As you
realized when working with the BD-worksheet ( Ex. 5.6) the "BINOMDIST"
function
works
only for values of n smaller than 1030. For larger values of n
one should use the approximation
of the
Binomial Distribution B(n, p) with the Normal Distribution N(n*p, n*p*(1-p)).
This
worksheet will help you make computations for such large values of n.
Start with the same layout as in the BD worksheet:
Let's add few new features to enable the Normal Approximations computations.
Add the new labels as in the image below.
Then write the corresponding formulas in the cells I3, K3
and
K6. Be sure that you use the
right cell references, like " = $I$1*$K$1 " for the cell I3.
You are now able to do any computation involving the Binomial Distribution.
To visualize Normal Approximation for the
Binomial Distribution let's input in the column C the values of the
Normal
Distribution N(n*p, SQRT(n*p*(1-p))):
In the cell C3 write the formula:
and then drag it down till the row with the value of n in the column A.
Now open the chart wizard and choose the "
line-column" type from the "custom types". Use column
A for the X-axis
labels (the rows from value 0 to the value
n), column C for the values of the Series 1 and column B for
the values of the Series 2.
Warning! You have to adjust the entries when you change the number of trials n.
Here is the chart for
n = 25 and p = 0.4:
As you see in the cells K5:K6 the normal
approximation is not as good as for n = 800. Here n*p = 10 which is
the
very limit at which we can use the normal
approximation.
Change the value of the parameter p to 0.1,
0.2, ... , 0.9. Observe in the cells K5:K6 how the precision
of the approximation
changes with p. The number of trials
being 25 one should NOT use the normal approximation for p < 0.4 (n*p < 10)
or p > 0.6 (n*(1-p) < 10)!
Questions. For Ex. 5.24 hand in three pages of Excel printouts.
They should show the answers
to
the parts (b), (c) and (d). For each part print ONLY the first page
of your NABD worksheet
For
Ex. 5.25 hand in two pages of Excel printouts. They should show the
answers
to
the parts (a) and (b). For each part print ONLY the first page of your
NABD worksheet