The Normal Distribution

The second parameter is the VARIANCE, so $\sigma = \sqrt{25} = 5$.

The empirical rule: about 68% within 1 standard deviation, 95% within 2 and 99.7% within 3.

$z = 1.25$ and $\Phi(1.25) = 0.8944$, so the upper tail is $1 - 0.8944 = 0.1056$.

By symmetry $\Phi(-z) = 1 - \Phi(z)$, so $1 - 0.8413 = 0.1587$.

$np = nq = 40 > 5$, so the approximation is valid. 45 is included in the event, so the boundary moves down to 44.5.

The area to the left is 0.95, so $z = 1.645$. Then $k = 100 + 15(1.645) = 124.7$.