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E270 Hw2name020enter Your Letter Answers Hereaabc1noteba2when Done
E270 HW2 NAME: 0 20 Enter your LETTER answers HERE a a ↓ b c 1 Note: b a 2 When done, using your last name and firstname, save THIS FILE as, a c 3 e270Lastname Firstname HW2 c b 4 (No space between E270 and Last name) b d 5 E-mail to [email protected] as an attachment. a c 6 c d 7 Example: b a 8 e270Smith Adam HW2 YES c b 9 e270 Smith Adam HW2 NO a b 10 c c 11 c c 12 b d 13 d a 14 a c 15 PAY ATTENTION b b 16 d b 17 c a 18 d c Next TWO questions are based on the following: The following table is a probability distribution for the random variable x. x f(x) 5 0... The expected value of x is: E(x) = ______. a 23 b 22 c 21 d The variance of x is: var(x) = _______. a 52 b 81 c 150 d 225 Next 7 questions (3-9) are based on the following: In the table below x denotes the Z-Lab Company’s projected annual profit (in $1,000), along with the probability of earning that profit.
The negative value indicates a loss. x f(x) -50 0..... The probability that Z-Lab will break even, that is, f(x = 0), is, a 0.30 b 0.25 c 0.20 d 0. The probability that Z-Lab will be profitable, that is, f(x > 0), is, a 0.60 b 0.65 c 0.70 d 0. The mean or expected value of Z-Lab’s profit is μ = E(x) = _________. a $108.3 thousand b $106.2 thousand c $102.5 thousand d $100.8 thousand 6 The variance of profit is var(x) = ________ a 11,180.56 b 6,868.75 c 4,185.25 d 3,942. On average, each profit (loss) amounts deviate from the mean profit by ______ thousand. a 115.83 b 105.74 c 82.88 d 76.
Suppose $200 thousand is added to each previously projected profit (loss) level (y = 200 + x), but probabilities are maintained as before. The updated expected value of profit and the variance of profit for Z-Lab, respectively, are: E(y) var(y) a 302.5 6,868.75 b 302.5 7,068.75 c 202.5 6,868.75 d 202.5 7,068. Suppose, instead of adding $200 thousand, each profit (and loss) amount is doubled (y = 2x) and probabilities maintained as before. The new expected value of profit and the variance of profit for Z-Lab, respectively, are: E(y) var(y) a ,738 b ,475 c 102.5 13,738 d 102.5 27,475 Next TWO questions are based on the following: Bob is a salesman. He receives 20% of the price of the item sold as sales commission plus a fixed salary of $400 per week.
Bob's average weekly sales is 15 items with a standard deviation of 5. The average price of items Bob sells is $250. Bob works 46 weeks a year. 10 Bob's average annual earnings is ________. a $49,600 b $50,700 c $51,800 d $52, In the previous question, what is the standard deviation of the annual salary? a $12,100 b $11,500 c $10,900 d $10,300 Next FOUR questions (12-15) are based on the following: Consider a binomial experiment with n = 10 and π = 0.45. Let x denote the number of successes.
12 f(x = 4) = _______. a 0.3173 b 0.2884 c 0.2622 d 0. f(x ≤ 3) = _______ f(x ≥ 3) = _______ a 0..7340 b 0..8104 c 0..9004 d 0.. E(x) = ______. a 6 b 5.5 c 5 d 4. var(x) = ______. a 2.950 b 2.825 c 2.645 d 2. Suppose you are receiving a large shipment of Gizmos. The manufacturing standards provide that 1% of Gizmos turn out defective. You randomly select a sample of n = 50 from each lot and return the shipment if more than 2 are found defective.
The probability of returning a shipment is: a 0.0894 b 0.0358 c 0.0138 d 0. A comprehensive test has 50 multiple questions. Each question has 5 choices. The test score is assigned from the scale of 100. That is, each question is worth 2 points.
If you guessed the answers for all 50 questions, what is the expected score? a 10 b 15 c 20 d 25 Next three questions are based on the following: John is a speed demon. The probability that he will get a speeding ticket while driving to and from work is 30 percent. Answer the next three questions based on a work week (n = 5). 18 What is the probability that John will get 2 tickets during the week (Monday-Friday)? a 0.3087 b 0.3364 c 0.3441 d 0. What is the probability that John will get at least one ticket during the work week? a 0.8985 b 0.8319 c 0.2496 d 0. If each ticket costs John $180 what is the average cost of speeding violation in the 5-day period? a $260 b $270 c $280 d $290 mailto: [email protected]