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Quiz2Solutions - P(Length too long = 25 1000 40 1000 = 5 8...

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STA 3032 - Section 7661 - Fall 2011 - Quiz 2 Please write your name and UF ID number and answer all questions on the paper that is provided to you. Do not write on the quiz sheet. Anything you write on the quiz sheet will not be graded. Show all work. Each question is worth 10 points. 1. Consider a population of 1000 aluminum rods. For each rod, the length is classified as too short, too long, or OK, and the diameter is classified as too thin, too thick, or OK. These 1000 rods form a sample space in which each rod is equally likely to be sampled. The number of rods in each category is presented below. Diameter Length Too Thin OK Too Thick Too Short 10 3 5 OK 38 900 4 Too Long 2 25 13 Compute the conditional probability P (diameter OK | length too long) Answer: P (diameter ok | Length too long)
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Unformatted text preview: P (Length too long) = 25 / 1000 40 / 1000 = 5 8 = 0 . 625 2. A factory has two machines that manufacture lightbulbs. The probability that a light-bulb comes from machine 1 is 45% and 55% of all lightbulbs come from machine 2. Machine 1 produces defects at a rate of 2% while machine 2 produces defects at a rate of 1%. What is the probability that a randomly selected lightbulb is from machine 1 given that it is defective? Answer: Let M 1 denote the lightbulb is from Machine 1, M 2 denote the lightbulb is from Machine 2 and D denote the lightbulb is defective. P ( M 1 | D ) = P ( D | M 1 ) P ( M 1 ) P ( D | M 1 ) P ( M 1 ) + P ( D | M 2 ) P ( M 2 ) = (0 . 02)(0 . 45) (0 . 02)(0 . 45) + (0 . 01)(0 . 55) = 18 29 ≈ . 62...
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