Explanation Given: In a survey of 1000 social-media account holders aged 18 years and older conducted by the AARP, it was found that 65 % of them have one or two such accounts. Also, 10 participants are picked at random. Approach: In Binomial experiment in which the probability of success in any trial is p , the probability of exactly x successes in n independent trials is given as, P ( X = x ) = C ( n , x ) p x q n − x , x = 0 , 1 , 2 , … , n Here, X is the binomial random variable. Calculation: Assume n denotes the number of participants chosen at random and X denotes the number of participants that have two or more social media accounts. From the given data, n = 10 It is given that 65 % of the participants have two or more social media accounts; that is p = 0.65 . Therefore, the probability of the participants that does not have two or more social media accounts is given as, q = 1 − p = 1 − 0.65 = 0.35 The probability that at most 7 out of 10 people have two or more social media accounts is given as, P ( X ≤ 7 ) = ( P ( X = 7 ) + P ( X = 6 ) + P ( X = 5 ) + P ( X = 4 ) + P ( X = 3 ) + P ( X = 2 ) + P ( X = 1 ) + P ( X = 0 ) ) Therefore, the probability is calculated as, P ( X ≤ 7 ) = ( C ( 10 , 7 ) ( 0.65 ) 7 ( 0.35 ) 3 + C ( 10 , 6 ) ( 0.65 ) 6 ( 0.35 ) 4 + C ( 10 , 5 ) ( 0

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Author: Tan

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Chapter 8.4, Problem 44E

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The probability that at most 7 out of 10 participants have one or two social media accounts.

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Chapter 8.4, Problem 43E

Chapter 8.4, Problem 45E

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The probability that at most 7 out of 10 participants have one or two social media accounts.

Solution Summary: The author explains how the probability of success in a binomial experiment is p.

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To find: The probability that at most 7 out of 10 participants have one or two social media accounts.

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To find:

The probability that at most 7 out of 10 participants have one or two social media accounts.