Statistics How To

Normal Probability Practice Problems and Answers

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These normal probability practice problems will help you practice calculating z-scores and using the z-table.

normal probability practice problems

General steps for solving normal probability practice problems:

  1. Use the equation above to find a z-score. If you don’t know how to look up z-scores (or if you want more practice, see this z-score article for videos and step-by-step instructions.
  2. Look up the z-score in the z-table and find the area.
  3. Convert the area to a percentage.

If you more need help with these steps, see the normal distribution word problems index, which outlines the steps in detail (with videos).

Normal Probability Practice Problems.

Click on the question for the answer!

1. Scores on a particular test are normally distributed with a standard deviation of 4 and a mean of 30. What is the probability of anyone scoring less than 40?

2. Annual salaries for a large company are approximately normally distributed with a mean of $50,000 and a of $20,000. What percentage of company workers may under $40,000?

3. IQ scores have a normal distribution with a mean of 100 and a standard deviation of 15. What percent of people have an IQ above 120?

4. The amount of time a student taking statistics spends on studying for a test is normally distributed. If the average time spent studying is 12 hours and the standard deviation is 4 hours, what is the probability that a student will spend more than 8 hours studying?

5. The amount of candy dispensed by a candy machine is normally distributed with a mean of 0.9 oz and a standard deviation of 0.1 ounces. If the machine is used 500 times, how many times will it dispense more than 1 oz of candy?

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If you prefer an online interactive environment to learn R and statistics, this free R Tutorial by Datacamp is a great way to get started. If you're are somewhat comfortable with R and are interested in going deeper into Statistics, try this Statistics with R track.

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Normal Probability Practice Problems and Answers was last modified: October 12th, 2017 by Stephanie

6 thoughts on “Normal Probability Practice Problems and Answers

  1. Lance R.

    About question 5, the probability associated with the Z score of 1 is 0.84, and we’re looking for the chance of the machine dispensing greater than 1oz candy. Shouldn’t we take 1-0.84 and multiply that probability to obtain an expected number of candy>1oz?

    I’m confused about the solution provided for this problem. Hope you can clarify.

  2. Andale Post author

    You are completely right. A step was missing from the end. That is now fixed.

  3. Derek Brooks

    Number 3’s answer is incorrect. If we want above 120, you need to subtract .9082 from 1. The answer should be .0918 or 9.18%. Same logic for problem 4. We want more than 8 hours of studying. Subtract .1587 from 1. The answer is 84%.

  4. Andale Post author

    Hi, Derek,
    Thanks for commenting. I’m actually seeing those as the correct answers (for example, the solution shows for q3 is .9.18%. ) — not sure where you are seeing different numbers?