Each of178newly 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 ofscratchesper item01234567Observedfrequency

144337381710145LetX= the number of scratches on a randomly chosen item, and assume thatXhas a Poisson distribution with parameter.

(a) Find an unbiased estimator ofand compute the estimate for the data. [Hint:E(X) =forXPoisson, soE(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:_X²=forXPoisson.] (Round your answer to three decimal places.)