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The Credit Risk Department of a major bank estimates the default rate on loans under $10,000 to be 1%. A random sample of 1100 new loans that are under $10,000 is going to be selected. Let p be the proportion of defaults on the loans in the sample. Answer the following. (If necessary, consult a list of formulas.) (a) Find the mean of p. (b) Find the standard deviation of p. (c) Compute an approximation for P (p <0.02), which is the probability that 2% or fewer of the loans in the sample will be defaulted on. Round your answer to four decimal places.

The Credit Risk Department of a major bank estimates the default rate on loans under $10,000 to be 1%. A random sample of 1100 new loans that are under $10,000 is going to be selected. Let p be the proportion of defaults on the loans in the sample. Answer the following. (If necessary, consult a list of formulas.) (a) Find the mean of p. (b) Find the standard deviation of p. (c) Compute an approximation for P (p <0.02), which is the probability that 2% or fewer of the loans in the sample will be defaulted on. Round your answer to four decimal places.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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The Credit Risk Department of a major bank estimates the default rate on loans under $10,000 to be 1%. A random sample of 1100 new loans that are under $10,000 is going to be selected. Let \( \hat{p} \) be the proportion of defaults on the loans in the sample. Answer the following. (If necessary, consult a list of formulas.) (a) Find the mean of \( \hat{p} \). [Box for answer] (b) Find the standard deviation of \( \hat{p} \). [Box for answer] (c) Compute an approximation for \( P(\hat{p} \leq 0.02) \), which is the probability that 2% or fewer of the loans in the sample will be defaulted on. Round your answer to four decimal places. [Box for answer]
Transcribed Image Text:The Credit Risk Department of a major bank estimates the default rate on loans under $10,000 to be 1%. A random sample of 1100 new loans that are under $10,000 is going to be selected. Let \( \hat{p} \) be the proportion of defaults on the loans in the sample. Answer the following. (If necessary, consult a list of formulas.) (a) Find the mean of \( \hat{p} \). [Box for answer] (b) Find the standard deviation of \( \hat{p} \). [Box for answer] (c) Compute an approximation for \( P(\hat{p} \leq 0.02) \), which is the probability that 2% or fewer of the loans in the sample will be defaulted on. Round your answer to four decimal places. [Box for answer]
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