The aim of this worksheet is to let you explore the distributions B(n,p) for various values of the
parameters n and p.  Also, this worksheet will be used to solve exercises from Chapter 5.
 

As summarized at page 368 of the textbook, the  distribution  of the count X of successes in the
binomial setting is called binomial distribution with parameters n and p.

The parameter n is the number of  observations which are all independent,
and p is the probability of succession any one observation.

The possible values of X are the whole numbers from 0 to n.
 
 

Excel calculate both the individual and cumulative binomial probabilities through the "BINOMDIST" function.

Type the first row title and labels   into your Excel worksheet.  The values of the parameter n is inputted in
the cell I1 and that of the parameter p in the cell K1.  The column A list the possible values of X.

In the cell B3 you enter the formula to compute the individual probabilities for X ~ B(n,p).  The BINOMDIST windows
give clear explanations for each argument:
 
 
 

Now
Drag down the formula to the row having in the column  A  the value of the parameter n.

Next you make the probability histogram for X.   A nice chart can be produced with the Chart Wizard's "Column" first
subtype.  You should use the column A for the (X)-axis labels:
 
 

Click Finish and then adjust the width of the bars.   You should get something like:

Now,

Change the value of the parameter p to 0.1, 0.2, ... , 0.9.  Observe how the probabilities for the values of X change
with p.  Also observe the symmetry for the pairs (0.1, 0.9), (0.2, 0.8), etc.  You should check the values from the column B with
the corresponding ones from the table from the textbook.

Warning.  If you change the parameter n you have to adjust the column B and the entries in the Chart Wizard.

Here is an example with n = 25:
 

Next let set the worksheet for computing probabilities like P(a < X <= b) for X~B(n,p) and 0 <= a <= b <= n.
You will use this part of the worksheet to solve exercises from Ch. 5.

Set the labels as in the image below and then use the "cumulative" option of the BINOMDIST function to compute
the probability with the inputted parameters in the cell J3.

To visualize the selected values of the distribution X~B(n,p) you should copy the selected values from the column B to the
column C and then add a new series to your chart.  You should get something like:

Change the value of the parameter p to 0.1, 0.2, ... , 0.9.  Observe how the probability computed in the cell J3
changes with p.
 

Question .   For Ex. 5.6 of the textbook hand in two Excel printouts:

The first should show a chart like this with the cell containing the answer to part (a) with font size 16.

The second should answer part (b) with a chart like  the last one .