Deck 18: Decision Theory and the Normal Distribution

Question 1

In a normal distribution, there is a greater chance of seeing an observation one standard deviation above the mean than one standard deviation below the mean.

Answer 1

False

Question 2

σ has a greater impact on the shape of the normal distribution than μ.

Answer 2

True

Question 3

In many business break-even analyses, the normal distribution can be used to estimate demand.

Answer 3

True

Question 4

σ describes the dispersion or spread of the normal distribution.

Question 5

Using EOL requires one to identify the loss per unit when sales are below the break-even point.

Question 6

In determining the EOL with the normal distribution, as D increases, the unit normal loss integral, N(D), also increases.

Question 7

If a variable other than demand is random (price, fixed or variable cost, etc.)the problem of break-even analysis becomes much more complex.

Question 8

μ has a greater impact on the shape of the normal distribution than σ.

Question 9

If the price/unit were doubled at the same time that the variable cost/unit doubled, the break-even point would be

A)unaffected.
B)doubled.
C)halved.
D)increased by a factor of four.

Question 10

The binomial distribution can be used when there are a small number of states of nature and/or alternatives.

Question 11

When computing Z for a break-even analysis: as σ increases, Z decreases.

Question 12

The price/unit minus the variable cost/unit is

A)per unit profit.
B)the break-even point.
C)the Z value.
D)EOL.

Question 13

EVPI and minimum EOL are equivalent.

Question 14

If fixed costs were to double unexpectedly, the break-even point would be

A)unaffected.
B)doubled.
C)halved.
D)increased by a factor of four.

Question 15

A Z score of 0.5 means that the observation equals the mean.

Question 16

In many business decisions, there are numerous states of nature and/or alternatives.These problems are best handled by

A)constructing a large decision table and using Excel.
B)constructing a large decision tree.
C)using the normal distribution.
D)using the integral loss distribution.

Question 17

Cost volume analysis deals only with costs while break-even analysis deals with both costs and revenues.

Question 18

If variable cost/unit falls, the fixed cost rises, and the selling price/unit remains constant, the break-even point

A)stays the same.
B)decreases.
C)increases.
D)Unable to say without more information.

Question 19

A positive Z score for customer demand means that the company will realize a profit.

Question 20

The unit normal loss integral can be used to compute EOL.

Question 21

Harry Sprague makes custom bowling balls.His fixed cost is $255,000, variable cost is $45.50, and selling price is $55.50.To what value must he reduce his variable cost if he wants a break-even point of 10,000 units?

A)$39
B)$37
C)$35
D)$30

Question 22

If the fixed costs are $15,000 and the variable cost/unit is $35 and the break-even is 100 units, what is the selling price per unit?

A)$185
B)$110
C)$65
D)$130

Question 23

An Asian fusion cafe sells an average of 1240 wasabi lattes with a standard deviation of 80.What level of customer demand represents the 65th percentile for wasabi lattes?

A)1209
B)1253
C)1271
D)1293

Question 24

If the fixed costs are $15,000 and the variable cost/unit is $35 and the selling price is $375 units, what is the break-even?

A)$38.18
B)$40.22
C)$42.16
D)$44.12

Question 25

When using the normal distribution to approximate demand, which of the following is not true?

A)We assume demand is normally distributed.
B)We assume demand is a random variable.
C)We assume 50 percent of the time demand is less than the mean.
D)We assume the fixed cost follows a normal distribution.

Question 26

Given the following opportunity loss function, determine the loss when 500 units are sold. Opportunity loss = 2 (600 - X)for X ≤ 600, otherwise 0.

A)200
B)600
C)1,200
D)0

Question 27

Given the following opportunity loss function, determine the loss when 600 units are sold. Opportunity loss = 2 (600 - X)for X ≤ 600, otherwise 0.

A)2
B)600
C)1,200
D)0

Question 28

A food truck sells an average of 1240 black bean lattes with a standard deviation of 80.What level of customer demand represents the 15th percentile for black bean lattes?

A)1066
B)1157
C)1183
D)1204

Question 29

Tony B.is attempting to start a landscaping business.He estimates that to break even, he will need about 150 customers.He believes that he will lose approximately $500 per customer for each customer fewer than the 150.At the moment, he believes there is an 80% probability that he will be able to secure between 130 and 170 customers, and that there is a 50/50 chance that demand will be greater than 160 customers.What is the mean or expected number of sales?

A)130
B)150
C)160
D)170

Question 30

Given the following opportunity loss function, determine the loss when 400 units are sold. Opportunity loss = 3 (1,000 - X)for X ≤ 1,000, otherwise 0.

A)1,200
B)600
C)3
D)1,800

Question 31

If the fixed costs are $10,000 and the variable cost/unit is $10 and the break-even is 100 units, what is the selling price per unit?

A)$200.
B)$110.
C)$59.
D)Unable to say without more information.

Question 32

For volumes greater than the break-even point, the opportunity loss function is

A)a function of K, the loss per unit.
B)0.
C)dependent on how much the volume is greater than the break-even point.
D)halved.

Question 33

The opportunity loss function gives us information about

A)the variable costs we should expect to incur.
B)cost and revenues as a function of demand.
C)the number of products we should expect to sell.
D)profits lost if demand is less than the break-even point.

Question 34

Loss/unit when sales are below the break-even point is equal to

A)(total revenue - total cost)/number of units.
B)selling price.
C)price/unit minus variable cost per unit.
D)EOL.

Question 35

The Truck Toys Company manufactures traditional wooden toy trucks.It has determined its variable cost/unit to be $1.50/truck.Fixed costs, however, are quite high because old equipment is used in the manufacturing process and costly packaging is needed to market the toy trucks.The fixed costs are estimated at $11,000/month.The company sells their toy trucks at a price of $7.75/each.How many toy trucks must be sold annually to break even?

