find solutions

1. Find the mean, variance, and standard deviation for the probability density function, f(x)=0.1,0?X?10.Graph the probability density function, then find and graph the cumulative distribution function on the same axes.

2. Find the mean, variance, and standard deviation for the probability density function f(x)=(1/2)e^(?x/2), 0?X Graph the probability density function, then find and graph the cumulative distribution function on the same axes.

3. Find the mean, variance, and standard deviation for the probability density function. ,f(x)=1.5x^2, ?1?X?1 Graph the probability density function, then find and graph the cumulative distribution function on the same axes.

Question:

a) Ms. Shokha wants to make an investment today that will have a future value of $500 one year from today. If she has a choice of a 5% discount rate or a 6% discount rate, which investment should she choose?

b) Calculate the average annual return for a $3,000 investment with an ending price of $5,500 four years later, with no intermediate cash flows.

c) Consider an investment with the following cash flows:

Year

Cash flows

2003

$20,000

2004

$40,000

2005

$25,000

2006

$35.000

What are the most the investor would invest so that the return on the investment is at least 10%?

d) Suppose the expected risk-free asset is 6% and the return on the market is 10%. Further, suppose you have a portfolio comprised of the following securities with equal investments in each:

(i) What is the expected return for each security in the portfolio?

(ii) What is the expected return on the portfolio?

them? (14) Assume a basketball team has a 45%% chance of winning any individual game and that all games are independent of each other Out of their next 5 garnes, what is the probability they win exactly Jok Show work here. (a) 2.20% (b) 18.7% (9) 31.19% (d) 27.6% (15) 20% of students fail Calculus the first time they take it. Assuming independence between students, what is the probability that exactly 3 out of 6 randomly selected Calculus students failed the class the first time? (2) 8.29% (b) 18.694 (c) 27.39% (d) 33.190 play Seeking to estimate the population proportion of American workers with health insurance. researchers collect a sample of 1,|12 people and find that 58%% of them have health insurance. Give a 00" confidence interval for the population proportion of American workers with health insurance. Round values to nearest whole percentage (a) (574%. 590%) (b) (50% 60%) (C) (52%, 64%) (d) (54%. 62%%) (f7) What is the value of z-critical (2*) for a confidence level of 72%%? 191 1 88 (6) 0.58 (0) 1.08 (4)1.528. (15 points) Twenty participants were given a list of 20 words to process. The 20 participants were randomly assigned to one of two treatment conditions. Half were instructed to count the number of vowels in each word (shallow processing). Half were instructed to judge whether the object described by each word would be useful if one were stranded on a desert island (deep processing). After a brief distractor task. all subjects were given a free recall task. The number of words correctly recalled was recorded for each subject. Here are the data: Shallow Processing: 13 12 11 9 11 13 14 14 14 15 Deep Processing: 12 15 14 14 13 12 15 14 16 1'! Perform a hypothesis testing under alpha=0.01. and answer the question: Did the instructions given to the participants significantly affect their level of recall? Chapter 9 . Sales and Operations Planning: Planning Supply and Demand in a Supply Chain 245 CASE STUDY Mintendo Game Girl It is late June, and Sandra Huchim, head of operations at TABLE 9-8 Mintendo, and Bill Smith. head of sales of We "R" Toys, Costs for Mintendo/We "A" Toys are about to get together to discuss production and mar- Item Cost keting plans for the next 6 months. Mintendo is the man- Material cost $12/unit ufacturer of the popular Game Girl handheld electronic Inventory holding cost $2/unit/month game that is sold exclusively through We *R" Toys retail Marginal cost of a stockout $ 10/unit/month stores. The second half of the year is critical to Game Girl's success, because a majority of its sales occur dur- Hiring and training costs $3,000/worker ing the holiday shopping period. Layoff cost $5,000/worker Sandra is worried about the impact that the upcom- Labor hours required 0.25/unit ing holiday surge in demand will have on her production Regular-time cost $15/hour line. Costs to subcontract assembly of the Game Girls are expected to increase. and she has been trying to keep Overtime cost $22.50/hour costs down, given that her bonus depends on the level of Cost of subcontracting $18/unit production costs. Bill is worried about competing toy stores gaining overtime per month. The various costs are shown in share in the handheld electronic game market during the Table 9-8. Christmas buying season. He has seen many companies Sandra, concerned about controlling costs during lose their share by failing to keep prices in line with the the periods of surging demand over the holidays, pro- performance of their products. He would like to maxi- poses to Bill that the price be lowered by $5 for the mize the Game Girl market share in the handheld elec- month of September. This would likely increase Septem- tronic game market. ber's demand by 50 percent due to new customers being Both Sandra's and Bill's teams produce a joint attracted to Game Girl. In addition. 30 percent of each of forecast of demand over the next six months, as shown the following two months of demand would occur in in Table 9-7. September as forward buys. She believes strongly that We "R" Toys sells Game Girls for $50 apiece. At this leveling of demand will help the company. the end of June, the company has an inventory of 50,000 Bill counters with the idea of offering the same Game Girls. Capacity of the production facility is set promotion in November, during the heart of the buying purely by the number of workers assembling the Game season. In this case, the promotion increases Novem- Girls. At the end of June, the company has a workforce ber's demand by 50 percent, owing to new customers of 300 employees, each of whom works 8 hours of regu- being attracted to Game Girl. Additionally, 30 percent of lar time at $15/hour for 20 days each month. Work rules December's demand would occur in November as for- require that no employee work more than 40 hours of ward buying. Bill wants to increase revenue and sees no better way to do this than to offer a promotion during the peak season. TABLE 9-7 Demand for Game Girls Questions Month Demand Forecast 1. Which option delivers the maximum profit for the supply chain: Sandra's plan, Bill's plan, or no promotion plan at July 100,000 all? Assume starting and ending inventory of 0. August 110,000 2. How does the answer change if a discount of $10 must be September 130,000 given to reach the same level of impact that the $5 discount received? October 180,000 3. Suppose Sandra's fears about increasing outsourcing costs November 250,000 come to fruition and the cost rises to $22/unit for subcon- December 300,000 tracting. Does this change the decision when the discount is $573. Let y be a random variable following a normal distribution with mean @ and variance g. What is the pdf function for this distribution? b) Let , = 0 and of = 1, now rewrite the pdf function from (a) using these values in place of the distribution parameters. c) Give a rough sketch of the normal distribution, by showing the curve, indicating where the mean is and what percent of the data falls within +1, +2, and + 3 standard deviations from the mean. 4. Given that z is a standard normal random variable, find the value for z for each situation. a) The area to the left of z is 0.2119. b) The area between -z and z is 0.9030. c) The area between -z and z is 0.2052. d) The area to the left of z is 0.9948