 and 1100?
    8. Assuming population µ = 1130 and σ = 5, how common are values between 1125 and 1135?
    9. The American Robin Redbreast has a mean weight of 77 g, with a standard deviation of 6 g. How common are Robins in the 59 g−71 g range?
    10. Population µ = 0.25% and σ = 0.05%, how common are values between 0.35% and 0.45%?
    11. Population µ = 156.5 and σ = 0.25, how common are values between 155 and 156?

    Assume all distributions to be normal or approximately normal, and calculate percentages using the 68−95−99.7 rule.

      1. Given mean 63 and standard deviation of 168, find the approximate percentage of the distribution that lies between −105 and 567.
      2. Approximately what percent of a normal distribution is between 2 standard deviations and 3 standard deviations from the mean?
      3. Given standard deviation of 74 and mean of 124, approximately what percentage of the values are greater than 198?
      4. Given σ = 39 and µ = 101, approximately what percentage of the values are less than 23?
      5. Given mean 92 and standard deviation 189, find the approximate percentage of the distribution that lies between −286 and 470.
      6. Approximately what percent of a normal distribution lies between µ + 1σ and µ + 2σ?
      7. Given standard deviation of 113 and mean 81, approximately what percentage of the values are less than −145?
      8. Given mean 23 and standard deviation 157, find the approximate percentage of the distribution that lies between 23 and 337.
      9. Given σ = 3 and µ = 84, approximately what percentage of the values are greater than 90?
      10. Approximately what percent of a normal distribution is between µ and µ+1σ?
      11. Given mean 118 and standard deviation 145, find the approximate percentage of the distribution that lies between −27 and 118.
      12. Given standard deviation of 81 and mean 67, approximately what percentage of values are greater than 310?
      13. Approximately what percent of a normal distribution is less than 2 standard deviations from the mean?
      14. Given µ + 1σ = 247 and µ + 2σ = 428, find the approximate percentage of the distribution that lies between 66 and 428.
      15. Given µ − 1σ = −131 and µ + 1σ = 233, approximately what percentage of the values are greater than −495?

The following problems are based on section 6.3 in your text.

      1. Given a distribution with a mean of 70 and standard deviation of 62, find a value with a z-score of −1.82.
      2. What does a z-score of 3.4 mean?
      3. Given a distribution with a mean of 60 and standard deviation of 98, find the z-score of 120.76.
      4. Given a distribution with a mean of 60 and standard deviation of 21, find a value with a z-score of 2.19.
      5. Find the z-score of 187.37, given a distribution with a mean of 185 and standard deviation of 1.
      6. What does a z-score of −3.8 mean?
      7. Find the z-score of 125.18, given a distribution with a mean of 101 and standard deviation of 62.
      8. Given a distribution with a mean of 117 and standard deviation of 42, find a value with a z-score of −0.94.
      9. Given a distribution with a mean of 126 and standard deviation of 100, find a value with a z-score of −0.75.
      10. Find the z-score of 264.16, given µ = 188 and σ = 64.
      11. Find a value with a z-score of −0.2, given µ = 145 and σ = 56.
      12. Find the z-score of 89.79 given µ = 10 and σ = 79.
      13. Find the probabilities, use the table from the lesson above.
      14. What is the probability of a z-score less than +2.02?
      15. What is the probability of a z-score greater than +2.02?
      16. What is the probability of a z-score less than −1.97?
      17. What is the probability of a z-score greater than −1.97?
      18. What is the probability of a z-score less than +0.09?
      19. What is the probability of a z-score less than −0.02?
      20. What is P(Z < 1.71)?
      21. What is P(Z > 2.22)?
      22. What is P(Z < −1.19)?
      23. What is P(Z > −2.71)?
      24. What is P(Z < 3.71)?
      25. What is the probability of the random occurrence of a value greater than 56 from a normally distributed population with mean 62 and standard deviation 4.5?
      26. What is the probability of a value of 329 or greater, assuming a normally distributed set with mean 290 and standard deviation 32?
      27. What is the probability of getting a value below 1.2 from the random output of a normally distributed set with µ = 2.6 and σ = .9?
      28. Find the probabilities, use the table from the lesson or an online resource.
      29. What is the probability of a z-score between +1.99 and +2.02?
      30. What is the probability of a z-score between −1.99 and +2.02?
      31. What is the probability of a z-score between −1.20 and −1.97?
      32. What is the probability of a z-score between +2.33 and −0.97?
      33. What is the probability of a z-score greater than +0.09?
      34. What is the probability of a z-score greater than −0.02?
      35. What is P(1.42 < Z < 2.01)?
      36. What is P(1.77 < Z < 2.22)?
      37. What is P(−2.33 < Z < −1.19)?
      38. What is P(−3.01 < Z < −0.71)?
      39. What is P(2.66 < Z < 3.71)?
      40. What is the probability of the random occurrence of a value between 56 and 61 from a normally distributed population with mean 62 and standard deviation 4.5?
      41. What is the probability of a value between 301 and 329, assuming a normally distributed set with mean 290 and standard deviation 32?

Attributions

This chapter contains material taken from Math in Society (on OpenTextBookStore) by David Lippman, and is used under a CC Attribution-Share Alike 3.0 United States (CC BY-SA 3.0 US) license.

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Math For Our World by Gail Poitrast is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License, except where otherwise noted.

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