Homework Assignment #6 (Chapter 13) Autumn 2018

1. A number with 30% of the data above it is
2. at the 30th percentile.
3. at the 70th percentile.
4. always bigger than the mean.
5. always smaller than the mean.
6. The scores on a history exam are Normally distributed with a mean of 48 points and a standard deviation of 6 points. If the instructor wishes to assign A's to thestudents who obtain exam scores in the top 10% of the distribution, approximately what is the minimum score required to get an A?
7. A. 48.6 B. 53.4 C. 55.8 D. 64.5 E. 108.3
8. The mean length of time, per week, that students at a certain school spend on their homework is Normally distributed with a mean of 25 hours and a standard deviation of 1.32 hours. If Sean is at Q3in this distribution, this means that Sean spends approximately ___________ hours per week on his homework.
9. A. 28.96 B. 27.64 C. 26.32 D. 25.92 E. 24.08
10. The length of students' college careers at a particular university is known to be Normally distributed, with a mean length of 5.5 years and a standard deviation of 1.75 years. Approximately 84% of the students in this distribution have college careers that last less than
11. A. 5.5 years B. 6.75 years C. 7.25 years D. 8.12 years E. 9 years
12. In Mille Lacs Lake, walleye fish are abundant. The lengths of walleyes follow a Normal distribution with a mean of 31 inches and a standard deviation of 3.6 inches. Based on this information, which of the following statements is true?
13. Approximately 32% of walleyes have lengths longer than 34.6 inches.
14. Approximately 95% of walleyes have lengths smaller than 38.2 inches.
15. Approximately 16% of walleyes have lengths longer than 38.2 inches.
16. Approximately 5% of walleyes have lengths smaller than 23.8 inches.
17. Approximately 16% of walleyes have lengths smaller than 27.4 inches.
18. Scores on the American College Testing (ACT) college entrance exam follow a Normal distribution with a mean of 18 and a standard deviation 6. Miguel's standard score on theACT was 2.1. What percentage of individuals who took this exam had scores that werehigher than Miguel's score?
19. A. 1.79% B. 2.1% C. 21.19% D. 86.43% E. 98.21%
20. Lengths of human pregnancies are Normally distributed with a mean of 266 days and astandard deviation of 16 days. When the length of Lauren's pregnancy was converted to az- score, it is found that z = 0. Based on this information, which of the following is a false statement?
21. Lauren's length of pregnancy was 266 days.
22. Lauren's length of pregnancy was equal to the median of the distribution.
23. A calculation error was obviously made because z-scores can never equal 0.
24. D.Lauren's pregnancyis at the 50thpercentile.
25. The distribution of heights of adult women is Normal, with a mean of 65 inches and a standard deviation of 3.5 inches.Sarah'sheight has a z-score of 0.5 when compared to all adult women in this distribution. What does this z-score tell us about how Sarah compares to other adult women in terms of height?
26. Sarah's height is below the mean.
27. Sarah is more than one standard deviation away from the mean.
28. Sarah is 66.75 inches tall.
29. All of the above are true statements.
30. The weight losses for participants in a large exercise and diet study vary according to a Normal distribution with mean 14.5 pounds and standard deviation 3 pounds. Approximately what percentage of the participants lose more than 19 pounds?
31. A. 3.5% B. 6.68% C. 15%
32. D. 69.15% E. 93.32%
33. The weight losses for participants in a large exercise and diet study vary according to a Normal distribution with mean 14.5 pounds and standard deviation 3 pounds. Approximately what percentage of the participants lose between 11.5 pounds and 20.5 pounds?
34. A. 2.5% B. 16% C. 70.5% D. 81.5% E. 95%