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AleksAgata [21]
3 years ago
6

Two friends are opening a coffee shop. As they write their business plan, they research the amount of debt similar businesses ca

n have in the first two years of opening. It is known that
72% of coffee shops have a debt of over $50,000 within the first two years of opening. If a random sample of 36 coffee shops is obtained, what is the probability that more than half of them had a debt of over $50,000 within the first two years of opening?
Mathematics
2 answers:
never [62]3 years ago
8 0

Answer:   0.9984

Step-by-step explanation:

Let p be the proportion of coffee shops have a debt of over $50,000 within the first two years of opening.

As per given , p= 72%=0.72

Sample size : n= 36

Required probability :-

P(\hat{p}>0.50)=P(\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}>\dfrac{0.50-0.72}{\sqrt{\dfrac{0.72(1-0.72)}{36}}})\\\\=P(z>-2.94)\ \ \ [\because z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}]\\\\=P(z

Hence, the probability that more than half of them had a debt of over $50,000 within the first two years of opening = 0.9984

Tom [10]3 years ago
3 0
The answer is 50,036
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