1. value: 10.00 points It is claimed that Proactine, a new medicine for acne, is 75 percent effective. It is applied to the affected area of a group of 15 people. Calculate the probability for the following (Round your answers to 3 decimal places): (a) All 15 will show significant improvement Probability (b) Fewer than 9 of 15 will show significant improvement Probability (c) That 12 or more people will show significant improvement Probability 2. value: 10.00 points A study of the attendance at the University of Alabama's basketball games revealed that the distribution of attendance is normally distributed with a mean of 9,600 and a standard deviation of 1,800. (a) What is the probability a particular game has an attendance of 13,500 or more? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) Probability (b) What percent of the games have an attendance between 8,000 and 11,500? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) Probability (c) Ten percent of the games have an attendance of how many or less? Attendance 3. value: 10.00 points The distribution of the number of school-age children per family in the Whitehall Estates area of Boise, Idaho, is: Number of children Percent of families 0 25 1 30 2 40 3 3 4 2 (a) Determine the mean and standard deviation of the number of school-age children per family in Whitehall Estates. (Round your answers to 2 decimal places.) Mean Standard deviation (b) A new school is planned in Whitehall Estates. An estimate of the number of school-age children is needed. There are 500 family units. How many children would you estimate? Children Some additional information is needed about only the families having children. (c-1) Convert the preceding distribution to one for families with children. (Round your answers to 5 decimal places.) Number of Children (X) 1 2 3 4 Probability given Children P(X) (c-2) What is the mean number of children among families that have children? (Round your answer to 2 decimal places.) Mean 4. value: 10.00 points First National Bank thoroughly investigates its applicants for small home-improvement loans. Its default record is very impressive: The probability that a homeowner will default is only .005. The bank has approved 400 small home-improvement loans. Assuming the Poisson probability distribution applies to this problem: (a) What is the probability that no homeowners out of the 400 will default? (Round your answer to 4 decimal places.) Probability (b) How many of the 400 are expected not to default? Expected value (c) What is the probability that 3 or more homeowners will default on their small home-improvement loans?(Round your answer to 4 decimal places.) Probability 5. value: 10.00 points Daniel-James Insurance Company will insure an offshore Mobil Oil production platform against weather losses for one year. The president of Daniel-James estimates the following losses for that platform (in millions of dollars) with the accompanying probabilities: Amount of Loss ($ millions) 0 40 300 Probability of Loss .98 .016 .004 Click here for the Excel Data File (a) What is the expected amount Daniel-James will have to pay to Mobil in claims? (Enter your answer in millions to 2 decimal places. Omit the "$" sign in your response.) Expected amount $ million (b) What is the likelihood that Daniel-James will actually lose less than the expected amount? (Round your answer to 2 decimal places.) Probability (c) Given that Daniel-James suffers a loss, what is the likelihood that it is for $300 million? (Round your answer to 2 decimal places.) Probability (d) Daniel-James has set the annual premium at $2.0 million. Does that seem like a fair premium? Will it cover its risk? 6. value: 10.00 points The manager of Tee Shirt Emporium reports that the mean number of shirts sold per week is 1,170 with a standard deviation of 315. The distribution of sales follows the normal distribution. What is the likelihood of selecting a sample of 25 weeks and finding the sample mean to be 1,100 or less?(Round z value to 2 decimal places and final answer to 4 decimal places.) Probability 7. value: 10.00 points The manager of Tee Shirt Emporium reports that the mean number of shirts sold per week is 1,210, with a standard deviation of 325. The distribution of sales follows the normal distribution. What is the likelihood of selecting a sample of 25 weeks and finding the sample mean to be 1,100 or less?(Round z value to 2 decimal places and final answer to 4 decimal places.) Probability Loss 0 40 300 Probability 0.98 0.016 0.004