Exam 2 - Solutions

Exam 2 - Solutions - STATISTICS 321 Dr Soma Roy Exam 2(4...

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STATISTICS 321 – Dr. Soma Roy Name : Exam 2 – May 21, 2009 (4 sides ) Maximum points: 50 1. Consider writing onto a computer disk and sending it through a certifier that counts the number of missing pulses. Suppose this number X has a Poisson distribution with parameter λ = 0 . 2. (a) (2 points) Show that the probability that a randomly selected disk has exactly one missing pulse is equal to 0.16. Let X = number of missing pulses on a disk, X Poisson ( λ = 0 . 2). Then, we want P ( X = 2) = e - 0 . 2 0 . 2 1 1! = 0 . 16 (b) (4 points) What is the probability that 3 disks that are independently selected will have fewer than 2 missing pulses in total ? Let Y = 3 X = total number of missing pulses on 3 disks, Y Poisson ( λ = 3 × 0 . 2 = 0 . 6). Then, we want P ( Y < 2) = P ( Y = 0) + P ( Y = 1) = e - 0 . 6 0 . 6 0 0! + e - 0 . 6 0 . 6 1 1! = 0 . 88 (c) (4 points) If 5 disks are independently selected, what is the probability that 2 of the disks each contain exactly one missing pulse? Let W = number of disks, each with one missing pulse in a sample of 5 disks, W Binomial (5 ,. 016) (From (a)). Then, we want P ( W = 2) = 0 . 15 2. (8 points) A machine that produces ball bearings has initially been set so that the true average diameter of the bearings it produces is 0.500 inches. A bearing is acceptable if its diameter is within
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This note was uploaded on 06/15/2010 for the course CHEM 124 taught by Professor Hascall during the Winter '08 term at Cal Poly.

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Exam 2 - Solutions - STATISTICS 321 Dr Soma Roy Exam 2(4...

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