1. We discovered that 1,014 GSS 2018 respondents watched television for an average of 2.97 hours perday, with a standard deviation of 3.00 hours. Answer the following questions assuming the distributionof the number of television hours is normal.

a. What is the Z score for a person who watches 8 hours per day? b. What proportion of people watch television more than 5 hours per day? How many respondents does this correspond to in the sample? c. What number of television hours per day corresponds to a Z score of +1? d. What is the percentage of people who watch between 1 and 5 hours of television per day?

2. You are asked to do a study of shelters for abused and battered women to determine the necessarycapacity 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 the shelters each night is normal, so cananswer the following questions posed by the city council:

a. If the city's shelters have a capacity of 350, will that be enough places for abused women on 95% of all nights? If not, what number of shelter openings will be needed? b. The current capacity is only 220 openings, because some shelters have been closed due to the spread of COVID-19. What is the percentage of nights that the number of abused women seeking shelter will exceed current capacity?

3. 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 astandard deviation of 40. a. What proportion of scores are above 100? b. What is the Z score for a test score of 200? c. What percentage of scores falls between 100 and 160?