Question

50 percent of all persons in the U.S. population have at least some college education. Choose 10 persons at random. Find the probability of the following. Hint: Use the binom.dist function or the table starting on page 770. Exactly 5 have some college education. At most 5 have some college education.

Answer 1

We can solve this problem with the help of Excel:

We are given with n = 10 person and probability of success, p = 50% = 0.50

Go to Megastat>Probability.

Then go to Discrete Probability Distribution, and it will move on to the binomial distribution.

Select n = 10 and p = 0.50 and press OK.

The output generated is as follows:

		10	n
		0.5	p
			cumulative
	X	P(X)	probability
	0	0.00098	0.00098
	1	0.00977	0.01074
	2	0.04395	0.05469
	3	0.11719	0.17188
	4	0.20508	0.37695
	5	0.24609	0.62305
	6	0.20508	0.82813
	7	0.11719	0.94531
	8	0.04395	0.98926
	9	0.00977	0.99902
	10	0.00098	1.00000
		1.00000
		5.000	expected value
		2.500	variance
		1.581	standard deviation

The bar chart for the data is:

Find the probability of the following:

(a) Exactly 5 have some college education.

From the output, the probability of exactly 5 have some college education is 0.24609.

(b) At most 5 have some college education.

Probability( At most 5 have some college education) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)

= 0.00098 + 0.00977 + 0.04395 + 0.11719 + 0.20508 + 0.24609

= 0.62305