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

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The area of this region is: Thus, there is an 82% chance that the wait-time is between 0.3 and 4.4 minutes. 5.1.2 Uniform Distribution Continuous Uniform Distribution When the PDF of a random variable is a constant, we call this a uniform distribution. That is, values of the random variable are uniformly distributed. The PDF of a random variable, , whose values are in the interval is: ( ) { The expected value of this random variable is: ( ) The variance of this random variable is: ( ) ( ) Statistics for Decision-Making in Business © Milos Podmanik Page 164
Density Resulting in a standard deviation of: √ ( ) Example 1: The amount of revenue that a farmers market generates on a given Saturday is uniformly distributed between $5,000 and $22,000. SOLUTION: a. Find the PDF for this random variable. b. Find the probability that the between $6,000 and $8,000 is generated. c. Find the expected value of this random variable and explain its real-world meaning. d. Find the standard deviation of this random variable and explain its real-world meaning. a. The lower limit is and the upper limit is . Thus, ( ) This is constant function is only valid for values between 5000 and 22000. It is valued as 0 everywhere else. 0.00007 0.00006 0.00005 0.00004 0.00003 0.00002 0.00001 0 Revenue PDF 5000 22000 Revenue ($) b. We want ( ). The probability will be the length times the width. Statistics for Decision-Making in Business © Milos Podmanik Page 165
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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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This means that if samples of HFCS
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Are we confident in accusing a lung
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3.2 Joint Probability In the previo
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Company 1 Choices Y Y Y Y Y Y Y Y N
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There is less than a 1% chance that
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We can now see that the situation i
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sequence, one ball is chose at rand
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3.3 Probability of Unions Imagine t
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Physical .20 .10 .30 Mental .40 .30
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SOLUTION: We first arrange this inf
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Homework Problems - 3.3 1. A gaming
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3.4 Conditional Probability In many
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) : The Arizona Cardinals make it t
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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 and 124: Which, in its final state gives: Th
Page 125 and 126: Combination - Order Does NOT Matter
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: Suppose we wish to find ( ), that i
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
Page 175 and 176: We wish to know the area of the sha
Page 177 and 178: We can easily find that the probabi
Page 179 and 180: In the second section, we can check
Page 181 and 182: Chapter 6 Sampling Distributions an
Page 183 and 184: Thus, the standard deviation would
Page 185 and 186: 1.7 to 1.8 1.8 to 1.9 1.9 to 2 2 to
Page 187 and 188: 2.4 to 2.5 2.5 to 2.6 2.6 to 2.7 2.
Page 189 and 190: The Central Limit Theorem (CLT) has
Page 191 and 192: can set this up in our applet by ha
Page 193 and 194: 3) We cannot use this sample to cal
Page 195 and 196: Thus, we need to find the lower and
Page 197 and 198: We see that the standard deviation
Page 199 and 200: √ The lower limit is: √ And the
Page 201 and 202: following data was collected on the
Page 203 and 204: { So, we have a set of twenty 1‟s
Page 205 and 206: DULY CAUTIONED: The assumptions her
Page 207 and 208: Homework Problems -6.2 1. In a samp
Page 209 and 210: Since this is a mathematical questi
Page 211 and 212: Example 3: Many older homes have el
Page 213 and 214: 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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