A machine that manufactures automobile pistons is estimated

A machine that manufactures automobile pistons is estimated to produce a defective piston of the time. Suppose that this estimate is correct and that a random sample of pistons produced by this machine is taken.

Estimate the number of pistons in the sample that are defective by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). Do not round your response.

Quantify the uncertainty of your estimate by giving the standard deviation of the distribution. Round your response to at least three decimal places.

Solution

A machine that manufactures automobile pistons is estimated to produce a defective piston of the time. Suppose that this estimate is correct and that a random sample of pistons produced by this machine is taken.

Estimate the number of pistons in the sample that are defective by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). Do not round your response.

Expectation = 2.7

Quantify the uncertainty of your estimate by giving the standard deviation of the distribution. Round your response to at least three decimal places.

standard deviation = 1.618

produce a defective piston 3% of the time....sample of 90 pistons produced by the machine is taken.

p=0.03

n=90

Expectation = np = 2.7

Variance = np(1 - p) = 2.619

Standard deviation = 1.61833