Four Bolts, All In Spec

A machine turns out bolts whose lengths are normally distributed:

$L \sim N(\mu = 50.0 \text{ mm},\; \sigma = 0.8 \text{ mm})$

A bolt passes inspection only if its length lies between 49.0 mm and 51.2 mm. Note that these two limits are not the same distance from the mean.

Four bolts are drawn independently from the machine's output.

What is the probability that all four pass inspection?

Use these standard-normal CDF values, where $\Phi(z) = P(Z \le z)$:

$\Phi(1.25) = 0.8944, \qquad \Phi(1.50) = 0.9332$

Round to four decimal places.