newconnect.mheducation.com 011 Chapter 5-18SP STATISTICS FOR ECONOMICS 2468 Help
ID: 3065772 • Letter: N
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newconnect.mheducation.com 011 Chapter 5-18SP STATISTICS FOR ECONOMICS 2468 Help Save& Exit Submit Check my weark For the most recent year available, the mean annual cost to attend a private university in the United States was $20,232. Assume the distribution of annual costs follows the normal probability distribution and the standard deviation is $4,350. Ninety-five percent of all students at private universities pay less than what amount? (Round your z value to 2 decimal places and final answer to the nearest whole dollar.) ok nt nces K Prev 5 of 6 Next>Explanation / Answer
From the given information:
Mean = $20232
Standard Deviation = $4350
We have to find the 95% percent of all the student at private universities pay less than what amount
ie 95th Percentile of this normal dostribution
To compute the 95th percentile, we use the formula X= + Z, and we will use the standard normal distribution table, Previously we started with a particular "X" and used the table to find the probability.
So we begin by going into the interior of the standard normal distribution table to find the area under the curve closest to 0.95, and from this we can determine the corresponding Z score. Once we have this we can use the equation X= + Z, because we already know that the mean and standard deviation are $20,232 and $4350, respectively.
When we go to the table, we find that the value 0.95 is not there exactly, however, the values 0.9495 and 0.9505 are there and correspond to Z values of 1.64 and 1.25, respectively. The exact Z value holding 95% of the values below it is 1.64 which was determined from a table of standard normal probabilities with more precision.
Using Z=1.64 the 95th percentile I for men is: X = 20232 + 1.64 (4350) = 27366.
Interpretation: Ninety Five percent of all the student at private universities pay less than what amount is $27366
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