Statistics Binomial Distribution Help.?

If you have a TI-84, you can use the binompdf function--find "binompdf" in the catalog, then type in binompdf(400, 0.4, 170)

how it works: first you want to determine the number of ways this can happen. this is equivalent to 400 C 170, or 400! / 170! (400-170)! (the exclamation mark means factorial, for example 5! would be 5*4*3*2*1) then...

400 C 170 * (0.4)^170 * (0.6)^230

0.4 comes from the prob. that any given smoker acquired the habit by age 14, 0.6 is the probability that they didn't. you're raising it to the power of the times that this given event (started smoking, didn't start smoking) occurred.

hope this helps

Well, for a sample of this size, the Normal approximation to the binomial is perfectly adequate.

Mean for a binomial distribution = np = 400 x 0.4 = 160.

And standard deviation = ?(npq) = ?(400 x 0.4 x 0.6) = 9.7979

So the z-value for X = 170 is (170 - 160) / 9.7979  =  1.0206

and the corresponding value of P(X = 170) is 0.8461 (from the table of areas of the Normal distribution).