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

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( ) ( ) We rewrite our formula with the above defined components: . / ( ) This is known as the binomial probability density function, or binomial pdf. To make this more clear, we first define a random variable, . In the case of a binomial experiment (one in which there are two possible outcomes for each trial), the set listing all possible values that can be achieved (between 0 and the number of trials). For example, if in coin tosses, then * +. That is, between 0 and 10 heads can possibly be achieved in 10 tosses of the coin (though not all have the same probability). To indicate a binomial pdf calculation, we often write: The probability that takes on successes is . / ( ) , or, ( ) . / ( ) We summarize a binomial pdf below, along with the necessary assumptions to use this. Binomial Probability Density Function (pdf) If the following assumptions are met: 1) An experiment is carried out with trials, 2) Each trial can result in only one of two possible values: a success or a failure, 3) The probability of a success in each trial is (it is always the same), and 4) Each trial is independent of all other trials (the outcome of one trial in no way affects the outcome of any other trial), then the experiment is a binomial experiment and the probability of calculated by successes can be ( ) . / ( ) Statistics for Decision-Making in Business © Milos Podmanik Page 150
Example 1: A fair-two sided coin is tossed 10 times. The goal is to get 8 heads. a) In how many different ways can this event occur b) Verify that all assumptions are met to conduct a binomial experiment. c) What is the probability of this event SOLUTION: a) Since there are 10 events and 8 successes desired, there are: b) . / 1) There are trials 2) Each outcome is either a head (success) or a tail (failure) 3) The probability of success on any trial is 4) One toss does not influence the outcome of any other toss Thus, all assumptions have been met. c) ( ) . / ( ) ( ) Thus, there is about a 4.3% of tossing 8 heads in 10 tosses. The fact that the probability of getting 8 heads in 10 tosses is higher than getting 9 heads in 10 tosses should not surprise us. Getting 9 heads is a rather extreme request. Getting 8 heads, while still extreme, is a bit more likely. Let‟s now build the probability distribution histogram for . We first display the probabilities in a table below by applying the binomial pdf: Statistics for Decision-Making in Business © Milos Podmanik Page 151
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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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Page 105 and 106: Homework Problems - 3.3 1. A gaming
Page 107 and 108: 3.4 Conditional Probability In many
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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:
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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 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: , - (
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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 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 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
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Page 181 and 182: Chapter 6 Sampling Distributions an
Page 183 and 184: Thus, the standard deviation would
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Page 189 and 190: The Central Limit Theorem (CLT) has
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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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6. This is the probability that we
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