The life of electric lightbulbs is known to be a normally distributed random variable with unknown mean μ and standard deviation 200 hours. The value of a lot of 1,000 bulbs is (1,000) (1/5,000) μ dollars. A random sample of n bulbs is to be drawn by a prospective buyer, and 1,000(1/5,000) X–bar dollars paid to the manufacturer. How large should n be so that the probability is 0.90 that the buyer does not overpay or underpay the manufacturer by more than $15?
Answer to relevant QuestionsA joint random variable (X1, X2) is said to have a bivariate normal distribution if its joint density is given by for –∞ < s < ∞ and –∞ < t < ∞. (a) Show that E(X1) = μX1 and E(X2) = σX2. (b) Show that variance ...During the course of a day a machine turns out two items, one in the morning and one in the afternoon. The quality of each item is measured as good (G), mediocre (M), or bad (B). The longrun fraction of good items the ...Show that the structure function for a three-component system that functions if and only if component 1 functions and at least one of components 2 or 3 functions is given by Show that the structure function for a four-component system that functions if and only if components 1 and 2 function and at least one of components 3 or 4 functions is given by ɸ(X1, X2, X3, X4) X1 X2 max (X3, X4). Jake’s Machine Shop contains a grinder for sharpening the machine cutting tools. A decision must now be made on the speed at which to set the grinder. The grinding time required by a machine operator to sharpen the cutting ...
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