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Each of 166 newly manufactured items is examined and the number of scratches per item is...

Each of 166 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 6 7
Observed
frequency 16 36 42 37 19 9 5 2

Let X = the number of scratches on a randomly chosen item, and assume that X has a Poisson distribution with parameter μ.

(a) Find an unbiased estimator of μ and compute the estimate for the data. [Hint: E(X) = μ for X Poisson, so

E(X) = ?]

(Round your answer to two decimal places.)


(b) What is the standard deviation (standard error) of your estimator? Compute the estimated standard error. [Hint: σX2 = μ for X Poisson.] (Round your answer to three decimal places.)

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