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Construct the probability distribution for the random variable X, draw the probability histogram, compute and interpret the mean and standard deviation of the probability distribution
The table below represents the data of the enrollment levels in grades 1-8 in the United States in 1997:
(a)
Construct the probability distribution for the random variable X (Hint:%20(Section%206.1%20topic).doc_files/image002.gif){kind=small}
.
(b) Draw the probability histogram.
(c) Compute and interpret the mean of the probability distribution.
(d) Compute the standard deviation of the probability distribution.
|
x(grade level) |
Frequency (In thousands) |
|
1 |
3,755 |
|
2 |
3,689 |
|
3 |
3,597 |
|
4 |
3,507 |
|
5 |
3,458 |
|
6 |
3,493 |
|
7 |
3,520 |
|
8 |
3,415 |
(c)
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(d)
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(a.)
Enter the X-values into L1 and the frequencies into L2. Press 2nd
[QUIT]. Press 2nd [List] and select MATH. Select 5:sum(and type in
L2. Press ENTER. The answer is the sum of the frequencies in L2. Press STAT and
select 1:Edit. Move the cursor to highlight ‘L2’ at the top of the second list
and press ENTER. With the cursor flashing at the bottom of the screen type in L2
%20(Section%206.1%20topic).doc_files/image008.gif){kind=small}
(the sum
of L2). This will convert the frequencies in L2 into probabilities. To confirm
that you now have a probability distribution represented in L1 and L2, press 2nd
[QUIT]. Press 2nd [List] and select MATH. Select 5:sum(and type in
L2. Press ENTER. The answer is the sum of the probabilities in L2. This sum
should equal 1.
(b.) To draw the probability histogram, press 2nd [STATPLOT] and press ENTER. Turn ON plot 1, select Histogram for Type, type in 2nd [L1] for Xlist and 2nd [L2] for Freq. Press WINDOW and set Xmin = 1, Xmax = 9, Xscl = 1, Ymin = 0 and Ymax = .14. Choosing ‘Xmax = 9’ leaves some space at the right of the graph in order to complete the histogram. The Ymax value was selected by looking through the values in L2 and then rounding the largest value UP to a convenient number. Press GRAPH to view the histogram.
(c. –d.) Press STAT and highlight CALC. Select 1:1 Var Stats, press ENTER and press 2nd [L1] , 2nd [L2] ENTER to see the descriptive statistics.