QM222 Modeling Business Decisions
Spring 2023
Name: ________________________________
Section: _________________________
Time to Mortgage Approval
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A large mortgage company, House4U, has been tasked by the CEO to reduce the amount
of time it takes to approve new applications for mortgage loans. The approval process must go
through formal underwriting, which includes a review of the application and obtaining and
reviewing the following: credit bureau report , pay stubs, copies of tax returns, additional work
history information, bank statements and other asset information, title search, and the property
appraisal.
You are hired as a consultant and begin by collecting the data needed to begin your analysis.
You select a random sample of 36 mortgage loans which were approved during the last month.
You calculate the sample mean and standard deviation in Excel (see the dataset called
“approvaltime.xlsx”).
1. What is the standard error of the average # of days for mortgage loan approval? Show your
calculations. The SE should be the SD of all the days divided by the a random sample of 36
rooted so thus it should be around 3.95 as an Error
2. You want to know about the average time to approval for ALL House4U loans (not just the
sample), but you don’t have time to collect data on all loans. What is the approximate
probability that House4U loans have an average time to approval of 46 days or less? Explain
your reasoning using distance from mean in standard errors.
Well the mean is equal to 54-46= 8 days less than the mean. That means 8/23.7= 0.337 SDs
lower than the mean calculating it throw excel would give you about 63.2 percent chance of that
happening
3. Assume that a sample of 49 approved mortgages was used and the same average # days and
standard deviation for days until approval was found. In this case, do you think the
probability of an average mortgage loan-approval time of 46 days or less would be greater
than or less than your answer to Q2 above? Explain your answer in 1-2 sentences.
I think that the number should be higher or the likelihood higher because the SE would we
smaller making the 46 closer to happening in general
4. Go back to the original data (36 loans in sample data). Do you think that the probability that
House4U has a mean approval time of 46 days or less would be greater than or less than your
answer to Q2 if the standard deviation was only 18 days? Explain why or why not in 1-2
sentences.
It would actually be the same based on the calculations of NORMDIST the SD did not affect the
likelihood of it
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QM222 Modeling Business Decisions
Spring 2023
5. One might believe that the time to approve a loan follows a normal distribution. However,
when interest rates are low there are many more applicants. As a result, the distribution of
time-to-close each application is bimodal and looks like the diagram below.
Probability
days until approval
If the average remains 54 days until approval and the standard deviation remains 24 days, would
your answer to Q2 change? Explain in 1-2 sentences.
I don’t think that the answer would change once again. I think that the bimodal structure will
only affect SD and we have proven how that does not affect the likelihood of it happening. Thus,
it doesn’t affect it especially if the components are the same.
6. You decided to look at older sample data (before interest rates dropped so low) and found
that the approval time for individual mortgage loans followed a normal distribution. Using
the same mean of approximately 54 days and standard deviation of 24 days what is the
approximate probability that an individual application for a mortgage will take 78 days or
more?
Its around a 15.8 percent chance that a mortgage above 78 days will occur. I used the normal dist
and calculated how such answers will incur
7. Suppose that the National Association of Mortgage Brokers published a report stating that
the mean time for approval of all mortgage loans in the US is µ=50 days. The CEO of
House4U is concerned that his firm’s approval time is different from the national average.
State the Null Hypothesis he should test.
Null: µ=50 days
8. Now that you have obtained the sample data from House4U, with 95% confidence, does the
data support the CEO’s concern? Show your calculations and conclude with your finding.
The confidence interval of 95 percent falls within the zone of permissibility. Meaning that it
is indeed possible that the average could well be 50 days and not the tested 54. Using the
calculations of such: (54-50)/3.95= 1.01 aprox. The null hypothesis is not rejected.
UPLOAD THIS WITH YOUR ANSWERS AS A WORD OR PDF DOCUMENT.
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