For each? situation, identify the sample size? n, the probability of success? p,

Question

For each? situation, identify the sample size? n, the probability of success? p, and the number of successes x. Give the answer in the form? b(n,p,x). Do not go on to find the probability. Assume the four conditions for a binomial experiment are satisfied. Complete parts? (a) and? (b) below. a. In the 20088 presidential? election, 5252?% of the voters voted for a certain candidate. What is the probability that 2626 out of 5050 independently chosen voters voted for this? candidate? The probability is ?b(n,p,x)equals=b left parenthesis nothing comma nothing comma nothing right parenthesisb,,. ?(Type integers or decimals. Do not? round.) b. The manufacturer of a certain vehicle recovery system claims that the probability that a stolen vehicle using its product will be recovered is 8282?%. What is the probability that exactly 77 out of 1010 independently stolen vehicles with this product will be? recovered? The probability is ?b(n,p,x)equals=b left parenthesis nothing comma nothing comma nothing right parenthesisb,,. ?(Type integers or decimals. Do not? round.)

Explanation / Answer

Solution:

    We have to identify the sample size? n, the probability of success? p, and the number of successes x for the following situations.

Part a) We are given that : In the 2008 presidential? election, 52?% of the voters voted for a certain candidate.

and we are asked to find the probability that 26 out of 50 independently chosen voters voted for this? candidate?

Thus p = probability of success = probability of the voters voted for a certain candidate = 52%= 0.52

n = sample size = number of independently chosen voters = 50

x = number of successes = number of chosen voters voted for this? candidate = 26

Thus the probability is ?b(n,p,x) = b( 50 , 0.52 , 26 )

Part b) We are given that : The manufacturer of a certain vehicle recovery system claims that the probability that a stolen vehicle using its product will be recovered is 82?% and we have to find the probability that exactly 7 out of 10 independently stolen vehicles with this product will be? recovered.

Thus p = probability of success = probability of stolen vehicle using its product will be recovered = 0.82

n = sample size =number of independently stolen vehicles with this product = 10

x = number of independently stolen vehicles with this product will be? recovered = 7

Thus The probability is b(n,p,x) = b ( 10 , 0.82 , 7 )

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