Question

A coin is weighted so that the probability of obtaining a head in a single toss is .4. If the coin is tossed 25 times, what is the probability of obtaining fewer than 10 head? For this problem, I found the mean and standard deviation first. I got 10 for the mean and 2.45 for the standard deviation. Then I used the formula p(x<10) ---> (z<10-10/2.45) = 0. Then I used the table at the back of my textbook and got 0.5000. But my textbooks says my answer is wrong. It says that the correct answer is .4207.

Answer 1

I'm confused. How is it .4207 and not .5000?

Answer 2

what method are you using to find the mean and SD, they can't be right.

Long way:
you want ...
C(25,0) (.4)^0 (.6)^25 + C(25,1)(.4)(.6^24) + .... + C(25,9((.4^9)(.6^16)
=

Answer 3

I used n times p for the mean and the square root of npq for the standard deviation