You are asked to conduct a study of shelters for women who have experienced domestic violence in order to determine the necessary capacity in your city to provide housing for most of these women. After recording data for a whole year, you find that the mean number of women in shelters each night is 250, with a standard deviation of 75. Fortunately, the distribution of the number of women in shelters each night is normal, so you can answer the following questions posed by the city council.

1. If the city's shelters have a capacity of 350, will that be enough places for abused women on 95% of all nights?

No

Yes

2. What number of shelter openings will be needed?

37

75

370

250

A criminologist developed a test to measure recidivism, where low scores indicated a lower probability of repeating the undesirable behavior. The test is normed so that it has a mean of 140 and a standard deviation of 40.

3. The current capacity is only 220 openings because some of the shelters have been closed. What is the percentage of nights that the number of abused women seeking shelter will exceed current capacity?

62.21%

65.54%

34.46%

40%

4. What is the percentile rank of a score of 172?

28.81 percentile

40thpercentile

80thpercentile

78.81stpercentile

5. What percentage of scores falls between 100 and 160?

28.81%

53.28%

19.15%

34.13%

6. What is the z-score for a test score of 200?

1.50

1

0.5

-1.50

7. What proportion of respondents should score above 190?

2.753

.0125

1.250

.1056

8. Suppose an individual is in the 67th percentile in this test. What istheircorresponding recidivism score?

155.9

140

157.6

112.9

According to National Collegiate Athletic Association (NCAA) data, the means and standard deviations of eligibility and retention rates (based on a 1,000-point scale) for the 2013-2014 academic year are presented, along with the fictional scores for two basketball teams, A and B. Assume that rates are normally distributed.

9. What is the percentile rank of Team A's eligibility rate?

43.25thpercentile

36.54thpercentile

35.94thpercentile

17thpercentile

10. What proportion of the teams have retention rates below Team B?

43.25

4.325

0.4325

0.04325

11. On which criterion (eligibility or retention) did Team A do better than Team B? Calculate appropriate statistics to answer this question.

Team A has better retention and eligibility than Team B.

Team B has better retention and eligibility than Team A.

Team B has better retention,but Team A has better eligibility.

Team A has better retention,but Team B has better eligibility.