Q1-Q3 are based on a data set with a mean of 80 and a standard deviation of 10.

Questions in this HW has margin of error in their answer key (when needed), so rounding differences will not be a problem.

1. For the above data set, what's the z-score for X=65?

2. For the above data set, what's the z-score for X=96?

3. For the above data set, what'sthe z-score for X=80?

4. A data set has a mean of 44. In this data set, a raw score X=40 corresponds to the standardized score z = -1. What is the standard deviation for this data set?

5. A data set has a standard deviation of 2.5. In this data set, a raw score X=30 corresponds to the standardized score z = 1.30. What is the mean of this data set?

Hint: take advantage of the formula for Z-score

6. A data set has a standard deviation of 5. In this data set, a raw score of X=10 corresponds to the standardized score z = -2.40 (note negative value). What is the mean of this data set?

7. We consider the following data set as a population. What is the population standard deviation? Take your answer to 2 decimals.

{8, 6, 3, 9, 4}

8. True of False: A standardized score z=0 indicates that the raw score X is 0.

Group of answer choices

True

False

Suppose the scores of a certain certain high school diploma test follow a normal distribution in the population with a mean of 195 and standard deviation of 30.

Using the 68-95-99 rule, answer Questions 9-16.

9. About ______ percent of the students have a score between 165 and 225.

Note: If your answer is 12.3%, then just put "12.3" in the blank. Use the same format for the rest of the questions.

10. About ______ percent of the students have a score below 195.

11. About ______ percent of the students have a score below 225.

12. About ______ percent of the students have a score that is eitherbelow 135 or above 255.

13. About ______ percent of the students have a score above 255.

14. About ______ percent of the students have a score between 135 and 195.

15. About ______ percent of the students have a score between 225 and 255.

16. The middle 95% of the students have a score between ________ and ________ .

17. Recently, class A had a Math exam, but class B had a Verbal exam.

• Joe in class A has a math score of 160. The math scores in class A have =140 and =10.
• Eric in class B has a verbal score of 80. The verbal scores in class B have =50 and =12.

Suppose students in classes A and B have very similar academic background. Further suppose that both classes are huge and we can consider the 2 data sets as 2 populations.

Which of the following statements is correct?

Group of answer choices

(A) Joe outperformed Eric

(B) Eric outperformed Joe

(C) About 97.5% of the students in Class A had a math score lower than Eric's score 160

(D) About 50% of the students in Class B had a verbal score lower than the mean 50

18. A sample consists of 26 scores. What is the degrees of freedom for the sample standard deviation?

19. For the following sample of scores, the sample variance is _______. {7, 2, 4, 6, 4, 7, 3, 7}

20. Suppose the lives (in hours) of a certain type of light bulbs follow a normal distribution with mean 2000 and standard deviation 400. If we randomly pick a light bulb from the factory's production line, what is the probability that the light bulb's life is exactly 2000?