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

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Probability We see clearly that the number of successes with the highest probability is 2 or 3. The histogram follows: 0.300 0.250 0.200 Rolling a 1 or 2 in 8 Die Rolls 0.150 0.100 0.050 0.000 1 2 3 4 5 6 7 8 9 Successes Notice that this distribution is not symmetric. It is said to have to be skewed to the right, since the distribution has its probabilities heavily concentrated towards the left and so has a tail to the right (hence the name) Distribution Types There are three single-peaked (called unimodal) distributions, as illustrated below: 1.1.3 Expected Value Statistics for Decision-Making in Business © Milos Podmanik Page 154
Expected Value of a Binomial Random Variable It can be shown that the expected value of , or the average number of successes we expect to see, given that is a binomial random variable, is: ( ) Example 3: Pristine Air Conditioning uses a digital phonebook to call homeowners in a large city regarding a $55.99 A/C maintenance special. In an hour, a telemarketer can make about 10 calls. If the probability that a randomly called homeowner signs up for the maintenance special is 0.40, a. what is the probability that telemarketer gets at least 80% of his hourly customers to sign up b. Represent this probability in a histogram. c. Find and explain the expected value of the random variable. SOLUTION: a) We first need to determine whether or not this is a binomial probability. Since the probability of success is 0.40 on every one of 10 trials and we assume that the size of the population does not significantly impact the percentage of success (as removing one potential customer from the pool reduces the size of the callable population), we conclude that this is a binomial experiment. Thus, the number of called homeowners that accept the offer. We want to know the probability of getting business from 8, 9, or all 10 of the called individuals. We want: ( ) ( ) ( ) because each of these accounts for disjoint pieces of the sample space. With and , we have: . / ( ) ( ) . / ( ) ( ) . / ( ) ( ) Thus, there is only about a 1.23% chance that the A/C company gets the business of 80% or more of the homeowners called. b) The histogram is below. The probability we are looking at is the sum of probabilities after 7 successes: Statistics for Decision-Making in Business © Milos Podmanik Page 155
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Statistics for Decision- Making in
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A Note to Students This book is far
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6.3 Confidence Interval for ̂ 202
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of transporting such an animal. Not
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Although far from last, we will con
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Account Type Revenue ($) 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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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 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
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Page 131 and 132: Object 4 Object 5 Also notice that
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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
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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
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Page 157 and 158: f. What is the probability that g.
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 167 and 168: Density Without going into detail h
Page 169 and 170: a. What is the probability that the
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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
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Page 197 and 198: We see that the standard deviation
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Page 201 and 202: following data was collected on the
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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. The middle 50% score between abo
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5. b. This might indicate that the
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6. This is the probability that we
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