Interpreting Z-Scores printable pdf download

STA 2e: Sect. 3.2 Worksheet #1

Name __________________________

68%-95%-99.7% R

ULE

NTERPRETING Z

SCORES

If a person has a negative z-score, did the person score higher or lower than the mean? ……………

2. If a person has a negative z-score, it does not always mean that the person did not do well. Name a sport

where having the lowest z-score would be the most desirable.

………………………

For #3 – 9: The mean weight of adult American men is 180 pounds with standard deviation of 25 pounds.

The weights are approximately normally distributed. Use the 68%-95%-99.7% Rule to approximate each

of the following.

Using the values given above, label the normal curve at the right with the numerical values for µ, µ ± σ, µ ±

2σ and µ ± 3σ.

4. What percent of all adult American men have a weight less than

130 pounds?

……………

5. What percent of all adult American men have a weight between

130 and 205 pounds?

……………

6. What percent of all adult American men have a weight less than 230 pounds?

……………

7. What percent of all adult American men have a weight less than 105 pounds?

……………

8. The heaviest 16% of all men in weight weigh more than how many pounds?

……………

9. What weight separates the lowest 2.5% of all American men in weight from the remaining weights? ………

For #10 –17: Elephants have the longest pregnancy of all mammals. One species of elephant has a

mean gestation period of 525 days and standard deviation of 32 days. Pregnancy length follows an

approximately normally distribution. Use the 68%-95%-99.7% Rule to approximate each of the following.

10. Using the values given above, label the normal curve at the right with the numerical values for µ, µ ± σ, µ ±

2σ and µ ± 3σ.

11. The longest 16% of all elephant pregnancies last at least how many days?

…………

12. The middle 68% of all elephant pregnancies last between …………

and ………… days.

13. Only 2.5% of all elephant pregnancies last longer than ………… days.

14. What percent of elephant pregnancies last less than 461 days? …………

15. What percent of elephant pregnancies last between 525 and 557 days?

…………

16. What percent of elephant pregnancies last between 493 and 589 days?

…………

17. What percent of elephant pregnancies last less than 557 days?

…………

Interpreting Z-Scores

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