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### Example 5: **Binomial**

It has been stated that about 41% of adult workers have a high school diploma but do not pursue any further education. If 20 adult workers are randomly selected, find the probability that at most 12 of them have a high school diploma but do not pursue any further education. How many adult workers do you expect to have a high school diploma but do not pursue any further education?

Let

Find

Using the TI-83+ or the TI-84 calculators, the calculations are as follows. Go into 2nd DISTR. The syntax for the instructions are

*To calculate (*
If "number" is left out, the result is the binomial probability table.

*To calculate
*
If "number" is left out, the result is the cumulative binomial probability table.

*For this problem:
After you are in 2nd DISTR, arrow down to A:binomcdf. Press ENTER. Enter
20,.41,12). The result is
*

#### Note:

The probability at most 12 workers have a high school diploma but do not pursue any further education is 0.9738

The graph of

The y-axis contains the
probability of

The number of adult workers that you expect to have a high school diploma but not
pursue any further education is the mean,

The formula for the variance is

### Example 6

The following example illustrates a problem that is *not* binomial.
It violates the condition of independence. ABC College has a student advisory
committee made up of 10 staff members and 6 students. The committee wishes to
choose a chairperson and a recorder. What is the probability that the
chairperson and recorder are both students? All names of the committee are put
into a box and two names are drawn *without replacement*. The first name
drawn determines the chairperson and the second name the recorder. There are
two trials. However, the trials are not independent because the outcome of the
first trial affects the outcome of the second trial. The probability of a student on
the first draw is