MATH 1200: Finding Binomial Probabilities

The Problem

If 60% of all women are employed outside the home, find the probability that in a sample of 20 women,

a). Exactly 15 are employed outside of the home.
b). At least 10 are employed outside of the home.
c). At most 5 are not employed outside of the home.

Symbolic Solution | Calculator Solution

a). Exactly 15 are employed outside the home.
Symbolic Solution

From the text of the problem, we see that n = 20, the number in the sample. If we call "success" as "women employed outside the home" we have p = 60% = 0.6. We also have that x = 15. Thus q = 1 - p = 0.4. Since

we have

Thus, P(15) .075

Calculator Solution

From the text of the problem, we see that n = 20, the number in the sample. If we call "success" as "women employed outside the home" we have p = 60% = 0.6. We also have that x = 15.

There is a program on the TI83/84 that does the above formula for us. It is of the form: binompdf(n, p, x).

Press 2nd VARS [DISTR], arrow down to 0:binompdf( and press ENTER. Now we enter the parameters n, p, x. Type 20,.6, 15) and then press enter.

Thus, P(15).075