Can you please answer the following 4 question which have multiple parts to each one
Please show work.
thank you
Assume that 12% of people are left-handed. If if people are selected at random, nd the probability of each outcome described below. a) Find the probability that the rst lelty is the seventh person chosen. I: [Round to four decimal places as needed.) b) Find the probability that there are some lefties among the 3" people. I: [Round to tour decimal places as needed.) c} Find the probability that the rst lefty is the second or third person. I: [Round to four decimal places as needed.) d) Find the probability that there are exactty 3 lefties in the group. I: [Round to tour decimal places as needed.) e) Find the probability that there are at least 5 le'lties in the group. I: [Round to tour decimal places as needed.) You play two games against the same opponent. The probability you win the rst game is 0.7. Ifyou win the rst game. the probability you also win the second is 0.6. It you lose the rst game. the probability that you win the second is 0.4. Complete parts a] through e]. a] Are the two games independent? Explain your answer 0 A. No; the outcome ofthe rst game determines the probability ofwinning the second game. 0 B. Yes: all events are independent. 0 C. No; no events are independent. 0 D. Yes; the outcome of the rst game has no impact on the semnd game. b] What's the probabiiity you lose both games? (Type an integer or a decimal.) c} What's the probability you win both games? (Type an integer or a decimal.) You play two gImes against the same opponent. The probability you win the rst game is 0.7. llyou win thI rst game. the probability you also win the second is 0.6. If you lose the rst game, the probability that you win the second is 0.4. Compiete parts a) through e). 0) What's thI probability you win both games? (l'ype an integer or a decimal.) d) Let random variable X be the number of games you win. Find the probability model for X. x u 1 2 PM e) Find the expected value and standard deviation of X. EO') = (l'ype an integer or a decimal.) sour] = (Round in three dedmal places as needed.) The probability model below describes the number of repair calls that an appliance repair shop mayr receive during an hour. Repair Calls | o | 1 | 2 | 3 Q1 Probability | 0.1 | 0.3 | 0.4 | 0.2 On average, the shop receives 1.? calls an hour, with a standard deviation of 0.90 Illls. Suppose that the appliance shop plans an 8hour day. Complete parts (a) through (d) below. (a) Find the mean and standard deviation of the number of repair Illls they should expect in a day. The mean number of repair calls they should expect in a day is (Type an integer or a decimal.) The standard deviation of the repair calls they should expect in a day is (Round to two decimal places as needed.) (b) What assumption did you make about the repair calls? 0 A. The shop receives the same number of calls each day. Q B. Each call lasts less than 1 hour. 0 C. The hours are independent. 0 D. The shot) is (men on weekends. The probabilin model below describes the number of repair trails that an appliance repair shop may receive during an hour. Repair Cars | u | 1 i 2 | a Q Probability | 0.1 | 0.3 i 0.4 | 0.2 On average, the shop receives 1.1-lls an hour, with a standard deviation of 0.90 raiis. Suppose that the appiian- shop plans an 8-hour day. Complete parts (a) through (d) below. 0 A. The shop reloives the same number of calls each day. Q B. Each call lasts leg; than 1 hour. 0 c. The hours are independent. 0 D. The shop is open on weekends. (c) Use the mean and standard deviation to descrihe what a typical amour day will be like. Assume that a variation oft standard deviation is typical. Atypical Ehour day will have about to repair oalls. (Round to the nearest integer as needed. Use ascending order.) (d) At the end of a day, a worker comments 'Boy. I'm tired. Today was sure unusually busyl' How many repair calls would justify such an observation? Assu me that a variation of 2 standard deviations is unusual. The smallest observation that would be considered unusual is repair calls. (Round up to the neare integer.) An insurance policy cosh $150 and will pay policyholders $12,000 ifthey suer a major injury {resulting in hospitalizalion) or $2000 iltney suer a minor injury (resulting ln lost time from work]. The company estimates thal 1 in every 200? policyholders will suer a major injury and that 1 in 466 will suffera minor lnjury. 3) Create a probability model for the prot on a policy. b} What's the company's expeded pml on the policy? a) What's the standard deviation? 3) First nd lhe probability and prot for each outcome. x Pevenl] Prot no injury major injury minor injury (Round to slx decimal places as needed.) b} Find the expected prot on the policy. E(X)=$ (Round to two decimal places as needed.) c) Find the sundard deviation on the policy. An insurance policy cools $150 and ill pay policyholders $12,000 iltney suer a major injury (resulting in hospitalization) or $2000 iflhey suer a minor injury (resulting in i061 time from work]. The company estimates that 1 in every 2037 policyholders wiii suer a major Injury and that 1 in 436 will sullera minor injury. a)Crea1e a probabiiity model lorthe prot on a policy. b} What's the companys prected prot on the policy? 1:) What's the sfandard deviation? x P(event) Prot no injury major injury minor injury (Round to six decimal places as needed.) b} Find the expec'hed prot on the policy. E(X) = 3 (Round to two decimal plaoes as needed.) c) Find the slandard deviation on the policy. o = SDlX) = 5 (Round to tum decimal places as needed.)
