1 1. For a group of customers in a bank you are given the following information. P(a customer will default on current credit charges) = .07 Total credit charges for a customer is Normal($350, $100) If a customer defaults, assume 20% of the charges can be recovered; the

remaining is written off as bad debt

Answer the following. Where appropriate, show the formulae you entered in Excel and

then show the answer corresponding to that.

A. What is the chance that a customer will default and produce a write-off of more

than $250 in debt? Note that to get this answer, the event “a customer will

default” and the event “Write-off is greater than $250” are independent. (10 pts)

B. If there are 500 customers in this group, what are the mean and standard deviation

of the number of customers that meet the description from the above question? (5

pts)

C. Again, assuming 500 customers, what is the chance at least 25 of them will meet

the description in the first question above? (10 pts)

D. Suppose nothing is recovered from default—the whole amount is written off as

bad debt. Show in two cells the Excel formulae you will sequentially enter to

simulate the total amount of bad debt from 500 customers: cell 1 will have a

binomial formula; cell 2 will have a normal distribution formula. For the latter, if

you have a random sample of “n” customers that defaults from the value in cell 1,

then you have to redefine the mean ($350) and SD ($100) of the normal

distribution given above. This idea and calculation are from your prerequisite

STA301! (5 pts)

2. You observe a sequence of parts from a production line. These parts use a

component supplied by two different suppliers, S1 and S2. Assume 60 parts are from Supplier 1 and 40 from Supplier 2, for a total of 100

parts P(Part works properly if component is from S1) = .95 P(Part works properly if component is from S2) = .98 Use 500 replications in your simulation in Excel What is the probability that at least 97 parts work properly (30 pts)?

3. This is a conceptual question involving simple expected value calculation you

learned in your prerequisite course, STA301. (10 points)

A standardized test consists of only multiple choice questions, each with 5

possible choices. You want to ensure that a student who randomly guesses on each

question will obtain an expected (or mean) score of zero. How would you accomplish this? Show the algebra in your answer! What is the key mathematical principle you learn in answering this

question? Would an instructor use this principle on a test? Why or why not? 2

SOLUTION TEMPLATE for Assignment 1 (10% of Total Grade): Type written answers only!

Minus 15 points if you hand write anything; State numerical answers up to 3 rd decimal place

NAME: Section Time: 1.

A. State the probability equation:

State the Excel Formula:

State the numerical answer:

B. State the probability equation:

State the Excel Formula:

State the numerical answer:

C. State the probability equation:

State the Excel Formula:

State the numerical answer: 2.

A. State the probability equation:

State the Excel Formula:

State the numerical answer:

B. State the mathematical equation for mean:

State the mathematical equation for SD:

State the numerical answers for mean and SD:

C. State the probability equation:

State the Excel Formula:

State the numerical answer:

D. State the Excel Formula for number who will default and then provide the

corresponding numerical answer:

State the definition of the new Normal Mean and Normal SD:

State the numerical answer of the new Normal Mean and Normal SD:

State the Excel Formula for the total amount of charges, and then provide the

corresponding numerical answer: 3.

Good from S1 Good from S2 Total Good At least 97 Good 3

Rep 1 F1 F2 F3 F4 State the Excel formula used in cell F1:

State the Excel formula used in cell F2:

State the Excel formula used in cell F3:

State the Excel formula used in cell F4:

Finally, below provide the Excel formula used to calculate the overall probability (based

on 500 replications), and the corresponding numerical answer to the question: what’s

the chance at least 97 parts are good: 4.

Show the algebraic equation you set up to find the expected value, and then state the

number of points you set for each correct answer and wrong answer to get the numerical

expectation of zero: State the key statistical principle you learn from the above: Explain why an instructor would or would not use this approach on a multiple-choice

test: