Normal Distribution Practice

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.

3. 
   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?
4. 
   Yes
5. 
   No
6. 
   Question 2
   2 Points
   What number of shelter openings will be needed?
7. 
   250
8. 
   370
9. 
   75
10. 
    374

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?

1. 
   62.21%
2. 
   65.54%
3. 
   34.46%
4. 
   40%
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. 
   78.81st percentile
8. 
   80th percentile
9. 
   40th percentile
10. 
    28.81th percentile
11. 
    Question 5
    2 Points
    What is the z-score for a test score of 200?