San Diego State University Operations And Supply Chain Management Assignment Help - Mean

Question - A soft-drink machine at a steak house is regulated so that the amount of drink dispensed is
approximately normally distributed with a mean of 200 milliliters and a standard deviation of 15
milliliters. The machine is checked periodically by taking a sample of 9 drinks and computing the
average content. If x falls in the interval 191 < x < 209, the machine is thought to be operating
satisfactorily; otherwise, we conclude that μ does not equal 200 milliliters.
a) Find the probability of committing at type I error when μ = 200 milliliters.
μ = 200, n = 9, ơ = 15 and ơ x = 15/3 = 5
So, z1 = (191-200)/5 = -1.8, and z2 = (209 - 200)/5 = 1.8,
with a α = 2P(Z < -1.8) = (2)(0.0359) = 0.0718
b) Find the probabil ...Read More ity of committing a type II error when μ = 215 milliliters.
If μ = 215, then z - 1 = (191-215)/5 = -4.8 and z2 = (209-215)/5 = -1.2, with
β= P(-4.8 < Z < -1.2) = 0.1151 - 0 = 0.1151 ...Read Less

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