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Question 793:



No answer provided yet.For these two questions we need to use the formula for the z-score for a sample mean. The formula to find the area is (data-point-mean)/standard error of mean. The standard error of the mean is the population standard deviation divided by the square root of the sample size. The standard error for this sample size = 5000/SQRT(200) = 353.55

a. For between area questions, we need to find the area from the z statistics for both values, then subtract the smaller from the larger. For $33000, we get the z-score of (33000-34000)/353.55 = -2.8284. For the larger value we get (34000-34000)/353.55 = 0/353.55 = 0. The amount of area under the normal curve up to -2.8284 = .002338 and 50% for 0. Subtracting the smaller from larger area we get 50-.002338 = .497661. To lookup the areas you can use a table of normal values or the excel function =NORMSDIST().

b. Using the value of 37000, we get the z-score for the sample as (37000-34000)/353.55 = 8.4852. That's a really high z-score (it means what are the chances of sampling 200 people with a mean that is 8.48 standard errors above the mean--extremely rare). Looking up the area for 8.48 we get the area of .99999, meaning getting a mean above 37000 is less than .000001. 

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