A)1,760 toy trucks
B)5,500 toy trucks
C)21,120 toy trucks
D)1,879 toy trucks

Question 36

Demand is estimated to be 800 units.If Z is taken to be 1.5, when the estimated average demand is 400 units, determine σ for these data.

A)71,111
B)-71,111
C)266
D)-266

Question 37

If the break-even volume doubles, this suggests that

A)variable cost has increased.
B)fixed cost has increased.
C)selling price has decreased.
D)the variable or fixed costs have increased or selling price has decreased.

Question 38

Given the following opportunity loss function, determine the loss when 1,100 units are sold. Opportunity loss = 3 (1,000 - X)for X ≤ 1,000, otherwise 0.

A)0
B)-300
C)300
D)3

Question 39

Given the following opportunity loss function, determine the loss when 400 units are sold. Opportunity loss = 5 (800 - X)for X ≤ 800, otherwise 0.

A)-1,200
B)2,000
C)0
D)1,800

Question 40

If the fixed costs are $25,000 and the variable cost/unit is $35 and the selling price is $375 units, what is the break-even?

A)67.50
B)69.25
C)71.75
D)73.50

Question 41

Average demand is estimated at 1,200 units/month.It is believed there is a 20% chance for demand to be higher than 1,800.Determine the μ and σ of a normal distribution that estimates demand.

Question 42

Given the following opportunity loss function, determine the loss when 5,000 units are sold.Opportunity loss: 6.5(8,000 - X)for X ≤ 9,000.

Question 43

The parfumerie at Amour Fou projects that the annual worldwide demand for their new fragrance Odeur de Fromage will be normally distributed with a mean of 122 units and a standard deviation of 44.The break-even point is 100 units, and for each unit sold less than that number, the company will lose $750.What is the expected opportunity loss?

Question 44

The IRU Company manufactures traditional wooden pencils.They have determined their variable cost/unit to be $0.012/pencil.Fixed costs, however, are quite high because of old processing equipment and costly packaging.The fixed costs are estimated at $140,000/month.IRU sells their pencils at a price of $13.248/gross.(There are 144 pencils in a gross.)How many grosses of pencils must be sold annually to break even?

Question 45

Determine N(D)for the following D values: 0.01, 0.21, 0.77, and 1.20.

Question 46

Tony B.is attempting to start a landscaping business.He estimates that to break even, he will need about 140 customers.He believes he will lose approximately $500 per customer for each customer fewer than the 140.At the moment, he believes that there is an 80% probability that he will be able to secure at least 130 customers and that there is a 50/50 chance that demand will be greater than 150 customers.He has several marketing research firms offering (for a price, of course)to conduct a survey that will provide additional information regarding the probability of demand.How much should he be willing to spend if he decides to have a survey made?

A)≅ $4,000
B)≅ $3,000
C)≅ $5,000
D)≅ $2,700

Question 47

The computed EOL will be the same as the computed

A)EMV.
B)unit normal loss.
C)break-even point.
D)EVPI.

Question 48

To determine the EOL with the normal distribution

A)one must compute D.
B)one must compute Z.
C)one must use the standard normal table.
D)one must know the EVPI.

Question 49

If D = 1.00, then N(1.00)is approximately

A)0.69000.
B)1.00000.
C)0.08332.
D)0.35090.

Question 50

The break-even point was determined to be 3,000 units/month.Next month begins an increased lease payment for the production facility.The overall effect will be to increase the fixed costs by 10%.How will the break-even point be affected?

Question 51

Jack Spratt makes candlesticks.His fixed cost is $5,000, variable cost is $3.50, and selling price, $8.50.To what value must he reduce his variable cost if he wants a break-even point of 900 units?

Question 52

Given the following opportunity loss function, determine the loss when 7,000 units are sold.Opportunity loss: 6(9,000 - X)for X ≤ 9,000.

Question 53

Don Loprie takes out tiny classified ads in newspapers across the nation.His fixed cost is $13,000, variable cost is $25.50, and selling price, $38.75.To what value must he reduce his variable cost if he wants a break-even point of 900 units?

Question 54

In accordance with their government contract, the break-even point was determined to be 5,000 units/month.Next month begins an increased lease payment for the production facility such that the fixed cost rises to $13,000.If the selling price is $38.75, what is the variable cost?

Question 55

The sales team projects that the annual demand for their new and improved Mediocrity Plus™ product will be normally distributed with a mean of 143,000,000 units and a standard deviation of 27,500,000.The break-even point is 123,000,000 units and for each unit sold less that that number, the company will lose $875.What is the expected opportunity loss?

Question 56

Which of these statements is best?

A)P(loss)= P(break-even < demand).
B)P(profit)= P(demand > break-even).
C)The mean of a distribution is less than or equal to the expected value of the distribution.
D)As σ increases, the spread of a distribution decreases.

Question 57

If D = 1.01, s = 900, K = 10, and the selling price is $11, the EOL is

A)≅ 10,000.
B)≅ 9,100.
C)≅ 736.
D)≅ 810.

Question 58

If the break-even point was estimated to be 500 units when fixed costs are estimated at $1,200/month, what would the EMV be if average demand is estimated at 750?

Question 59

If D = 0.75, s = 500, K = 6, and the selling price/unit = 5, determine EOL.

Question 60

break-even analysis answers what common management question?

Question 61

Briefly describe the opportunity loss function.

Question 62

In terms of fixed costs, variable cost/unit, and the selling price/unit, what is the break-even point?