Question

Suppose that X has a distribution N(10, 1). Determine c such that P(X<c)=2P(X>c)

Answer 1

$$P(X<c)=2P(X>c)=2(1-P(X\leq c))$$

$$P(X<c)=2-2P(X\leq c)$$

$$P(X<c)=\dfrac{2}{3}$$

$$P(Z<\dfrac{c-10}{1})=\dfrac{2}{3}$$

$$c-10=0.4307273$$

$$c=10.4307273$$