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1)Given the probability distributions shown to the​right, complete the following parts. a. Compute the expected value for each distribution. b. Compute the standard deviation for each distribution. c. Compare the results of distributions A and B. Distribution A: X Distribution A: P(X) Distribution B: X Distribution B: P(X) 0 0.57 0 0.02 1 0.19 1 0.09 2 0.13 2 0.13 3 0.09 3 0.19 4 0.02 4 0.57 2)The following table contains the probability distribution for the number of traffic accidents daily in a small town. Complete parts​(a) and​(b) to the right. 0 0.27 1 0.32 2 0.16 3 0.09 4 0.07 5 0.05 6 0.04 a. Compute the mean number of accidents per day. 3)Determine the mean and standard deviation of the variable X in the binomial distribution where n=3 and π=0.90. 4) Assume a Poisson distribution. a. If λ=2.5​, find P(X=0​). b. If λ=8.0​, find ​P(X=1). c. If λ=0.5​, find ​P(X=2​). d. If λ=3.7​, find P(X=10​). 5) The number of arrivals per minute at a bank located in the central business district of a large city was recorded over a period of 200​minutes, with the results shown in the table below. Complete​(a) and​(b) to the right. Arrivals Frequency 0 14 1 25 2 48 3 43 4 31 5 21 6 10 7 5 8 3 a. Compute the expected number of arrivals per minute.6) A recent survey reported that 58​% of​18- to​29-year-olds in a certain country own tablets. Using the binomial​distribution,a. What is the probability that in the next six​18- to​29-year-olds surveyed, four will own a​tablet?7) Suppose that you and two friends go to a​restaurant, which last month filled approximately 81 % of the orders correctly.a. What is the probability that all three orders will be filled​correctly?8) A​toll-free phone number is available from 9 a.m. to 9 p.m. for your customers to register complaints about a product purchased from your company. Past history indicates that an average of 1.0 calls are received per minute.What properties must be true about the situation described here in order to use the Poisson distribution to calculate probabilities concerning the number of phone calls received in a​1-minute period? Select all the assumptions for a Poisson distribution. Multiple Choice, Choices are below (A,B,C, or D)A.The number of phone calls received in a given​1-minute period is independent of the number of phone calls received in any other​1-minute period.B.At least 30 calls are received.C.The probability that two or more phone calls received in a time period approaches zero as the length of the time period becomes smaller.D.The probability of a phone call is the same in any given​1-minute period.