  # A machine is supposed to cut plastic into sheets that are 600 inches long. The company wants to estimate the mean length the machine is cutting the plastic, accurate to within 0.04 inch. Determine the sample size required to construct a 92% confidence interval. Assume that the population is normal with a standard deviation of 0.25 inch. (a) 120 (b). 32 (c). 100 (d). 945 (e). 115

Question

A machine is supposed to cut plastic into sheets that are 600 inches long. The company wants to estimate the mean length the machine is cutting the plastic, accurate to within 0.04 inch. Determine the sample size required to construct a 92% confidence interval. Assume that the population is normal with a standard deviation of 0.25 inch. (a) 120 (b). 32 (c). 100 (d). 945 (e). 115

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Step 1

The given information is as follows:

A machine wants to cut plastic into sheets and the sheets are 600 inches long.

The confidence level is 100*(1–α)%  = 92%.

From this, the level of significance is α = 0.08.

The population standard deviation in the length of plastic is σ = 0.25 inch.

Furthermore, it is given that the estimate of mean length should be accurate within 0.04 inch. That is, the margin of error is E = 0.04 inch.

Step 2

Obtain the critical value for the given situation:

The confidence level is 92%.

The critical value corresponding to the given situation is obtained as z(α/2) = 1.751 from the calculation given below:

Step 3

Obtain the required sample size under the given criteria:

Here, z(α/2) = 1.751, σ = 0.25, E = 0.04.

The required sample size under the given criteria ...

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