# Math Help - Statistics Normal to Binomial Approximation

1. ## Statistics Normal to Binomial Approximation

65% of children (ages 12-17) keep their savings in a savings account. You randomly select 45 children and ask each if he or she keeps his or her savings in a savings account. Find the probabiltiy that at most 25 children will say yes.

I'm quite certain this is a normal to binomial approximation, in which the mean = np and the standard deviation is the square root of npq. This would make the mean = 29.25 and the standard dev = 3.2.

I started solving by finding the continuity correction for 25, making it P(x is less than/equal to 24.5). I then found the corresponding z-score with the formula: z = (x - mean) / standard dev. So I did (24.5-29.25) / 32 = -1.48. However, when I matched this z score with the corresponding area on the Normal Distribution Tables, it did not equal 0.1210, which is the correct answer from the answer key. I would appreciate it if someone could explain how to find the answer of 0.1210. Thanks very much for your time.

2. it should be $25.5$

you have to add $0.5$ instead of subtract it and you get $\Phi(-1.17) = 0.1210$