Statistics for Decision- Making in Business - Maricopa Community ...

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This amount looks very good! In fact, on average, the company received . This customer is definitely profitable to the company, in the long-run. Of course, we know that an accident could occur the first year, in which an $800 loss would be incurred right away. Notice what we really did here. We took the sum of the amounts and divided by 100: ( ) By properties of a common denominator we can write: ( ) ( ) ( ) ( ) ( ) ( ) In reality, we multiplied each monetary value by its respective probability. This idea is known as expected value, since it is what we expect to happen in the long-run. Expected Value and Random Variable Expected value is the expected, or average, quantity that should occur in the long-run, provided that each quantity occurs with a certain probability. Suppose there are quantities, , each of which occurs with a certain probability, , respectively, then the expected value, denoted , - is , - A capital , , is used to denote what is called a discrete random variable, a variable that takes on one of (a natural number of) values with a certain probability. This value is defined by what it measures in the given situation. Importantly, , that is, we must account for 100% of all possible outcomes in order for the expected value to be meaningful. Statistics for Decision-Making in Business © Milos Podmanik Page 136
An expected value is actually not something terribly new. To see this more explicitly, suppose a student earns three test scores: 95%, 80%, and 85%. Then the average percentage is: Observe that we can use properties of fractions to separate the sum as follows: ( ) ( ) ( ) While one-third in this situation is not a probability (since the scores have already been ) “ ” -third of the overall class grade. Example 1: A company sells consumer electronics, such as televisions, stereos, and computers. For each product, the company offers the consumer a warranty that protects any problems that might occur within the first two years, with the exception of accidental damage and theft. For a particular television that runs $1200, it offers a 2-year warranty for $ ’ determines that 3% of these televisions malfunction each year. Is the company offering the warranty at a profitable price Explain your answer and define the random variable. SOLUTION: We should determine what will happen, on average. We first see that the warranty is a 2-year warranty and the defect rate is for one year. If 3% malfunction each year, then 6% of all televisions are expected to malfunction within the first two years. This means that the company will make $175 with a 94% probability and will lose $1200- $175=$1025 with a 6% probability, since it will still receive the payment, but will have to either replace the product or offer a credit to the consumer. Letting , -, is , then the expected amount to be gained, or , - ( ) Statistics for Decision-Making in Business © Milos Podmanik Page 137
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Statistics for Decision- Making in
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A Note to Students This book is far
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6.3 Confidence Interval for ̂ 202
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which has undergone no additional r
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of transporting such an animal. Not
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Although far from last, we will con
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Account Type Revenue ($) New $5,296
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For the present time, we‟ll proce
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Row Labels Average of Revenue ($) M
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(SOURCE: Essentials of Modern Busin
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1.3Statistics in Excel When conduct
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We can make it a bit more presentab
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For measures such as the range, Exc
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We get: We can do the same for Old.
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Chapter 2 Visual Representations of
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We now have to enter a formula for
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We know from the data that this val
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Alternatively, it is possible to in
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16 14 12 10 8 6 Series1 4 2 0 SD D
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Selected the copied graph. In Chart
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2. The following data represents pe
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Frequency 2.2 Visualizing Quantitat
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You can either choose to have Excel
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If we had additional variables, the
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Select PivotChart and select the fi
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Frequency To make solid black lines
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Relative Frequency Histogram of Cal
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a. Using Excel, find the mean and r
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̅ ̅ account for this discrepancy,
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2.3.2 Percentile Another useful too
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2.3.4 Rank What if, on the other ha
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Check the “Analysis ToolPak” an
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You‟ll immediately notice that a
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̅ 2.4 Descriptive Statistics - Var
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√ ∑( ̅) √ √ This is what w
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This gives us a nice measure of how
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We can immediately see the mean and
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Lastly, a normal curve is the most
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Frequency ̅ Histogram of TV's Owne
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58.3 34.6 35.5 45.4 38.6 63.8 53.9
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Chapter 3 Probability and Decision
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Proportion of Rainy Days 1.2 Propor
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Page 89 and 90: 3.2 Joint Probability In the previo
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Page 99 and 100: 3.3 Probability of Unions Imagine t
Page 101 and 102: Physical .20 .10 .30 Mental .40 .30
Page 103 and 104: SOLUTION: We first arrange this inf
Page 105 and 106: Homework Problems - 3.3 1. A gaming
Page 107 and 108: 3.4 Conditional Probability In many
Page 109 and 110: ) : The Arizona Cardinals make it t
Page 111 and 112: We could just as well have written,
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Page 121 and 122: 1 st Bushel 2 nd Bushel U1 U1 U2 U2
Page 123 and 124: Which, in its final state gives: Th
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Page 139 and 140: Where The expected value is: , - (
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Page 143 and 144: Probability 0.7 0.6 0.5 0.4 0.3 0.2
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Page 147 and 148: For men, we see that the most frequ
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Page 151 and 152: Example 1: A fair-two sided coin is
Page 153 and 154: ( ) ( ) ( ) ( ) Example 2: A fair,
Page 155 and 156: Expected Value of a Binomial Random
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Page 159 and 160: Probability For instance, we see th
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Page 163 and 164: Suppose we wish to find ( ), that i
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Page 173 and 174: As you can see, this is a difficult
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Page 183 and 184: Thus, the standard deviation would
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2.4 to 2.5 2.5 to 2.6 2.6 to 2.7 2.
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The Central Limit Theorem (CLT) has
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can set this up in our applet by ha
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3) We cannot use this sample to cal
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Thus, we need to find the lower and
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We see that the standard deviation
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√ The lower limit is: √ And the
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following data was collected on the
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{ So, we have a set of twenty 1‟s
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DULY CAUTIONED: The assumptions her
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Homework Problems -6.2 1. In a samp
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Since this is a mathematical questi
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Example 3: Many older homes have el
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Hypothesis Test Conclusion Test Say
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Hypothesis Test Conclusion Since yo
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SOLUTION: d. A generic conclusion s
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9. Based on the “Structure of a H
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1.2 Descriptive VS. Inferential Sta
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Relative Frequency 35% 30% 25% 20%
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Symmetric: 35 30 25 20 15 10 5 0 10
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Repair Cost Mean 971 Standard Error
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el freq Nitrous Oxide (thous. Tons)
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Probability Pizza Size Distribution
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e. ( ) f. ; the average response ti
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2. a. The long-run proportion of al
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e. 20% of all children are expected
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e. The middle 50% score between abo
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6. This is the probability that we
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