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Normal Distribution and Z-Score

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1.The amounts of money requested on home loan applications at a particular bank follow the normal distribution, with a mean of $80,000 and a standard deviation of $24,000. A loan application is received during the day.

By hand:

a. Find the probability that the amount requested amount is $90,000 or more?
b. Find the probability that the amount requested is between $75,000 and $90,000?
c. How much is requested on the largest three percent of loans?
d. How much is requested on the smallest ten percent of the loans?

Note: Use a 0.05 level of significance where needed.

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Solution provided by:
Anwesha Ghosh, MSc
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  • MSc, Osmania University
  • MSc, Indian Institute of Technology - Roorkee (I.I.T.-ROORKEE)
  • BSc, Banaras Hindu University
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