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. The Empirical Rule is a summary of what we have done above. It is a nice ruleof-thumb. 5. a. The distribution would maintain its exact shape, though would be shifted 10 units to the right. b. The distribution would become wider and have a lower peak. This must happen to make sure the area is still 1 when the distribution becomes wider. c. The distribution would become narrower and have a higher peak. If a distribution becomes narrower, its height must increase to maintain an area of 1. d. The mean, , determines where the distribution is centered without altering its shape. The standard deviation, , will make a distribution wide and low-peaked if it large, and will make a distribution narrow and high-peaked if small. 6.1 The Sampling Distribution for ̅ 1. Answers vary 2. Answers vary – emphasis on the ability to have a population distribution with any unknown shape. 3. a. 0.2525 b. 0.2514 c. 0.9044 d. 95.1 and 104.9 4. a. 0.0272 Statistics for Decision-Making in Business © Milos Podmanik Page 240
5. b. This might indicate that the production process is outside of the norm. This type of average is unlikely in a sample of size where The company should investigate why the average thickness of its glass samples is so thick. a. It should be approximately normal, regardless of the distribution of revenues. b. 0.3869 c. The standard deviation of means would change from $6,957 to $4,400. This would change ( ) . This makes sense, since the distribution of means is less spread, and so there will be fewer mean sales amounts beyond $420,000. d. $421,255.50; If the team averages more than this amount for each team member, then they will receive the paid vacation days. 6. We know that , ̅- , so , so √ A person‟s √ √ income varies, on average, by about $2,906.89 from the population average of incomes. 7. a. rooms and rooms (NOTE: be sure to use sdev.p() since this is a population standard deviation we want) b. It should be approximately normal based on the Central Limit Theorem; the sample size of 30 satisfies the minimum required sample size to meet normality assumptions. c. Answers will vary slightly due to sampling variability of the simulation process; , ̅- and , ̅- . We see that , ̅- as expected. We also see that √ √ , which is what we obtained via simulation. d. Answers will vary slightly due to sampling variability of the simulation process; , ̅- and , ̅- . We see that , ̅- as expected. We also see that , which is what we obtained via simulation. √ √ e. Answers will vary slightly due to sampling variability of the simulation process; , ̅- and , ̅- . We see that , ̅- as expected. We also see that , which is what we obtained via simulation. √ √ f. The population standard deviation can be thought of as the distribution of means from a sample of size . That is, , ̅- . Since it is the smallest possible sample size, it will have the highest degree of variability. g. 0.000 or about 0% chance h. As with tossing a coin repeatedly, when something is repeated over-and-over again, the amount of variation in the outcomes becomes relatively small. That is, any mild outliers get averaged in to a large sample of typical values, and its effect is dispersed. In small samples, the opposite holds – deviate values are highly corrosive to the sample mean. √ 6.2 Confidence Interval for ̅ 1. Answers vary Statistics for Decision-Making in Business © Milos Podmanik Page 241
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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,
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That is, the probability that the c
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This can happen in one of two ways:
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f. All numerical red cards are remo
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3.5 Combinations and Permutations R
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1 st Bushel 2 nd Bushel U1 U1 U2 U2
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Which, in its final state gives: Th
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Combination - Order Does NOT Matter
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( ) There is only a .9% chance that
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1. Are repeats/replacements allowed
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Object 4 Object 5 Also notice that
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e. 2. Your classmate was absent whe
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3.6 Expected Value Imagine that you
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An expected value is actually not s
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Where The expected value is: , - (
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SOLUTION: We first note that there
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Probability 0.7 0.6 0.5 0.4 0.3 0.2
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Statistics for Decision-Making in B
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For men, we see that the most frequ
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So, we had 10 trials and wanted to
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Example 1: A fair-two sided coin is
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( ) ( ) ( ) ( ) Example 2: A fair,
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Expected Value of a Binomial Random
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f. What is the probability that g.
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Probability For instance, we see th
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Density 0.25 Time Speng Waiting in
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Suppose we wish to find ( ), that i
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Density Resulting in a standard dev
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Density Without going into detail h
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a. What is the probability that the
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Statistics for Decision-Making in B
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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.
Page 189 and 190: The Central Limit Theorem (CLT) has
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Page 201 and 202: following data was collected on the
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Page 207 and 208: Homework Problems -6.2 1. In a samp
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Page 213 and 214: Hypothesis Test Conclusion Test Say
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Page 219 and 220: 9. Based on the “Structure of a H
Page 221 and 222: 1.2 Descriptive VS. Inferential Sta
Page 223 and 224: Relative Frequency 35% 30% 25% 20%
Page 225 and 226: Symmetric: 35 30 25 20 15 10 5 0 10
Page 227 and 228: Repair Cost Mean 971 Standard Error
Page 229 and 230: el freq Nitrous Oxide (thous. Tons)
Page 231 and 232: Probability Pizza Size Distribution
Page 233 and 234: e. ( ) f. ; the average response ti
Page 235 and 236: 2. a. The long-run proportion of al
Page 237 and 238: e. 20% of all children are expected
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Page 243 and 244: ̅ We have that ̅ and √ . So our
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