For mean 25 and standard deviation 3, how much area is under the bell shaped curve within 2 standard deviations of the mean?

Feb 24, 2017

$0.6826$

Explanation:

$P \left(25 - 3 < X < 25 + 3\right) = P \left(22 < X < 28\right)$

$P \left(22 < X < 28\right) = P \left(\frac{22 - 25}{3} < z < \frac{28 - 25}{3}\right)$

#P(22 < X < 28) =P(-1 < z < 1)

from Normal Distribution Table,
$P \left(- 1 < z < 1\right) = 0.6826$