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A candy company claims that its new chocolate almond bar averages 11 almonds per bar. Let x denote the number of almonds in the next bar that you buy. Use the Poisson distribution to find P(x $ 1) if the candy company's claim is correct. If x actually turns out to be 1, what do you think of the claim? (Leave no cells blank - be certain to enter "O" wherever required. Round your answer to 4 decimal places.) P(x * 1) The claim Is trueSuppose that x has a Poisson distribution with / = 2.5. (a) Compute the mean, My variance. of. and standard deviation, @, (Do not round your intermediate calculation, Round your final answer to 3 decimal places.) UX = OX 2 = OX = (b) Calculate the intervals [/, # 20,] and [x #30, ]. Find the probability that x will be inside each of these intervals, Hint, When calculating probability, round up the lower interval to next whole number and round down the upper interval to the previous whole number. (Use the value for standard deviation from part a. Round all your answers to 4 decimal places. Negative amounts should be indicated by a minus sign.) [ux + 20x] P [ux + 3ox] PAmong 13 metal parts produced in a machine shop, 3 are defective. If a random sample of 4 of these metal parts is selected, find: (a) The probability that this sample will contain at least two defectives. (Do not round the intermediate answers. Round your answer to 4 decimal places.) Probability (b) The probability that this sample will contain at most one defective. (Round your answer to 4 decimal places.) ProbabilitySuppose that x has a Poisson distribution with u = 2. (b) Starting with the smallest possible value of x, calculate p(x) for each value of x until p(x) becomes smaller than .001. (Round your answers to 4 decimal places.) (d) Find Ax = 2). (Round your answer to 4 decimal places.) P(x 2) (e) Find Ax $ 4). (Round your answer to 4 decimal places.) P(X:4)(fl Find Ax 21. (Round your answers to 4 decimal places.] (hi Find A1s x$ 4). (Round your answer to 4 decimal places.) P(1 5 x54) (1) Find A2