# Project #34696 - Statistics

Homework: Midterm

The answers to all questions which are not multiple choice should be in decimal form (i.e. proportions not percentages) and rounded to two values after the decimal point (rounded to the nearest hundredths)

1.) A music store owner finds that 30% of the customers entering the store ask an assistant for help and that 20% of the customers make a purchase before leaving. It is also found that 15% of all customers both ask for assistance and make a purchase.

What is the probability that a customer does at least one of these two things?

2.) Consider the following joint probability table for two random variables X and Y.

 X=1 X=7 X=9 Marginal probability Y=0 0.12 0.10 ? 0.28 Y=2 ? 0.04 0.05 ? Y=6 0.04 ? ? ? Marginal probability 0.21 0.30 ?

What is P(X=9 and Y≥2)?

3.) A personnel officer for a firm that employs many part time salespeople tries out a sales aptitude test on a large sample of employees: 40% of employees show high aptitude on the test and 12% of the employees both show high aptitude and achieve good sales records. The firm s experience shows that 30% of all employees achieve good sales. Let A be the event shows high aptitude and let B be the event achieves good sales . What is the probability of not achieving good sales given that an employee shows high aptitude on the test?

4.) X, Y, and Z are random variables. Var(X) = 10, Var(Y) = 20, Z = Y - 2X. If X and Y are independent, what is Var(Z)?

5.) Consider a population of 1000 people, 400 of whom are college graduates. It is known that 150 of the college graduates earn at least \$30,000 per year, and 100 of the non-college graduates make at least \$30,000 per year.

What is the probability that a randomly chosen person makes at least \$30,000 per year?

If a randomly chosen person is observed to make at least \$30,000 per year, what is the probability that this person is a college graduate?

If a randomly chosen person is observed to make less than \$30,000 per year, what is the probability that this person is not a college graduate?

6.) Suppose 5% of the microchips produced by a leading microchip manufacturer are defective. An inspector inspects 10 microchips.

What is the probability that all 10 microchips in the sample are not defective?

What is the probability that at most 9 microchips are defective?

7.) A portfolio has an expected return of 0.11 with a variance of 0.01. Assume that the return of the portfolio is normally distributed. What is the probability that you obtain a return exceeding 15%?

8.) The weight of parcels received at a warehouse loading dock is normally distributed with a mean of 300 lbs. and a standard deviation of 50 lbs. What is the weight w such that 20% of the parcels are heavier than w?

9.) Dristar is a supplier of energy drinks, and the company aims at determining the monthly stocking plan to cater to the demand in DC in the summer months. The company can stock 20000 cartons, or 40000 cartons, or 60000 cartons in its warehouses. Each carton, if sold, fetches a profit of \$9 to the company. However, each unsold carton at the end of the month incurs a loss of \$5. The demand in DC is uncertain. Two scenarios, i.e. favorable and unfavorable, are considered. In the favorable scenario that happens with probability 0.6, the demand is estimated to be 60000 cartons and, in the unfavorable scenario that happens with probability 0.4, the demand equals 20000 cartons. You, as a manager, have been asked to come up with an inventory plan that maximizes profits for the company.

What is the expected demand for energy drinks in the summer months in DC?

Calculate the standard deviation of the demand.

Using the expected profit as decision criterion, what is the expected profit of the optimal plan?

A marketing research firm called PerfectPred can provide you with perfect information about the demand scenario, i.e., whether it is favorable or not. What is the maximum amount you accept to pay for that information?

 Subject Mathematics Due By (Pacific Time) 07/03/2014 12:00 am
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