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

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( ) And this is precisely what we have written for the denominator! In simplified notation, ( ) Calculator Clinic – Using Permutations To evaluate a permutation, 1. first enter in your home screen 2. Go to and move to the left to the PRB tab. 3. Select 2: nPr. This will return you to your home screen. 4. Enter and press ENTER TIP: Sometimes the value of the numerator or denominator is so large that the computer throws an overflow error. It is advisable to enter the entire probability in, numerator and denominator to avoid this potential problem. Let‟s now consider the case where it is important to Statistics for Decision-Making in Business © Milos Podmanik Page 124
Combination – Order Does NOT Matter (Eliminated) If order is to be eliminated (in cases where order is not important), then the number of ways to select things from the given is called a combination and is denoted: ( ) NOTE: ( ) , that is, factorial is not distributable!! Subtract first, then use factorial. Additionally, the factorial of a product is not the product of factorials, that is, . For our numerator, we had selected 2 uncontaminated bushels from a total of 18 uncontaminated bushels, eliminating the number of repeats, which was 2, or . According to our new notation, this can be written as: ( ) And this is precisely what we have written for the numerator! For our denominator, we had selected 2 (general) bushels from a total of 20 (general) bushels, since we want to know the total number of ways 2 objects can come out of 20, order aside. ( ) And this is precisely what we have written for the denominator! In simplified notation, ( ) Calculator Clinic – Using Combinations Follow the steps for finding permutations, but in Step 3, use 3: nCr instead. Example 2: Every week, Cori stops at Chipotle Mexican Grill for lunch with his colleagues. Each time, he drops a business card into the fishbowl for a chance to win lunch for his entire office. After the seventh visit, Cori begins to wonder his chances of winning. He estimates that there are approximately 40 cards in the bowl. If two were to be drawn, what is the probability Cori wins both draws Statistics for Decision-Making in Business © Milos Podmanik Page 125
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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
Page 73 and 74: We can immediately see the mean and
Page 75 and 76: Lastly, a normal curve is the most
Page 77 and 78: Frequency ̅ Histogram of TV's Owne
Page 79 and 80: 58.3 34.6 35.5 45.4 38.6 63.8 53.9
Page 81 and 82: Chapter 3 Probability and Decision
Page 83 and 84: Proportion of Rainy Days 1.2 Propor
Page 85 and 86: This means that if samples of HFCS
Page 87 and 88: Are we confident in accusing a lung
Page 89 and 90: 3.2 Joint Probability In the previo
Page 91 and 92: Company 1 Choices Y Y Y Y Y Y Y Y N
Page 93 and 94: There is less than a 1% chance that
Page 95 and 96: We can now see that the situation i
Page 97 and 98: sequence, one ball is chose at rand
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,
Page 113 and 114: That is, the probability that the c
Page 115 and 116: This can happen in one of two ways:
Page 117 and 118: f. All numerical red cards are remo
Page 119 and 120: 3.5 Combinations and Permutations R
Page 121 and 122: 1 st Bushel 2 nd Bushel U1 U1 U2 U2
Page 123: Which, in its final state gives: Th
Page 127 and 128: ( ) There is only a .9% chance that
Page 129 and 130: 1. Are repeats/replacements allowed
Page 131 and 132: Object 4 Object 5 Also notice that
Page 133 and 134: e. 2. Your classmate was absent whe
Page 135 and 136: 3.6 Expected Value Imagine that you
Page 137 and 138: An expected value is actually not s
Page 139 and 140: Where The expected value is: , - (
Page 141 and 142: SOLUTION: We first note that there
Page 143 and 144: Probability 0.7 0.6 0.5 0.4 0.3 0.2
Page 145 and 146: Statistics for Decision-Making in B
Page 147 and 148: For men, we see that the most frequ
Page 149 and 150: So, we had 10 trials and wanted to
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
Page 157 and 158: f. What is the probability that g.
Page 159 and 160: Probability For instance, we see th
Page 161 and 162: Density 0.25 Time Speng Waiting in
Page 163 and 164: Suppose we wish to find ( ), that i
Page 165 and 166: Density Resulting in a standard dev
Page 167 and 168: Density Without going into detail h
Page 169 and 170: a. What is the probability that the
Page 171 and 172: Statistics for Decision-Making in B
Page 173 and 174: As you can see, this is a difficult
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We wish to know the area of the sha
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We can easily find that the probabi
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In the second section, we can check
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Chapter 6 Sampling Distributions an
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Thus, the standard deviation would
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1.7 to 1.8 1.8 to 1.9 1.9 to 2 2 to
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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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5. b. This might indicate that the
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̅ We have that ̅ and √ . So our
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6. This is the probability that we
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