1. Class 05. Using the Normal Intro to Descriptive Statistics
EMBS Section 3.1, 3.2. and first part of 3.3

2. 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

3. You can’t make it skewed. You can’t change the 68/95/99 breakdown.
EMBS Fig 6.4, p 249
You can’t make it skewed.
You can’t change the 68/95/99 breakdown.
It is a pdf (prob density function). The height is probability density. Areas under the curve are probabilities

4. If X~N(μ,σ)
And Y=a+b*X,
Then
Y~N(a+b*μ,b*σ)
Temp(C)~N(10,10)
Temp(F)= 32 + (9/5) Temp(C)
Temp(F)~N(50,18)

5. 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)

6. 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?

7. P(underfilled bottle)
Worksheets….
Lorex Worksheet
Minimum required 10
$186
$148.80
Target
P(underfilled bottle)
Expected Good Cases
Expected Bad Cases
Total Cases
Expected Revenue
10.0
600
10.1
10.2
10.3

8. Fill Test Data Normal(10.2,0.16)?
EXHIBIT 2
LOREX PHARMACEUTICALS
Filling Line Test Results with Target = 10.2
9.89
10.41
10.53
10.20
10.23
10.15
10.17
10.32
10.04
10.48
10.11
10.29
10.35
10.16
10.19
10.00
10.06
10.21
10.22
9.76
10.09
10.12
10.10
10.02
10.36
9.99
10.05
10.07
10.24
10.40
10.27
10.14
10.76
10.13
9.79
10.31
10.47
9.84
9.96
10.30
10.33
9.97
10.42
10.25
10.64
10.01
10.18
10.54
10.37
10.44
9.85
9.91
10.45
10.28
10.03
9.98

9. Fill Test Data Descriptive Statistics Summary Statistics
Amount
Mean
10.198
Standard Error
0.014
Median
10.190
Mode
#N/A
Standard Deviation
0.163
Sample Variance
0.026
Kurtosis
0.771
Skewness
0.245
Range
0.997
Minimum
9.758
Maximum
10.756
Sum
Count
144

10. Fill Test Data Histogram
Bin
Frequency
9.758 1
9.841 2
9.925 3
10.008 10
10.091 17
10.174 33
10.257 36
10.340 14
10.423 16
10.506 7
10.590
10.673
More

11. 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?

12. Completed and extended worksheet
Lorex Worksheet
Minimum 10
$186
$148.80
Target
P(underfilled bottle)
Expected Good Cases
Expected Bad Cases
Total Cases
Expected Revenue
Expected Cost
Expected Contribution
10.0
0.5
300.00
600
$100,440
$28,800
$71,640
10.1
0.266
440.41
159.59
$105,663
$29,088
$76,575
10.2
0.106
536.61
63.39
$109,242
$29,376
$79,866
10.3
0.030
581.76
18.24
$110,922
$29,664
$81,258
10.4
0.006
596.27
3.73
$111,461
$29,952
$81,509
10.5
0.001
599.47
0.53
$111,580
$30,240
$81,340
10.6
0.000
599.95
0.05
$111,598
$30,528
$81,070