The shipping costs for fresh fruit items have been estimated and assigned the probabilities shown below. The expected value of the shipping costs is closest to: (a) $36.33 (b) $39.21 (c) $41.28 (d) $45.11 Shipping Cost, $ 34 38 55 Probability 0.22 0.31 0.47
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The shipping costs for fresh fruit items have been
estimated and assigned the probabilities shown
below. The expected value of the shipping costs is
closest to:
(a) $36.33 (b) $39.21
(c) $41.28 (d) $45.11
Shipping Cost, $ 34 38 55
Probability 0.22 0.31 0.47
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- The Kwik Klean car wash loses $250 on rainy days and gains $1200 on non rainy days. If the probability of rain is 0.13, what is the expected net profit?(c) The price of a 14 oz cup of coffee in Sunshine cafés is a random variable C with an expected value of $3.00 and a standard deviation of $1. At any given shop, the price doesn't vary, but it varies independently across shops. Tomorrow morning, you plan to buy two 14 oz cups of coffee from the same shop while your friend plans on buying two from two different shops. (i) How much do you expect to spend on coffee tomorrow and with what standard deviation? (ii) How much do you expect your friend to spend and with what standard deviation? (iii) Who do you think has a better idea and why?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?
- Royalties received by an investor in an oil well vary according to the price of oil. Data collected from stripper wells in a West Texas oilfield were used to develop the royalty probability relationships shown. (a) Is the variable discrete or continuous as shown? (b) What is the expected value of royalty income, E(RI), per year (c) What are the chances that royalty income will be at least $10,500 per year? (d) Use a spreadsheet to plot the probability distribution of RI with the information shown. Royalties, $/Year 6000 8500 9500 10,500 12,500 15,500 Probability 0.10 0.21 0.32 0.24 0.09 0.04Times 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.What is the probability of P(Z< -1.07)
- A new product’s sales and profits are uncertain. The marketing department has predicted that sales might be as high as 9000 units per year with a probability of 15%. The most likely value is 6000 units annually. The pessimistic value is estimated to be 3500 units annually with a probability of 25%. Manufacturing and marketing together have estimated the most likely unit profit to be $33. The pessimistic value of $26 has a probability of 0.25, and the optimistic value of $37 has a probability of 0.3. Construct the probability distributions for sales and unit profits.The probability distribution for the number of automobiles sold during a day (x) at Bob Iron Motors is as follows. x f(x) 0 0.001 1 0.007 2 0.034 3 0.099 4 0.188 5 6 0.220 7 0.136 8 0.055 9 0.015 10 0.001 21 The expected value of the number of automobiles sold is, a 5.20 b 5.31 c 5.42 d 5.53The demand for a product of Carolina Industries varies greatly from month to month. The probability distribution in the following table, based on the past two years of data, shows the company's monthly demand. Unit Demand Probability 300 400 500 600 0.20 0.30 0.35 0.15 (a) If the company bases monthly orders on the expected value of the monthly demand, what should Carolina's monthly order quantity be for this product? (b) Assume that each unit demanded generates $70 in revenue and that each unit ordered costs $50. How much will the company gain or lose in a month (indoitars) if it places an order based on your answer to part (a) and the actual demand for the item is 300 units?
- a) There is small parking lot behind a Floral Shop that has two parking lot spaces. Let X be the number of cars parked in the parking lot at midday. The probability distribution of X is given by x 0 2 3 P(X = x) 0.1 0.25 a 0.35 (i) What is the value of a? (ii) (iii) What is the probability that there will be at most 1 car in the parking lot? Calculate the expected number of cars in the parking lot at midday (iv) Calculate the variance.The probability distribution for the number of automobiles sold during a day (x) at Bob Iron Motors is as follows. x f(x) 0 0.001 1 0.007 2 0.034 3 0.099 4 0.188 5 6 0.220 7 0.136 8 0.055 9 0.015 10 0.001 24 Suppose the gross profit per vehicle sold is $1,820 . The standard deviation of gross profit is, a $3,105.50 b $3,029.76 c $2,955.86 d $2,883.77A 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 0.25