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. 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? Yes No Question 2 2 Points What number of shelter openings will be needed? 250 370 75 374 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? 62.21% 65.54% 34.46% 40% 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. Question 4 2 Points What is the percentile rank of a score of 172? 78.81st percentile 80th percentile 40th percentile 28.81th percentile Question 5 2 Points What is the z-score for a test score of 200? -1.50 0.5 1 1.50 Question 6 2 Points What percentage of scores falls between 100 and 160? 28.81% 53.28% 19.15% 34.13% Question 7 2 Points What proportion of respondents should score above 190? 0.5 1 1.50 1.25 Question 8 1.5 Points Suppose an individual is in the 67th percentile in this test. What is his or her corresponding 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.Normal Distribution Practice data 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. 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. Question 10 1.5 Points What proportion of the teams have retention rates below Team B? 43.25 4.325 0.4325 0.04325 Question 11 1.5 Points What is the percentile rank of Team A’s eligibility rate? 43.25th percentile 36.54th percentile 35.94th percentile 17th percentile

It is required to complete a real-world application project. attached file.Choose either problem 46 or problem 48 on page 250. For the problem you choose, answer the following, showing your calculations: (a) Determine the vertex and interpret the meaning of (h, k) in the problem situation. (6pts) (b) Determine the x- and y-intercepts of the function. Interpret the meaning of each in the problem situation. Are all intercepts meaningful to the given problem? Explain. (6pts) (c) Many real-world applications have a restricted domain and range. Determine an appropriate domain and range for the problem you chose.