Anyone help me with these questions pleasee

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Suppose a sitcom is filmed on set between zero and five days per week. The following table shows the probabilities of the sitcom being filmed zero, one, two, three, four, or five days in a week. Rx) 0 0.11213 1 0.14558 2 0.16942 3 0.22547 4 0.15375 5 0.19365 The expected number of days the sitcom will be filmed in one week, M, is 2.74408. Use the formula below to calculate the variance, 2, of the number days the sitcom films, x, where P(x) is the probability of the sitcom filming for a particular number of days. 82 = E [(x - M)2 . P(x)] Provide each answer with three decimal places of precision. What is the weighted probability of zero days of filming?What is the weighted probability of zero days of filming? (xo - M) 2 . P(xO) = What is the weighted probability of one day of filming? (X1 - M)2 . P(x1 ) = What is the weighted probability of two days of filming? (x2 - M)2 . P(X2) =What is the weighted probability of three days of filming? ( x3 - M) 2 . P(X3) = What is the weighted probability of four days of filming? (X4 - M)2 . P(x4 ) = What is the weighted probability of five days of filming? ( x5 - M)2 . P(X5) =\fSuppose Martin is a very talented used-car salesman. Whenever Martin talks to a new customer, there is a 70% chance that he convinces the customer to purchase one of his used cars. Brian, Martin's boss, is envious that Martin sells many more cars than he does. Because of his jealousy, Brian institutes a new rule that Martin is only allowed to talk to 35 customers per day. Thus, Martin continues to work each day until he speaks to 35 customers, at which point Brian sends him home. Let X represent the number of used cars that Martin sells on a given day. What are the mean, u, and variance, 02, of X? Please round your answers to the nearest two decimal places. Suppose Kristen is researching failures in the restaurant business. In the city where she lives, the probability that an independent restaurant will fail in the rst year is 49%. She obtains a random sample of 62 independent restaurants that opened in her city more than one year ago and determines if each one had closed within a year. What are the mean and standard deviation of the number of restaurants that failed within a year? Please give your answers precise to two decimal places. Maggie is practicing her penalty kicks for her upcoming soccer game. During the practice, she attempts 10 penalty kicks. If each attempt at the penalty kick is independent of the other attempts and if she scores 70% of the time, historically, what is the probability that she scores at least eight goals? Give your answer as a percentage precise to two decimal places. I:l% Suppose that the prevalence of a certain type of tree allergy is 0.32 in the general population. If 100 people randomly chosen from this population are tested for this allergy, what is the probability that exactly 32 of them will have this allergy? Please write your answer as a decimal, precise to at least four decimal places. The National Center for Health Statistics (NCHS) reports that 70% of U.S. adults aged 65 and over have ever received a pneumococcal vaccination. Suppose that you obtain an independent sample of 20 adults aged 65 and over who visited the emergency room and the pneumococcal vaccination rate applies to the sample. Determine the probability that exactly 15 members of the sample received a pneumococcal vaccination. Let X represent the number of successes in a binomial setting with n trials and probability p of success in each trial. The probability of obtaining exactly k successes is given by the formula P(X = k) = (* ) pk( 1 - park where (") is the binomial coefficient, also represented as n Ck, and is defined as n n! k!(n - k)! Follow the steps to compute P(X = 15). First determine the binomial coefficient. Do not round your answer. 20 15 =Compute (.7)15 , or the probability that exactly 15 adults have been vaccinated. Round your answer to six decimal places. Compute (.3)5 , or the probability that exactly 5 adults have not been vaccinated. Report as a decimal to ve decimal places. Do not round. Compute P(X = 15) = 20 C15 - (.7)\" - (3)5, the binomial probability that exactly 15 vaccinated adults are in the random sample of 20 adults. Round your answer to four decimal places. Overbooking is the practice of selling more items than are currently available. Overbooking is common in the travel industry; it allows a vehicle (airline, train, bus, cruise ship, hotel, and so forth) to operate at or near capacity, despite cancellations, no- shows, or late arrivals. Overselling is when more conrmed customers show up to use the vehicle than there is space available. When this happens, at least one customer will be denied the service that they paid for, either voluntarily (sometimes with an incentive provided by the supplier) or involuntarily. This is called getting "bumped." Suppose that for a particular ight, an airline believes that 2% of ticket holders do not make the ight. The jet making the trip holds 189 passengers. If the airline sells 192 tickets, what is the probability that the ight will be oversold and they will have to bump a passenger? Assume that cancellations are independent. Calculate the probabilities that one, two, and three people will be bumped, and then use those values to determine the probability that at least one passenger will be bumped. Give each answer to four decimal places. Avoid rounding within calculations. P(three people are bumped) = :] P(at least one person is bumped) = C] Suppose Tina is throwing a surprise party to celebrate her friend Trevor's birthday, and she asks her good friend Tom to help with the music. The two agree to create a joint song playlist for Trevor to listen to during the car ride to the party. Tina chooses to add 15 songs to the playlist, and Tom chooses to add 11 songs. Suppose the playlist they created is signicantly too long, and the car ride Will only last long enough for the three to hear seven of the songs on the playlist. Also, suppose that each time a song is selected to be played, it is randomly selected from the remaining songs without replacement. After careful consideration, Tina is a little worried about Tom's song choices and hopes that Trevor will not hear too many of his songs. Let X be the random variable representing the number of Tom's songs that are played during the car ride. Calculate the probability that Trevor will hear zero, one, or two of Tom's song choices. Round your answers to the nearest three decimal places. P(X=0)= Finally, calculate the probability that at most two of Tom's song choices are played during the car ride. Please round your answer to the nearest three decimal places