# Proportions of total number of cases in these

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proportions of total number of cases in these categories are shown below:EducationConvictedNot ConvictedTotal10 years or more0.10.330.43Nine years or less0.270.30.57Total0.370.631.00
(a) Find the probability that a randomly selected offender has nine years or lesseducation.(b) Given that the offender is convicted (B), what is the probability that the offenderhas ten or more years of Education(A) ?(c)Are A and B independent? Explain.4)(18 points) An investor has stocks of 20 different companies in her portfolio. OFthese companies, 13 are industrial and 7 are utility. She decides to sell stocks ofeight of these(a)there will be equal number of industrial and utility companies in herselection.(b) All utility stocks are in the selection(c)At least one utility stock is in the selection5)(15 points) The Centers for Disease control have determined that when a personis given a vaccine, the probability that the person will develop immunity to a virus is0.8. If ten people are randomly picked and given the vaccine, find:(a)the expected number and standard deviation of people who will developimmunity(b) the probability that exactly four will develop immunity(c)the probability that at least 9 personsdevelop immunity6) The automatic opening device of a military cargo parachute has been designed to openwhen the parachute is 200 meters above the ground. Suppose opening altitude has anormal distribution with mean value 200 m and standard deviation of 50m. Equipmentdamage will occur if the parachute opens at an altitude of less than 100m.(a)(10 points) What is the probability that there will be damage to aparachute?(b) (8 points) Suppose six parachutes are independently dropped. What is theprobability that there will be equipment damage to exactly two of them?
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