please show work;

Each of 167 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 scratches per item 0 1 2 3 4 5 5 7 Observed frequency 23 39 46 25 20 5 5 4 Let X = the number of scratches on a randomly chosen item, and assume that X has a Poisson distribution with parameter p. (a) Find an unbiased estimator of ,u and compute the estimate for the data. [Hint E(X) = ,u for X Poisson, so E(X) = ?1 (Round your answer to two decimal places.) [:1 (b) What is the standard deviation (standard error) of your estimator? Compute the estimated standard error. [Hint 0X2 = ,u for X Poisson.] (Round your answer to three decimal places.) [:J