summit problem 5, 7, and 9

9. | Criminal Justice: Inmates According to Harper's Index, 5070 inmates are serving time for drug dealing. A random sample of 16 federal inmates is selected. (a) What is the probability that 12 or more are serving time for drug dealing? (b) What is the probability that 7 or fewer are serving time for drug dealing? (c) What is the expected number of inmates serving time for drug dealing?7. | Insurance: Auto State Farm Insurance studies show that in Colorado, 55% of the auto insurance claims submitted for property damage are submitted by males under 25 years of age. Suppose 10 property damage claims involving automobiles are selected at random. (a) Let r be the number of claims made by males under age 25. Make a histo- gram for the r-distribution probabilities. (b) What is the probability that six or more claims are made by males under age 25? (c) What is the expected number of claims made by males under age 25? What is the standard deviation of the r-probability distribution?5. | Probability Distribution: Auto Leases Consumer Banker Association released a report showing the lengths of automobile leases for new automobiles. The results are as follows. Lease Length in Months Percent of Leases 13-24 12.7% 25-36 37.1% 37-48 28.5% 49-60 21.5% More than 60 0.2% (a) Use the midpoint of each class, and call the midpoint of the last class 66.5 months, for purposes of computing the expected lease term. Also find the standard deviation of the distribution. (b) Sketch a graph of the probability distribution for the duration of new auto leases