Business owner wants to know if it will be profitable to open a new coffee shop

Question

Business owner wants to know if it will be profitable to open a new coffee shop in a nearly town. In towns where the shop has been successful the shop's name is recognizable to people 56% of the He surveys a random 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 interpret this answer. If the business owner hopes the shop will be successful, which of the following true? He wants this answer to be as big as possible. It is big, if means it is less Likely no one recognizes the name of the shop, so the shop has a better chance of being successful. He wants this answer to be as small as possible lf it is small as possible. If its small means t is more likely no one recognizes the name of the shop, so the shop has a better chance of being successful He wants this answer to be as small as possible in it is small, it means If it is less likely one recognizes the name of the shop, so the shop has a better chance of being successful. He wants this answer to be as big as possible if it is big, means it is less likely no one recognizes the name of the shop, so the shop has a better dance of being successful

Explanation / Answer

We apply the binomial distribution to solve this question:

p = .56
n = 12
P(X=0) = ?

= 12C0(.56^0)(1-.56)^12
= .0000526

This means for this event to happen the probability is = .0000526

C is the right interpratation. The smaller is the probability that no one knowns about the place the more is the probability that it will be known

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