MBA 662 HW 4 - Tara McAllister (1)

Problem 1 Day Number of stoves sold a. 1 5 and cumulative distribution 2 2 to the rows area, and coun 3 2 4 3 5 3 6 6 probability distribution 7 4 cumulative distributio 8 4 Expectation of X = 9 3 10 5 11 5 b. Currently, Jessica is keeping 12 4 units. How frequent does J 13 4 14 4 Jessica is selling approxima 15 4 12.22826087 16 2 It will take approximately 1 17 4 or twice a month 18 3 19 5 20 2 c. The profit for each stove so 21 3 full refund. The returned un 22 3 stove sales? (Hint: define a 23 3 24 4 Y = Profit 150 25 5 P(Y=xi) 0.95 Expectation (Y) 145 533.6 the daily ex If we define a random varia

n for X in a tabular format, (this can be done by doing a quick pivot table, dragging "number unit sold" nt how many days are associated with each number of unit sold.) and calculate the Expectation of X. X=xi 0 1 2 3 4 5 6 out of 25 days 0 0 4 7 8 5 1 n of X P(X=xi) 0 0 0.16 0.28 0.32 0.2 0.04 on of X P(X<=xi) 0 0 0.16 0.44 0.76 0.96 1 = 3.68 g 50 units in stock, and she will place another order of 45 units once the inventory level drops to 5 Jessica place an order each month (25 work days)? (Hint: use the notion of expectation.) ately 3.68 units a day 12.23 days for Jessica to sell 45 units, so Jessica should place an order on every 12 work days old is $150. For each unit sold, there is a 5% chance that the unit will be returned by the customer for nit will then be sold to a discount store at a lower profit of $50. What is the expected daily profit from another variable Y as the actual profit for each unit sold taking into account the returns.) 50 0.05 xpected profit for stove sales able X as the number of units sold per day , use these data to estimate the probability distribution

Problem 2 Identify probability distribution for each of the following cases. Are they Binomial, Poisson, Normal, or Uni a. A professor receives, on average, 24.7 e-mails from students the day before the midterm exa Poisson Distibution Event of interest - student emails; Given area of opportunity - day before the midterm exam The probability of one student sending an email is independent of another student sending a you have the average number and the probabilty and also the probability that those events a b. company has an unusually high number of false insurance claims. It is known that the industr insurance claims. They believe the number of these 100 that are false will yield the informatio Binomial Distribution The sample consists of a fixed number of claims Each observation is classified as a legitimate claim or a false claim c. What type of probability distribution will most likely be used to analyze the number of blue c chip bags. When the production process is in control, the average number of blue chocolate c chocolate chips. Poisson Distribution Event of interest - blue chocolate chips per bag; Given area of opportunity - production proce The Poisson Distribution is used to model the number of events that occur in a fixed space wh d. A company has 125 personal computers. The probability that any one of them will require rep type of probability distribution? Binomial Distribution Sample consists of a fixed number of personal computers e. A multiple-choice test has 30 questions. There are 4 choices for each question. A student who chance of getting at least 20 questions right? Binomial Distribution fixed number of questions with 4 possible choices for each question What type of probability distribution will the consulting firm most likely employ to analyze th

iform distribution. Why? am. To compute the probability of receiving at least 10 e-mails on such a day, he will use what type of prob an email are happening ry proportion for false claims is 3%. The consulting firm has decided to randomly and independently sample on the company desires. chocolate chips per bag in the following problem? The quality control manager of a candy plant is inspecting chips per bag is 6.0. The manager is interested in analyzing the probability that any particular bag being ins ess here the events are rare or randomly occuring pair on a given day is 0.025. To find the probability that exactly 20 of the computers will require repair on a o has not studied for the test decides to answer all questions randomly. What type of probability distributio he insurance claims in the following problem? An insurance company has called a consulting firm to determ

Problem 3 - 5.15 Past records indicate that the probability of online retail orders that turn out to be fradulent is 0.08. Suppose that, on a given day, 20 online retail orders are placed. Assume that the number of online retail orders that turn out to be fradulent is distributed as a binomial ra a. what are the mean and standard deviation of the number of online retail orders that turn out mean sample size * probability 1.6 st dev sqrt(mean * (1 - prob)) 1.21326007 b. what is the probability that zero online retail orders will turn out to be fraudulent? P(x=0) 0.18869333 c. what is the probabilty that one online retail order will turn out to be fraudulent? P(x=1) 0.32816231 d. what is the probability that two or more online retail orders will turn out to be fraudulent? P(X>=2) 0.48314436

X - (# of trails, chance of success) 0 0.18869333 number of trials - 20 1 0.32816231 andom variable. chance of fraud - 0.08 2 0.27109061 3 0.14143858 t to be fraudulent? 4 0.05227078 5 0.01454491 6 0.00316194 7 0.0005499 8 7.77036E-05 9 9.00911E-06 10 8.61741E-07 11 6.81218E-08 12 4.44273E-09 13 2.37738E-10 14 1.03364E-11 15 3.59528E-13 16 9.76978E-15 17 1.99893E-16 18 2.897E-18 19 2.65172E-20 20 1.15292E-22

rs. number of trials 1000 chance of mishandling 2.19

Problem 3 - 6.9 Consumers spent an average of $15.30 on a meal at a restaurant in 2014. Assume that the amount spent on a restaurant meal is normally distributed and that the standard deviatio a. what is the probability that a randomly selected person spent more than $16? P(x>16) 0.18762017 b. what is the probability that a randomly selected person spent between $10 and $12? P(10<=x<=12)also, P(x<=12) - P(x<=10) 0.00402459 0.04947147 0.04544688 c. between what 2 values will the middle 95% of the amounts fall? 19.219928 11.380072 95% of the amounts will fall between $11.38 to $19.22

Problem 3 - 6.25 A study of the time spent shopping in a supermarket for a market basket of 20 specfic items showed an ap What is the probability that the shopping time will be… a. between 25 and 30 minutes? P(25<x<30) 0.25 b. less than 35 minutes? P(x<35) 0.75 c. what are the mean and standard deviation of the shopping time? mean 30 standard deviation 5.77350269

pproximately uniform distribution between 20 minutes and 40 minutes. x uniform distr a 20 b 40