The Normal distribution

The idea

$X \sim N(\mu, \sigma^2)$ is a symmetric bell-shaped distribution: about $68\%$ of values lie within one standard deviation of the mean and $95\%$ within two. Find probabilities with the calculator's Normal CD, or standardise with $Z = \frac{X - \mu}{\sigma}$.

1. Write $\mu$ and $\sigma$; check whether you were given the variance $\sigma^2$.
2. Sketch the curve and shade the region you want.
3. Use Normal CD with the bounds, or $Z = \frac{X - \mu}{\sigma}$ and tables.

Watch out In $N(50, 4^2)$ the standard deviation is $4$, not $16$.