Statistics, sampling distribution of mean , math homework help

  

I have attached the z-score table needed to help solve the math problem. https://sakai.udel.edu/access/content/group/534d2390-333b-47c0-97a0-8cd7492b7c33/Tables/normal.pdf
stat_homework.docx

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An insurance company sells homeowner’s insurance to compensate homeowners in case of damage to their
home. Suppose we assume that the probability distribution of x = insurance company’s payout on a $200,000 policy is
given below:
x
0
$10,000
$50,000
$100,000
$200,000
p(x)
0.81
0.150
0.025
0.010
0.005
The mean and standard deviation of x for one policy are $4,750 and $18,839.7850, respectively.
For the sampling scenario with 2,500 homeowners, find the probability that the average payout exceeds $6,000.
(5 decimal places)
…
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