The Credit Risk Department of a major bank estimates the default rate on loans under $10,000 to be 1%. The bank will make 1100 loans that are under $10,000 next month. Answer the following. (If necessary, consult a list of formulas.)(a)Find the mean of p, where p is the proportion of defaults on the 1100 loans under $10,000 to be made next month. (b)Find the standard deviation of p. (c)Compute an approximation for P≥p0.02, which is the probability that 2% or more of next month's loans under $10,000 will be defaulted on. Round your answer to four decimal places.

Givenpopulation proportion(p)=1%=0.01sample size(n)=1100

Answered: The Credit Risk Department of a major…

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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Question

The Credit Risk Department of a major bank estimates the default rate on loans under

$10,000

to be

. The bank will make

1100

loans that are under

$10,000

next month.

Answer the following. (If necessary, consult a list of formulas.)

(a)Find the mean of

, where

is the proportion of defaults on the

1100

loans under

$10,000

to be made next month.

(b)Find the standard deviation of

(c)Compute an approximation for

P≥p0.02

, which is the probability that

or more of next month's loans under

$10,000

will be defaulted on. Round your answer to four decimal places.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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