Question

X-N(45, variance) and p(x>51)=0.288 find standard deviation

Answer 1

$$P(X>51)=1-P(Z\le\dfrac{51-45}{\sigma})=0.288$$

$$\dfrac{51-45}{\sigma}=0.559237$$

$$\sigma=\dfrac{6}{0.559237}\approx10.7289$$