Download CHAPTER 6 NORMAL DISTRIBUTIONS

CHAPTER 6 NORMAL DISTRIBUTIONS
CONTROL CHARTS (SECTION 6.1 OF UNDERSTANDABLE STATISTICS)
Although the TI-83 Plus or TI-84 Plus does not have a control chart option built into STAT PLOT, we can
use one of the features in STAT PLOT combined with the regular graphing options to create a control chart.
Example
Consider the data from the data files in the Appendix regarding yield of wheat at Rothamsted Experiment
Station over a period of thirty years. Use the TI-83 Plus or TI-84 Plus to make a control chart for this data using
the target mean and standard deviation values.
Yield of Wheat at Rothamsted Expreiment Station, England (data file Tscc01.txt)
The following data represent annual yield of wheat in tonnes (one ton = 1.016 tonne)
for an experimental plot of land at Rothamsted Experiment Station U.K. over a period
of thirty consecutive years.
Source: Rothamsted Experiment Station U.K.
We will use the following target production values:
target mu = 2.6 tonnes
target sigma = 0.40 tonnes
1.73
1.66
1.36
1.19
2.66
2.14
2.25
2.25
2.36
2.82
2.61
2.51
2.61
2.75
3.49
3.22
2.37
2.52
3.43
3.47
3.20
2.72
3.02
3.03
2.36
2.83
2.76
2.07
1.63
3.02
First we enter the data by row. In list L1 put the year numbers 1 through 30. In list L 2 put the corresponding
annual yield. Again, read the data by row.
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Part I: TI-83 Plus and TI-84 Plus Guide
Then press y [STAT PLOT] and select 1:Plot1.
Highlight On. Select scatter diagram for type, L1 for Xlist, and L 2 for Ylist. Select the symbol you
like for Mark.
Next Press o.
For Y1 enter the target mean. In this case, enter 2.6.
For Y2 enter the mean + 2 standard deviations. In this case, enter 2.6 + 2(.4).
For Y3 enter the mean – 2 standard deviations. In this case, enter 2.6 – 2(.4).
For Y4 enter the mean + 3 standard deviations. In this case, enter 2.6 + 3(.4).
For Y5 enter the mean – 3 standard deviations. In this case, enter 2.6 – 3(.4).
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37
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Technology Guide Understandable Statistics, 8th Edition
The last step is to set the graphing window. Press p. Since there were 30 years, set Xmin to 1
and Xmax to 30. To position the graph in the window, set Ymin to –1 and Ymax to 5.
When you press s, the control chart appears.
LAB ACTIVITIES FOR CONTROL CHARTS
1. Look in the Appendix and find the data file for Futures Quotes for the Price of Coffee Beans
(Tscc04.txt). Make a control chart using the data and the target mean and target standard deviation given.
Read the data by row. Are there any out-of-control signals? Explain.
2. Look in the Appendix and find the data file for Incidence of Melanoma Tumors (Tscc05.txt). Make a
control chart using the data and the target mean and target standard deviation given. Read the data by row.
Are there any out-of-control signals? Explain.
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Part I: TI-83 Plus and TI-84 Plus Guide
39
THE AREA UNDER ANY NORMAL CURVE (SECTION 6.3 OF
UNDERSTANDABLE STATISTICS)
The TI-83 Plus and TI-84 Plus give the area under any normal distribution and shades the specified area.
Press y [DISTR] to access the probability distributions. Select 2:normalcdf( and press Í.)
Then type in the lower bound, upper bound, µ, and σ in that order separated by commas. To find the area under
the normal curve with µ = 10 and σ = 2 between 4 and 12, select normalcdf( and enter the values as shown.
Then press Í.)
Drawing the normal distribution
To draw the graph, first set the window to accommodate the graph. Press the p button and enter
values as shown.
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40
Technology Guide Understandable Statistics, 8th Edition
Press y [DISTR] again and highlight DRAW. Select 1:ShadeNorm(.
Again enter the lower limit, upper limit, µ, and σ separated by commas.
Finally press Í.
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Part I: TI-83 Plus and TI-84 Plus Guide
41
LAB ACTIVITIES FOR THE AREA UNDER ANY NORMAL CURVE
1. Find the area under a normal curve with mean 10 and standard deviation 2, between 7 and 9. Show the
shaded region.
2. To find the area in the right tail of a normal distribution, select the value of 5σ for the upper limit of the
region. Find the area under a normal curve with mean 10 and standard deviation 2 that lies to the right of
12.
3. Consider a random variable x that follows a normal distribution with mean 100 and standard deviation 15.
Shade the regions corresponding to the probabilities and find
(a) Shade the region corresponding to P(x < 90) and find the probability.
(b) Shade the region corresponding to P(70 < x < 100) and find the probability.
(c) Shade the region corresponding to P(x > 115) and find the probability.
(d) If the random variable were larger than 145, would that be an unusual event? Explain by computing
P(x > 145) and commenting on the meaning of the result.
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