Class 05. Using the Normal Intro to Descriptive Statistics
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Transcript of Class 05. Using the Normal Intro to Descriptive Statistics
Class 05. Using the NormalIntro to Descriptive Statistics
EMBS Section 3.1, 3.2. and first part of 3.3
What we learned last class
• To love the NORMAL distribution?– IT IS FLEXIBLE
• Parameter μ lets you center it anywhere.• Parameter σ lets you specify the width (variance,
uncertainty)– If X is highly variable, pick a large σ
– NORMDIST makes probability calculations easy.• No need for converting x to z in order to use the table in the
book. No need for NORMSINV[(x-μ)/σ].– It approximates the binomial when n is big
• Just set μ=n*p and σ = [n*p*(1-p)]^.5
EMBS Fig 6.4, p 249
You can’t change the 68/95/99 breakdown.
You can’t make it skewed.
It is a pdf (prob density function).
The height is probability density.
Areas under the curve are
probabilities
If X~N(μ,σ)And Y=a+b*X,
ThenY~N(a+b*μ,b*σ)
Temp(C)~N(10,10)
-20 -10 0 10 20 30 40
Temp(F)= 32 + (9/5) Temp(C)
-4 14 32 50 68 86 104
Temp(F)~N(50,18)
Case: Lorex Pharmaceuticals
• Lorex produces Linatol (liquid medicine for high blood pressure)– Sold in 10-ounce bottles.– 600*12 = 7,200 fill attempts per shift– Linatol costs them $0.40 per ounce to make.– Bottles filled to more than 10 ounces get sold for
$186 per case of 12.– Bottles under-filled get sold as seconds at a 20%
discount ($148.8 per case)
Case: Lorex Pharmaceuticals
• The Filling Machine has an adjustable target. Test have shown that the fill amounts will be independent (across fill attempts) and– Normally distributed– μ = target– σ = 0.16 fluid ounces
• In other words (symbols?)– X ~ N(target,0.16)
What target should they use?
Worksheets….
Lorex Worksheet Minimum required 10
$186 $148.80
Target P(underfilled bottle)Expected Good
CasesExpected Bad
Cases Total CasesExpected Revenue
10.0 600
10.1 600
10.2 600
10.3 600
Fill Test DataNormal(10.2,0.16)?
EXHIBIT 2LOREX PHARMACEUTICALS
Filling Line Test Results with Target = 10.2
9.89 10.41 10.53 10.20 10.23 10.1510.17 10.17 10.32 10.04 10.48 10.1110.29 10.35 10.16 10.16 10.17 10.1910.00 10.06 10.21 10.22 9.76 10.2210.04 10.19 10.09 10.12 10.06 10.1010.35 10.17 10.02 10.36 10.17 9.9910.05 10.07 10.32 10.24 10.04 10.4010.19 10.27 10.14 10.07 10.41 10.7610.21 10.13 10.11 10.40 10.27 10.209.79 10.24 10.20 10.29 10.00 10.31
10.53 10.14 10.35 10.21 10.23 10.1610.47 9.84 9.96 10.10 10.11 10.2310.24 10.36 10.30 10.23 10.19 10.1710.17 10.11 10.33 10.19 9.97 10.0010.15 10.42 10.36 10.19 10.05 10.1110.06 10.16 10.17 10.29 10.12 10.3010.13 10.21 10.15 10.25 10.33 10.6410.04 10.01 10.14 10.18 10.18 10.1010.20 10.25 10.07 10.42 10.54 10.2310.37 10.44 10.37 9.85 9.91 10.4510.24 10.44 10.40 10.45 10.28 10.1710.03 10.44 10.25 10.37 10.23 10.1910.01 10.13 10.24 10.22 9.98 9.9810.20 10.29 10.03 10.19 9.99 10.13
Fill Test DataDescriptive StatisticsSummary Statistics
Amount
Mean 10.198Standard Error 0.014Median 10.190Mode #N/AStandard Deviation 0.163Sample Variance 0.026Kurtosis 0.771Skewness 0.245Range 0.997Minimum 9.758Maximum 10.756Sum 1468.542Count 144
Fill Test DataHistogram
Bin Frequency9.758 19.841 29.925 3
10.008 1010.091 1710.174 3310.257 3610.340 1410.423 1610.506 710.590 310.673 1More 1
9.7589.841
9.925
10.008
10.091
10.174
10.257
10.340
10.423
10.506
10.590
10.673More
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15
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Histogram
Frequency
Bin
Freq
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Assignment for class 06• Find some numerical data• Get it into excel in one column with a label at the top• Data Analysis (File, Options, Addins, Go, check analysis
ToolPak, okay)– Descriptive Statistics
• Check “summary statistics”
• One sheet– A brief description of the data and where you got it.– A printout (or hand copy) of the summary statistics– A brief answer to the question…could these data have come
from a normal distribution…why or why not?
Completed and extended worksheet
Lorex Worksheet Minimum 10
$186 $148.80
Target P(underfilled bottle)Expected Good
CasesExpected Bad
Cases Total CasesExpected Revenue
Expected Cost
Expected Contribution
10.0 0.5 300.00 300.00 600 $100,440 $28,800 $71,640
10.1 0.266 440.41 159.59 600 $105,663 $29,088 $76,575
10.2 0.106 536.61 63.39 600 $109,242 $29,376 $79,866
10.3 0.030 581.76 18.24 600 $110,922 $29,664 $81,258
10.4 0.006 596.27 3.73 600 $111,461 $29,952 $81,509
10.5 0.001 599.47 0.53 600 $111,580 $30,240 $81,340
10.6 0.000 599.95 0.05 600 $111,598 $30,528 $81,070