# Probabilities and Statistics: Normal Distributions

Show all of your work.You will need a graphing calculator (or equivalent) for this assignment.

Formulas You Can Use

invNorm (percentile, µ, σ,)

x−µ

z=

σ

Problems #1 – 11: Use the following normal

distribution:

1. What is the mean?

2. What is the standard deviation?

3. What percent of data is above 23?

4. What percent of data falls between 19 and 27?

5. What percent of data falls between 15 and 31?

6. What percent of data falls between 15 and 27?

normalcdf (lower, upper, µ, σ )

7. What percent of data is less than 19?

8. What percent of data falls between 16 and 24?

9. What is the z-score for a value of 19?

10. What is the z-score for a value of 35?

11. What is the z-score for a value of 29?

Problems #12 – 24 Choose the best option for each question:

12. What z-score is associated with being 2 standard deviations below the mean?

13. If you receive a standard score (z-score) of zero on a graded exam, what does it tell you?

14. During a statistical study that involves a normal distribution, you find the mean to be 125.6 and the standard

deviation to be 8.4. What is the z-score associated with the value 142.4?

Problems #15 – 20: Use the following scenario to answer each question

You and your friend have recently taken two different standardized mathematics exams. You scored 92 on an exam

that had a mean of 100 and a standard deviation of 10. Your friend scored 333 on an exam that had a mean of 350 and

a standard deviation of 20.

15. Calculate your z-score.

16. Calculate your friend’s z-score.

17. Who’s test score was better?

18. What score is one standard deviation above the mean for your test?

19. What percent of students scored between 91 and 123 on your test?

20. What percent of students score higher than a grade that has a z-score equal to one?

Problems #21-22: Use the following set of data:

2, 3, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 8, 9

21. Find the mean for the data.

22. Find the standard deviation for the data.

Problems #23-24: Continue to answer each of the following questions …

23. Suppose adult Chinese women have heights that are normally distributed with a mean of 155 centimeters and a

standard deviation of 8 centimeters. Also suppose that adult Japanese women have heights that are normally

distributed with a mean of 158 centimeters and a standard deviation of 6 centimeters. Which country has a

higher percentage of women at least 167 centimeters tall?

24. Suppose the number of games played by a major league baseball player in their career is normally distributed

with a mean of 1,500 games and a standard deviation of 350 games. What percent of players play in fewer than

750 games in their career?

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