# Stat – Mult Choice – Normal Distribution Practice

I don’t know how to handle this Statistics question and need guidance.

1. 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.

2. Question 1

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

3. Question 2

2 Points
What number of shelter openings will be needed?

4. Question 3

2 Points
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?

5. 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.

6. Question 4

2 Points
What is the percentile rank of a score of 172?

7. Question 5

2 Points
What is the z-score for a test score of 200?

8. Question 6

2 Points
What percentage of scores falls between 100 and 160?

9. Question 7

2 Points
What proportion of respondents should score above 190?

10. Question 8

1.5 Points
Suppose an individual is in the 67th percentile in this test. What is his or her corresponding recidivism score?

11. 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.

Normal Distribution Practice data

12. Question 9

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

13. Question 10

1.5 Points
What proportion of the teams have retention rates below Team B?

14. Question 11

1.5 Points
What is the percentile rank of Team A’s eligibility rate?