Each of 152 newly manufactured items is examined and the number of scratches per

Question

Each of 152 newly manufactured items is examined and the number of scratches per item is recorded (the items are supposed to be free of scratches), yielding the following data Number of per item01 234 56 7 Observed frequency 14 38 36 26 10 14 122 Let X-the number of scratches on a randomly chosen item, and assume that X has a Poisson distribution with parameter . (a Find an unbiased estimator of and compute the estimate for the data. Hint: E - for X Poisson, so E ? Round your answer to two decimal places.) (b) What is the standard deviation (standard error of your estimator? Compute the estimated standard error. Hint: 2- for XPolsson (Round your answer to three decimal places.)

Explanation / Answer

a) mean E(Xbar) =2.53

b)std deviation from hint =(2.53)1/2 =1.591 ( please try 1.589 if this does not work due to rounding)

relative frequency frequency x p(x) xP(x) 14 0 0.092 0.000 38 1 0.250 0.250 36 2 0.237 0.474 26 3 0.171 0.513 10 4 0.066 0.263 14 5 0.092 0.461 12 6 0.079 0.474 2 7 0.013 0.092 152 total 1 = 2.53

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