Normal distribution calculator

solution

explanation

Step 1: Sketch the curve.

The probability that $ X < 76.7 $ is equal to the blue area under the curve.

Step 2:

Since $ \mu = 70 $ and $ \sigma = 10 $ we have:$$ P~(~ X < 76.7 ~) = P~(~X - \color{blue}{\mu} < 76.7 - \color{blue}{ 70 }~) = P~\left(\frac{ X - \mu}{\color{blue}{\sigma}} < \frac{ 76.7 - 70}{ \color{blue}{ 10}}\right) $$

Since $ \frac{x-\mu}{\sigma} = Z $ and $ \frac{ 76.7 - 70}{ 10 } = 0.67$ we have:

Step 3: Use the standard normal table to conclude that:

Note: Visit Z - score calculator Z - score calculator for a step by step explanation on how to use the standard normal table.