a. Explanation Calculation: Random variable x is a hypergeometric random variable with N = 12 , n = 8 , r = 6 . Hypergeometric distribution: Random variable x is said to follow a hypergeometric distribution, if the probability distribution is as follows: P ( x ) = ( r x ) ( N − r n − x ) ( N n ) Where, x = Maximum [ 0 , n − ( N − r ) ] , .... , Minimum ( r , n ) = Number of Successes drawn in the n elements N = Total number of elements . r = Number of Successes in the N elements . n = Number of elements drawn . As x follows hypergeometric distribution with N = 12 , n = 8 , r = 6 , thus x can take only values 2, 3, 4, 5, or 6. For x = 2 , p ( 2 ) = ( 6 2 ) ( 12 − 6 8 − 2 ) ( 12 8 ) = 6 ! 2 ! 4 ! 6 ! 6 ! 0 ! 12 ! 8 ! 4 ! = 15 × 1 495 = 0.030 For x = 3 , p ( 3 ) = ( 6 3 ) ( 12 − 6 8 − 3 ) ( 12 8 ) = 6 ! 3 ! 3 ! 6 ! 5 ! 1 ! 12 ! 8 ! 4 ! = 20 × 6 495 = 0 b. To determine Find the mean and standard deviation of x . c. To determine Draw p ( x ) and locate μ and μ ± 2 σ on the graph. d. To determine Compute the probability that x will fall in the interval μ ± 2 σ .

13th Edition

ISBN: 9780134080215

Author: James T. McClave, Terry T Sincich

Publisher: PEARSON

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Chapter 4.6, Problem 112LM

To determine

Display the probability distribution of x in a tabular form.

To determine

Find the mean and standard deviation of x.

To determine

Draw p(x) and locate μ and μ±2σ on the graph.

To determine

Compute the probability that x will fall in the interval μ±2σ.

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Chapter 4.6, Problem 111LM

Chapter 4.6, Problem 113LM

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Statistics (13th Edition)

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