Question 243376: I studied these questions for hours today and I cannot figure out what it wants. Any help in putting me on the right path with this would be much appreciated.
A nationwide real estate company claims that its average time to sell a home is 57 days. Suppose it is known that the standard deviation of selling times is 12.3 days and that selling times are normally distributed.
1) Assuming the company’s claim is true, if a random sample of 64 homes is selected, there is a 75% probability that the sample mean is greater than how
many days?
2) Do you have to know that selling times are normally distributed to answer the first question? Explain why or why not.
thank you for your time and assistance.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A nationwide real estate company claims that its average time to sell a home is 57 days.
Suppose it is known that the standard deviation of selling times is 12.3 days and that selling times are normally distributed.
1) Assuming the company’s claim is true, if a random sample of 64 homes is selected, there is a 75% probability that the sample mean is greater than how
many days?
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The distribution of the sample means of samples of
size 64 is N(57,12.3/sqrt(64))
--
Draw a normal curve with mean 57 and put a mark on the
axis at a point above which 75% of the population of
means lies.
---
The z-value of that point is invNorm(0.25) = -0.6744897....
---
Find the x-bar value that corresponds to that z-value:
x-bar = -0.6744897*(12.3/sqrt(64)) + 57 = 55.963
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Cheers,
Stan H.
2) Do you have to know that selling times are normally distributed to answer the first question? Explain why or why not.
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