Thirty percent of all customers who enter a store will make a purchase. Suppose
ID: 3022593 • Letter: T
Question
Thirty percent of all customers who enter a store will make a purchase. Suppose that six customers enter the store and that these customers make independent purchase decisions.
Use the binomial formula to calculate the probability that exactly five customers make a purchase. (Round your answer to 4 decimal places.)
Use the binomial formula to calculate the probability that at least three customers make a purchase. (Round your answer to 4 decimal places.)
Use the binomial formula to calculate the probability that two or fewer customers make a purchase. (Round your answer to 4 decimal places.)
Use the binomial formula to calculate the probability that at least one customer makes a purchase. (Round your answer to 4 decimal places.)
(1)Use the binomial formula to calculate the probability that exactly five customers make a purchase. (Round your answer to 4 decimal places.)
Explanation / Answer
1.
Note that the probability of x successes out of n trials is
P(n, x) = nCx p^x (1 - p)^(n - x)
where
n = number of trials = 6
p = the probability of a success = 0.3
x = the number of successes = 5
Thus, the probability is
P ( 5 ) = 0.010206 [ANSWER]
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Consider:
2.
Thus, the probability of at least 3 successes is
P(at least 3 ) = P(3) + P(4) + P(5) + P(6) = 0.25569 [ANSWER]
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3.
Then the cumulative probability is
P(at most 2 ) = P(0) + P(1) + P(2) = 0.74431 [ANSWER]
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4.
Thus, P(at least one) = 1 - P(0) = 0.882351 [ANSWER]
x P(x) 0 0.117649 1 0.302526 2 0.324135 3 0.18522 4 0.059535 5 0.010206 6 0.000729Related Questions
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