Business Statistics - 240
At many airports, a traveler entering the U.S. is sent randomly to one of several stations where his passport and visa are checked. If each of the 19 stations is equally likely, can the probabilities of which station a traveler will be sent to be modeled with a uniform model?
A uniform probability model CAN be used to model this variable
A commuter must pass through 5 traffic lights on her way to work and will have to stop at each one that is red. She estimates the probability model for the number of red lights she hits, as shown below.
PART A : Compute the mean, or expected value, of the random variable X. = 2.45 PART B : Compute the standard deviation of the random variable X = 1.4
A bicycle shop plans to offer 2 specially priced children's models at a sidewalk sale. The basic model will return a profit of $110 and the deluxe model $160. Past experience indicates that sales of the basic model will have a mean of 5.1 bikes with a standard deviation of 1.3, and sales of the deluxe model will have a mean of 3.7 bikes with a standard deviation of 0.5 bikes. The cost of setting up for the sidewalk sale is $400. Complete parts a) through d).
PART A : Define the random variables and use them to express the bicycle shop's net profit. A : B=number of basic bicyclessold, D=number of deluxe bicycles sold, Profit = 110B + 160D - 400 PART B : What is the mean of the net profit? = 753 PART C : What is the standard deviation of the net profit? = 163.86 PART D : Do you need to make any assumptions in calculating the mean? D : No, no assumptions are made in calculating the mean PART E : Do you need to make any assumptions in calculating the standard deviation? B : Yes, the sales must be independent
A collector is selling a quantity of action figures at an online auction. He has 17 cowboy figures. In recent auctions, the mean selling price of similar figures has been $12.06, with a standard deviation of $1.44. He also has 11 Indian figures which have had a mean selling price of $10.09, with a standard deviation of $0.89. His insertion fee will be $0.60 on each item, and the closing fee will be 7.75% of the selling price. He assumes all will sell without having to be relisted. Complete parts a through d.
PART A : Define your random variables, and use them to create a random variable for the collector's net income. Let Xi be the price of ith cowboy figure sold, Yi be the price of the ith Indian figure sold. Choose the correct net income below. Net income = (X1....) -28(0.60) - 0.0775 (X1...) PART B : Find the mean (expected value) of the net income. E(net income) = $274.72 PART C : Find the standard deviation of the net income. Ignore the insertion and closing fees in this calculation SD(net income) : $6.63 PART D : Do you have to assume independence for the sales at the online auction? Explain. A : Yes, independence must be assumed in order to compute the standard deviation
Which of these situations fit the conditions for using Bernoulli trials? Explain. a) You are rolling 8 dice and need to get at least two 2s to win the game. b) We record the distribution of favorite colors of customers visiting our website. c) A committee consisting of 10 men and 11 women selects a delegation of 6 to attend a professional meeting at random. What is the probability they choose all women? d) A study found that 42% of M.B.A. students admit to cheating. A business school dean surveys all the students in the graduating class and gets responses in which cheating was admitted by 271 of 539 students.
PART A : Does each roll of one die fit the conditions for using Bernoulli trials? Check all that apply C : Yes, all conditions are met PART B : Does each customer of our website fit the conditions for using Bernoulli trails? Check all that apply. D : No, there are more than two possible outcomes PART C : Does the choice of each person on the committee fit the conditions for using Bernoulli trails? Check all that apply. A : No, there are two outcomes, but the probability changes with each trail C : No, multiple trials are not independent PART D : Does each student in the graduating class fit the conditions for using Bernoulli trails? Check all that apply. C : Yes, all the conditions are met
Given independent random variables, X and Y, with means and standard deviations as shown, find the mean and standard deviation of each of the variables in parts a to d. a) 4X b) Y+2 c) X+Y d) X−Y
PART A : Find the mean and standard deviation for the random variable 4X Mean : 4 (90) = 360 Standard Deviation : 4 (13) = 52 PART B : Find the mean and standard deviation for the random variable Y+2. Mean : (Y + 2) = 15 + 2 Standard Deviation : (Y + 2) SD(Y) = 2 = 2 PART C : Find the mean and standard deviation for the random variable X+Y. Mean : X + Y = 90 + 15 = 105 Standard Deviation : X + Y = Square roots = 169 / 4 = 169 + 4 = 173 (square root) = 13.1529 PART D : Find the mean and standard deviation for the random variable X−Y. Mean : X - Y = 90 - 15 = 75 Standard Deviation = 169 + 4 = square rooted
The probability model below describes the number of repair calls that an appliance repair shop may receive during an hour. Complete parts a and b below. Repair Calls 0 / 1 / 2 / 3 Probability 0.2 / 0.3 / 0.3 / 0.2
PART A : How many calls should the shop expect per hour? = The shop should expect 1.5 calls per hour PART B : What is the standard deviation? = The standard deviation is 1.02
Mary is deciding whether to book the cheaper flight home from college after her final exams, but she's unsure when her last exam will be. She thinks there is only a 10% chance that the exam will be scheduled after the last day she can get a seat on the cheaper flight. If it is and she has to cancel the flight, she will lose $200. If she can take the cheaper flight, she will save $100. a) If she books the cheaper flight, what can she expect to gain, on average? b) What is the standard deviation?
