The annual commissions per salesperson employed by a retailer of mobile communication devices averaged $43,400, with a standard deviation of $5,000. What percent of the salespersons earn between $37,100 and $47,100? Multiple Choice 27.53% 66.66% 88.26% 33.34%
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- A major credit card company has determined that the amount its customers charge on their accounts is normally distributed with an average of R2800 per month and a standard deviation of R200.What proportion of customers charge more than R2750 per month on their account (rounded off to three decimals)?I am in possession of two coins. One is fair so that it lands heads (H) and tails (T)with equal probability while the other coin is weighted so that it always lands H. Bothcoins are magical: if either is flipped and lands H then a $1 bill appears in your wallet,but when it lands T nothing happens. You may only flip a coin once per period. Theinterest rate is i per period. You are risk-neutral and thus only concern yourself withexpected values (and not variance). For simplicity, in the questions below assumeyou will live forever.1. How much are you willing to pay for such a coin that you know is fair? 2. How much are you willing to pay for such a coin that you know is weighted? 3. I currently own the coins and know which is fair and which is weighted, but youcannot tell which is which. You may make an offer to purchase a coin of yourchoosing, which I am free to accept or reject. What is the most you are willingto offer? Explain how you arrived at this answer.A large number of MBA applicants are given an aptitude test. Scores are normally distributed with a mean of 460 and standard deviation of 80. What is the probability a randomly chosen applicant scores 600 or above in this test? a. 0.5401 b. 0.0401 c. 0.4599 d. 0.0852
- 15 Demand for residential electricity at a certain time period in Hamilton County is normally distributed with a mean of μ = 5595 megawatts (MW) and a standard deviation of σ = 405 MW Due to scheduled maintenance and unexpected system failures in a generating station, the utility company can supply a maximum of x = 6200 MW The probability that the utility will have to purchase electricity from other utilities or allow brownouts is ______. 0.0974 0.0811 0.0676 0.0563A new product has the following profit projections and associated probabilities: Profit Probability $150,000 0.10 $100,000 0.25 $ 50,000 0.20 $0 0.15 -$ 50,000 0.20 -$100,000 0.10 Use the expected value approach to decide whether to market the new product. Because of the high dollar values involved, especially the possibility of a $100,000 loss, the marketing vice president has expressed some concern about the use of the expected value approach. As a consequence, if a utility analysis is performed, what is the appropriate lottery? Assume that the following indifference probabilities are assigned. Do the utilities reflect the behavior of a risk taker or a risk avoider? Profit Indifference Probability $100,000 0.95 $ 50,000 0.70 $0 0.50 -$ 50,000 0.25George has projections for the 3 alternative investments in equity shares (stock): What is the Standard Deviation in portfolio 2?
- GeoMart sells travelers notebooks. Annual demand for these notebooks follows a Normal distribution with an average of 2,100 units and a standard deviation of 850. GeoMart buys these notebooks from its manufacturer for $ 1.50 per notebook and sells them for $ 3. There is an order waiting period of 5 weeks, which elapses from when an order is placed to the manufacturer until it is delivered to GeoMart. The accounting department estimated that the process of placing an order costs $ 2 and recommends that it be apply a 22 percent annual interest to the material for reasons of ‘holding cost’. The cost of not complying with the demand is estimated at 40 cents per unit, in addition to the loss of income (‘profit loss’), both then represent the cost of “loss of good faith” or 'Loss-of-goodwill'. (Conversion: 7 days a week, 52 weeks in a year.) Under this scenario answer the following: a) Assume that you want to minimize costs and determine: the optimal order size, the reorder point, the…the following probability distribution represents the number of people living in a household (x), and the probability of occurrence (p(x). compute the expected value (mean), the variance, and standard deviation for the random variable. calculations for the mean.x 1 2 3 4 5p(x) .33 .29 .27 .07 .04Players would draw a card from a standard 52 card deck. Whatever card they drew determined what they won. If they draw a face card (Jack, King, Queen) then they win $5. If they draw an Ace, they win $15. For all other cards, they win nothing. A. Fill out the probability distribution table with the probabilities of each possible outcome for this game. Round decimals to four places. x $15 $5 $0 P(x) B. What is the expected value of the distribution above? (Round to the nearest cent, two decimal places.) C. If players were charged $2 per game, would they make and average profit on the games over time, or would they take an average loss over time? D. If players were charged $3 per game, would they make and average profit on the games over time, or would they take an average loss over time?
- Times for a surgical procedure are normally distributed. There are two methods.Method A has a mean of 28 minutes and a standard deviation of 6 minutes, whilemethod B has a mean of 32 minutes and a standard deviation of 4 minutes. (a)Which procedure is preferred if the procedure must be completed within 28minutes? (b) Thirty-eight minutes? (c) Thirty-six minutes? Explain your reasoningfully.The weekly salary paid to employees of a small company that supplies part-time laborers averages s800 with a standard deviation of $500. (a) If the weekly salaries are normally distributed, estimate the fraction of employees that make more than $300 per week. (b) If every employee receives a year-end bonus that adds $100 to the paycheck in the final week, how does this change the normal model for that week? (c) If every employee receives a 5% salary increase for the next year, how does the normal model change? (d) If the lowest salary is $300 and the meltian salary is $550, does a normal model appear appropriate?An investment portfolio contains stocks of a large number of corporations. Over the last year the rates of return on these corporate stocks followed a normal distribution with mean 12.2% and standard deviation 7.2%.a. For what proportion of these corporations was the rate of return higher than 20%?b. For what proportion of these corporations was the rate of return negative?c. For what proportion of these corporations was the rate of return between 5% and 15%?