# Normal Probability Practice Problems and Answers

Probability and Statistics > Probability > Normal Probability Practice Problems

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

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?

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.

# 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

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

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?