1. ## probability

In June 2003, approximately 45% of a workforce were women. In a random sample of 20 workers:

a) What is the probability that six are women?
b) What is the probability that there were 12 or more men?

2. Originally Posted by brumby_3
In June 2003, approximately 45% of a workforce were women. In a random sample of 20 workers:

a) What is the probability that six are women?
b) What is the probability that there were 12 or more men?

Are you familiar with the binomial distribution?

3. ## RE

You mean the table? Yes.

4. Originally Posted by brumby_3
In June 2003, approximately 45% of a workforce were women. In a random sample of 20 workers:

a) What is the probability that six are women?
b) What is the probability that there were 12 or more men?

As Mr. Fantastic said, this follows a binomial distribution. For problem a we have a probability of success (p) = 0.45 where p is the probability of a person being a woman. The number of trials is 20 which we denote as (n). Finally, we want (k), where k is the number of successes. In problem a, a success is a person being a woman. So we want P(X = 6) where X denotes the binomial distribution.

Go here to my binomial lesson and plug in 20, 0.45, 6 and press the appropriate button:

Binomial Distribution

Follow the math on the green chalkboard section. I get an answer of 0.0746 or 7.46% that out of 20 people, EXACTLY 6 are women.

Problem b is similar. N = 20. But now, we want men, not women. So 1 - 0.45 = 0.65. If the probability of being a woman is 0.45 on each person chosen, then it's 1 - 0.45 = 0.65 to be a man. Now, the problem asks for P(X >= 12) This is the same as asking for P(X > 11). 12 or more men is the same as greater than 11 men.

So our k for this problem becomes 11, since we want 12 or more. Enter 11 for k and press the P(X > k) button. I get 0.7624 or 76.24. There is a lot of math on the chalkboard. It calculates P(X=0) all the way through P(X = 11). Since it is a greater than probability, it takes 1 - P(X<=11) to get our answer.

Read through the math and let me know if you have questions.