$P(10 - c < X < 10 + c) = 0.95$. Find c
attempt:
$P(10 - c < X < 10 + c) = \phi(\frac{10 + c - 10}{\sqrt{2}}) - \phi(\frac{10-c-10}{\sqrt{2}}) = \phi(\frac{c}{\sqrt{2}}) - (1 - \phi(\frac{c}{\sqrt{2}})) = 2\phi(\frac{c}{\sqrt{2}}) - 1$
$0.975 = \phi(\frac{c}{\sqrt{2}})$
not sure how to simplify to $\phi$. I know $\phi(0.975) \approx 0.834$ according to Z table. How do I compute the inverse?
$\phi^{-1}(0.975) = \frac{c}{\sqrt{2}}$
using the Z table.