Quality-control managers work in every type of production environment possible, from producing dictionaries to dowel cutting for boat plugs. The Cincinnati Dowel & Wood Products Co., located in Mount Orab, Ohio, manufactures wood dowels and wood turnings. Four-inch-diameter boat plugs are one of its products. The quality control procedures aimed at maintaining the 4-inch diameter are only valid if the diameters have a normal distribution. The quality-control manager recently obtained the following summary diameters taken from randomly selected boat plugs on the production line:

The boat plug diameters are specified to have a normal distribution with a mean of 4 inches and a standard deviation of 0.10. Determine if the distribution of the 4-inch boat plugs is currently adhering to specification. Use a chi-square goodness-of-fit test and a significance level of 0.05.

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Interv Frequency Interval Frequency 3.872 3.872-3.916 3.917-3.948 3.949-3.97:5 3.976-4.000 4.001-4.025 4.026- 4.052 4.053-4.084 4.085 4.128 2 4 6 4.128