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levicorey846
13.05.2021 •
Mathematics
A report published by the Federal Reserve Bank of New York in 2012 reported the results of a nationwide study of college student debt. Researchers found that the average student loan balance per borrower is $23,300. They also reported that about one-quarter of borrowers owe more than $28,000. Assuming that the distribution of student loan balances is approximately normal.
Requird:
Estimate the proportion of borrowers who owe more than 54,000.
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Ответ:
The proportion of borrowers who owe more than 54,000 is 0%.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean
and standard deviation
, the z-score of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Researchers found that the average student loan balance per borrower is $23,300.
This means that![\mu = 23300](/tpl/images/1322/2892/54223.png)
They also reported that about one-quarter of borrowers owe more than $28,000.
This means that the 1 subtracted by the p-value of Z is 0.25 when X = 28000, that is, when X = 28000, Z has a p-value of 0.75, so when X = 28000, Z = 0.675. We use this to find![\sigma](/tpl/images/1322/2892/42440.png)
Estimate the proportion of borrowers who owe more than 54,000.
This is 1 subtracted by the p-value of Z when X = 54000. So
1 - 1 = 0
The proportion of borrowers who owe more than 54,000 is 0%.
Ответ:
29
30
Step-by-step explanation: