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Probability and Statistics

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The proportion of adults living in a small town who are college graduates is estimated to be p = 0.6. To test this hypothesis, a random sample of 15 adults is selected. If the number of college graduates in the sample is anywhere from 6 to 12, we shall not reject the null hypothesis that p = 0.6; otherwise, we shall conclude that p /= 0.6.

Evaluate β for the alternatives p = 0.5 and p = 0.7.

Beta is The probability of Type 2 error.
I tried to use the binomial distribution with n=15 and p=.5 and .7 to get P(6<=x<=12|p=.5) and use 12 and 6 for x and substract the results but I can't get the correct answers which are 0.8454 for p=.5, and 0.8695 for p=.7
Is there another way of doing it? Are me x's right for the binomial distributio right?

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