Yash VaziraniD.OrtmeyerGB 210Fall, 2009

Graded Assignment #2(Due: Friday, 10/30)

My preference is that you work alone in completing this assignment. If, however, you are stumped about how to proceed you may seek help from one other source (me, a friend, a mentor, etc). If you do work with another person, you must tell me who you worked with (i.e. write the name of the person and describe who that person was – fellow student in GB210, other student, instructor, etc). Write this information on your assignment hand-in and explain what their contribution was and how it helped you to understand the problem.

Problems #1 and #2 do not require use of Megastat. Problems #3 and #4 do. Be certain to include your Megastat output for questions 3 and 4.

Problem #1 - Probability (no Megastat needed):Cooper Realty is a small real estate company located in Albany, New York, specializing primarily in residential listings. They recently became interested in determining the likelihood of one of their listings being sold within a certain number of days. An analysis of company sales of 800 homes in previous years produced the following data.

Days Listed Until SoldInitial Asking Price Under 30 31-90 Over 90 TotalUnder $150,000 50 40 10 100$150,000-$199,999 20 150 80 250$200,000-$250,000 20 280 100 400Over $250,000 10 30 10 50

Total 100 500 200 800

(a) If A is defined as the event that a home is listed for more than 90 days before being sold, estimate the probability of A200/800 = 25%

(b) If B is defined as the event that the initial asking price is under $150,000, estimate the probability of B100/800 = 12.5%

(c) What is the probability of 10/800 = 1.25%

(d) Assuming that a contract was just signed to list a home with an initial asking price of less than $150,000, what is the probability that the home will take Cooper Realty more than 90 days to sell?10/100 = 10%

(e) Are events A and B independent? Why or why not?No, A and B are not independent because the probability of A and the probability of A given B are not the same, therefore the events are not independent.

Problem #2 – Expected Value (no Megastat needed): The demand for a product of Carolina Industries varies greatly from month to month. The probability distribution in the following table, based on the past two years of data, shows the company’s monthly demand.

Unit Demand Probability300 .20400 .30500 .35600 .15

(a) If the company bases monthly orders on the expected value of the monthly demand what should Carolina’s monthly order quantity be for this product?445

(b) Assume that each unit demanded generated $70 in revenue and that each unit ordered costs $50. How much will the company gain or lose in a month if it places an order based on your answer in part (a) and the actual demand for the item is 300 units?(50 x 445) – (70 x 300) = -1250 (loss)

Problem #3 - Binomial RV (use MegaStat for this question and include your printout):A university found that 20% of its students withdraw without completing the introductory statistics course. Assume that 20 students registered for the course.

(a) Use W as the binomial random variable for this problem. Explain in words what W represents. Explain why this is an example of a binomial experiment, that is, what conditions have to hold for this to be analyzed as a binomial?

W represents the number of students that withdraw from the class. The experiment is considered binomial since there are two possible outcomes. The students can either withdraw from the class or they can choose to stay in it.

(b) Compute the probability that two or fewer students will withdraw.20.6%

(c) Compute the probability that exactly four will withdraw.21.8%

(d) Compute the probability that more than three will withdraw.58.9%

(e) Compute the expected number of withdrawals.4 withdrawals

Problem #4 – Binomial RV (use MegaStat for this question and include your printout).There is a 14% chance that a Noodles &Company customer will order bread with the meal. Use MegaStat to find the probability that in a sample of 10 customers:

(a) More than five will order bread (greater than 5).001%

(b) Two or fewer will order bread84.55%

(c) None of the 10 will order bread22.13%

(d) Is the probability distribution skewed left or right?Right

L;

20 n0.2 p

    cumulativeX p(X) probability0 0.01153 0.011531 0.05765 0.069182 0.13691 0.206083 0.20536 0.411454 0.21820 0.629655 0.17456 0.804216 0.10910 0.913317 0.05455 0.967868 0.02216 0.990029 0.00739 0.99741

10 0.00203 0.9994411 0.00046 0.9999012 0.00009 0.9999813 0.00001 1.0000014 0.00000 1.0000015 0.00000 1.0000016 0.00000 1.0000017 0.00000 1.0000018 0.00000 1.0000019 0.00000 1.0000020 0.00000 1.00000

1.00000

4.000 expected value3.200 variance

1.789 standard deviation

Group Work

Isaac and I worked together on the Megastat part of the project. He is a classmate in my GB 210 class from the same section. I found questions 3 and 4 challenging, and he helped me with how to go about answering them.