Question

Suppose x is a normally distrubuted random variable with a mean of 30 and standard deviation of 8. Find a value X0 of the random varible of such that. P(x>(Equal too) X)=0.5

Answer 1

$$P(X\geq X_0)=1-P(X<X_0)$$

$$=1-P(Z<\dfrac{X_0-\mu}{\sigma})=0.5$$

$$\dfrac{X_0-\mu}{\sigma}=0$$

$$X_0=\mu$$

$$X_0=30$$