Explanation Given: The binomial experiment consists of 4 trials in which the probability of success in any one trial is 2 5 . Approach: The formula to calculate the binomial trials is given as, P ( X = x ) = C ( n , x ) p x q n − x → ( 1 ) Here, p is the success in any trial, X is the random variable, the probability of exact x successes in n independent trials and q is the failure in any trial. Calculation: Assume X be the binomial random variable, Since the probability of success in any one trial is 2 5 . Calculate the probability of failure. q = 1 − 2 5 = 3 5 Since the number of the trial is 4. Then, Calculate the probability of zero success. Substitute 0 for x , 2 5 for p , 3 5 for q and 4 for n in the equation (1) to calculate the probability. P ( X = 0 ) = C ( 4 , 0 ) ( 2 5 ) 0 ( 3 5 ) 4 − 0 = ( 3 5 ) 4 = 0.1296 Calculate the probability of one success. Substitute 1 for x , 2 5 for p , 3 5 for q and 4 for n in the equation (1) to calculate the probability. P ( X = 1 ) = C ( 4 , 1 ) ( 2 5 ) 1 ( 3 5 ) 4 − 1 = 4 ( 2 5 ) ( 3 5 ) 3 = 0.3456 Calculate the probability of two successes. Substitute 2 for x , 2 5 for p , 3 5 for q and 4 for n in the equation (1) to calculate the probability. P ( X = 2 ) = C ( 4 , 2 ) ( 2 5 ) 2 ( 3 5 ) 4 − 2 = 6 ( 2 5 ) 2 ( 3 5 ) 2 = 0 To determine (b) To find: The mean and standard deviation of the probability distribution.

12th Edition

ISBN: 8220103649001

Author: Tan

Publisher: CENGAGE L

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Chapter 8.CRE, Problem 4CRE

To determine

(a)

To construct:

The probability distribution for the experiment.

To determine

(b)

To find:

The mean and standard deviation of the probability distribution.

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Chapter 8.CRE, Problem 3CRE

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(a) To construct: The probability distribution for the experiment.

Solution Summary: The author explains how to construct the probability distribution for the experiment.