I have the following problem:
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 $p= 0.6$?Besides, Evaluate $α$ assuming that $p = 0.6$. Use the binomial distribution.
Now, the solution for this part of the exercise is as follows:
$$ α = P(X≤5) + P(X≥13) = 0.0338 + (1-0.9948) = 0.0390 $$
Now, I know that $P(X≥13)$ is calculated as $ 1-P(X≤12) $, but from my probability table (and any online calculator) I found that$ P(X≤12)$ is $0.9729$ and not $0.9948$.
Can anyone help, this has been bugging me since yesterday and I'm just wondering if it is an error in the workbook I have been provided with.