| 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 |
| 19 |
| 20 |
| Next TWO questions are based on the following: |
| The following table is a probability distribution for the random variable x. |
| x | f(x) |
| 5 | 0.10 |
| 20 | 0.60 |
| 35 | 0.30 |
| 1 | The expected value of x is: E(x) = ______. |
| a | 23 |
| b | 22 |
| c | 21 |
| d | 20 |
| 2 | 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 | 0.10 |
| 0 |
| 100 | 0.35 |
| 150 | 0.20 |
| 200 | 0.15 |
| 250 | 0.05 |
| 3 | The probability that Z-Lab will break even, that is, f(x = 0), is, |
| a | 0.30 |
| b | 0.25 |
| c | 0.20 |
| d | 0.15 |
| 4 | The probability that Z-Lab will be profitable, that is, f(x > 0), is, |
| a | 0.60 |
| b | 0.65 |
| c | 0.70 |
| d | 0.75 |
| 5 | 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 | 3,942.55 |
| 7 | On average, each profit (loss) amounts deviate from the mean profit by ______ thousand. |
| a | 115.83 |
| b | 105.74 |
| c | 82.88 |
| d | 76.95 |
| 8 | 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 | 7,068.75 |
| 9 | 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 | 205 | 13,738 |
| b | 205 | 27,475 |
| 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 | $52,900 |
| 11 | 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 | 0.2384 |
| 13 | f(x ≤ 3) = | _______ | f(x ≥ 3) = | _______ |
| a | 0.2660 | 0.7340 |
| b | 0.2394 | 0.8104 |
| c | 0.2660 | 0.9004 |
| d | 0.2394 | 0.7606 |
| 14 | E(x) = ______. |
| a | 6 |
| b | 5.5 |
| c | 5 |
| d | 4.5 |
| 15 | var(x) = ______. |
| a | 2.950 |
| b | 2.825 |
| c | 2.645 |
| d | 2.475 |
| 16 | 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 | 0.0016 |
| 17 | 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 | 0.3717 |
| 19 | 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 | 0.1681 |
| 20 | 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 |
eebazoush
hw2.xlsx
