Thread: Statistics Normal to Binomial Approximation

Please help me with this question:

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.

it should be

you have to add instead of subtract it and you get