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Probability Type I or Type II Error: Soft-Drink Machine Example

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A soft-drink machine at a steak house is regulated so that the amount of drink dispensed is approximately normally distributed with a population mean of 200 millilitres and a standard deviation of 15 millilitres. The new machine is checked periodically by taking a sample of 9 drinks and computing the average content. If x̅ falls in the interval 191 < x̅ < 209, the machine is thought to be operating satisfactory; otherwise, we conclude that μ does not = 200 millilitres. (Hint: use the x statistic in your calculations).

a) Find the probability of committing a Type I error when μ = 200 millilitres.
b) Find the probability of committing a Type II error when μ = 215 millilitres.

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Solution provides steps necessary to find the probability of committing a Type I or Type II error.

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