A business owner wants to know if it will be profitable to open a new coffee sho
ID: 3159939 • Letter: A
Question
A business owner wants to know if it will be profitable to open a new coffee shop in a nearby town. In towns where the shop has been successful, the shop s name is recognizable to people 56% sample of 12 residents of the town. Find the probability that among these 12 surveyed residents, none of them have ever heard of the coffee shop. The probability is [|] (round your answer to 6 decimal places). Interpret this answer. If the business owner hopes the shop will be successful, which of the following is true? A. He wants this answer to be as big as possible. If it is big, it means it is less likely no one recognizes the name of the shop, so the shop has a better chance of being successful. B. He wants this answer to be as big as possible. If it is big, it means it is less likely no one recognizes the name of the shop, so the shop has a better chance of being successful. C. He wants this answer to be as small as possible. If it is small, it means it is more likely no one recognizes the name of the shop, so the shop has a better chance of being successful. D. He wants this answer to be as small as possible. If it is small, it means it is less likely no one recognizes the name of the shop, so the shop has a better chance of being successfulExplanation / Answer
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 = 12
p = the probability of a success = 0.56
x = the number of successes = 0
Thus, the probability is
P ( 0 ) = 0.0000526541 [ANSWER]
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This is the probability that 0 people recognize the restaurant. He wants this small, because that means many people recognize the shop.
Hence,
OPTION D. [ANSWER]
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