Question

A normal distribution has the mean of 150.5. if 70.54% of the area under the curve lies to the left of 177.5 find a. the standard deviation?​

Answer 1

$P(x<177.5)=0.7054$

$z=0.54$

$z=\frac{x-\mu}{\sigma}$

the standard deviation:

$\sigma=\frac{x-\mu}{z}=\frac{177.5-150.5}{0.54}=50$