Q1-Q7. One type of cholesterol is called low-density lipoprotein cholesterol (LDL, also called the "bad" cholesterol). Adults should check their cholesterol levels at least every 5 years. The lower the LDL cholesterol is, the healthier the person is. Suppose the LDL cholesterol scores in men follow a normal distribution N( = 140, = 32).

1. If an LDL level below 160 is considered as acceptable, what percent of men have an acceptable cholesterol level?

2. If an LDL level above 190 is considered as dangerous, what percent of men have a dangerous cholesterol level?

3. If an LDL level between 160 and 190 means the man should start taking preventive actions, what percent of men need preventive actions?

4. An LDL level below 100 is considered as optimal. If we randomly pick a man from the general public, what is the probability that this man has an optimal cholesterol level?

5. If an LDL level below 115 is considered as healthy, what percent of men have a no-so-healthy cholesterol level (that is, above 115)?

6. If we randomly pick a man from the general public, what is the probability that this man's LDL score is below 90?

7. If we randomly pick a man from the general public, what is the probablity that this man's LDL score is below 100 or above 180? Note: the answer is the total of the two areas of interest

Q8-Q14 are based on the following facts.

ACT scores follow N(20.8, 4.8).

SAT scores follow N(500, 110).

8. Joe'stook SAT and his score is on the 74th percentile. What is Joe's SAT score?

9. Amy took SAT and her score is on the 30th percentile. What is Amy's SAT score?

10. Jack's SAT score is 380. Jack is on the _________ percentile.

11. If we draw the two normal curves in the same figure, what would the two curves look like?

(A) ACT's curve is flatter and wider; SAT's curve is taller and narrower

(B) SAT's curve is flatter and wider; ACT's curve is taller and narrower

(C) ACT's curve is on the left; SAT's curve is on the right

(D) SAT's curve is on the left; ACT's curve is on the right

(E) B and C

(F) A and D

12. Tom took ACT and he did better than 75% of other ACT test takers. Which of the following is correct?

(A) Tom's ACT score is about 22.1.

(B) Tom is on the 25th percentile.

(C) Tom's z-score is 0.75.

(D) If Tom took SAT instead, he should have got about 574.

(E) Tom's z-score is 0.25.

13. What is the median of ACT scores in the population?

14. What is the mode of SAT scores in the population?

15. Because normal distribution is symmetric, _____________

(A) scores above the mean are distributed the same as scores below the mean.

(B) extreme scores are less likely to appear.

(C) there are infinitely many normal distributions.

(D) all of the above

16. For a normal distribution N(, ), the mean can take on any value and the standard deviation can take on any positive value. Therefore,

(A) normal distribution is also called standard normal distribution

(B) N(2, 5) and N(3, 6) are two different normal distributions

(C) there are an infinite number of possible normal distributions

(D) in some situations data may approximately follow N(-5, -2)

(E) B and C only

(F) all of the above

17. Knowing that data follow a normal distribution allows us to

(A) calculate the probability of obtaining a score greater than some specified value.

(B) understand how data points in the population ended up being in my sample

(C) calculate what range of values are likely or unlikely to occur

(D) all of the above

18. Assume that your class (a very large class) took an exam last week. The exam scores have a mean of 85 and standard deviation of 5. Your instructor told you that 30% of the students had a score of 90 or above.Which of the following is most likely to be correct?

(A) 50% of the scores are below 85.

(B) 20% of the students have scores between 85 and 90.

(C) The scores do not follow a normal distribution.

(D) Such a set of scores cannot appear in reality.

19. Suppose for all the sales managers in this country, their salaries have a mean of 135,000 and a standard deviation of 20,000. What % of sales managers have a salary of 155,000 or higher?

(A) 16%

(B) 15.87%

(C) 34.13%

(D) 68%

(E) there is not enough information

20. Let us use W to denote people's weight. Suppose for all the UCM students, W ~ N(150, 20). We then calculate the Z-score for each UCM student, and thus we have a new data set about the Z-scores of all the UCM students. What is the distribution of those Z-scores?

(A) N(150, 20)

(B) N(0, 1)

(C) will be a normal distribution, but mean and standard deviation are unknown

(D) N(-3, 3)

(E) the z-scores will not follow a normal distribution