PART A : If she books the cheaper flight, what can she expect to gain, on average? = On average, she can expect to gain $70 PART B : What is the standard deviation? = The standard deviation is $90
A commuter finds that she waits an average of 11.8 seconds at each of three stoplights, with a standard deviation of 6.2 seconds. Find the mean and the standard deviation of the total amount of time she waits at all three lights. What, if anything, did you assume?
PART A : The mean time she waits at all three lights is __ seconds. = 35.4 PART B : The standard deviation of the time she waits at all three lights is __ seconds. = 10.74 PART C : What, if anything, did you assume? C : It is necessary to assume the wait times at the lights are independent to calculate the standard deviation
A salesman normally makes a sale (closes) on 60% of his presentations. Assuming the presentations are independent, find the probability of each of the following. a) He fails to close for the first time on his sixth attempt. b) He closes his first presentation on his fifth attempt. c) The first presentation he closes will be on his second attempt. d) The first presentation he closes will be on one of his first three attempts.
PART A : The probability he fails to close for the first time on his sixth attempt is = 0.0311 PART B : The probability he closes his first presentation on his fifth attempt is = 0.0154 PART C : The probability the first presentation he closes will be on his second attempt is =0.24 PART D : The probability the first presentation he closes will be on one of his first three attempts is = 0.936
A company's employee database includes data on whether or not the employee includes a dependent child in his or her health insurance. a) Is this variable discrete or continuous? b) What are the possible values it can take on?
PART A : This variable is = DISCRETE PART B : Choose the correct answer below C : yes or no
A company that manufactures large LCD screens knows that not all pixels on their screen light, even if they spend great care when making them. They know that the manufacturing process has a blank pixel rate, on average, of 4.4 blank pixels in a sheet 8 ft by 10 ft that will be cut into smaller screens. They believe that the occurrences of blank pixels are independent. Their warranty policy states that they will replace any screen sold that shows more than 2 blank pixels. Suppose the number of blank pixels can be modeled by a Poisson distribution. Complete parts a) through d) below.
PART A : What is the mean number of blank pixels per square foot? The mean is 0.055 pixels PART B : What is the standard deviation of blank pixels per square foot? = The standard deviation is 0.234 pixels PART C : What is the probability that a 2 ft by 3 ft screen will have at least one defect? = A 2ft by 3ft screen will have at least one defect with probability 0.281 PART D : What is the probability that a 2 ft by 3 ft screen will be replaced because it has too many defects? = A 2ft by 3 ft screen will need to be replaced with probability 0.005
Suppose that the probabilities of a customer purchasing 0, 1, or 2 books at a book store are 0.2, 0.2, and 0.6, respectively. What is the expected number of books a customer will purchase?
The expected number of books that the customer will purchase is = (0 * 0.2) + (1 * 0.2) + (2 * 0.6) = 0 + 0.2 + 1.2 = 1.4
Suppose that the probabilities of a customer purchasing 0, 1, or 2 books at a book store are 0.2, 0.4, and 0.4, respectively. What is the standard deviation of this customer's book purchases?
The standard deviation of the customer's book purchases is = 0.75
