Problem #5: Let $X$ denote the vibratory stress (psi) on a wind turbine blade at a particular wind speed in a wind tunnel. Suppose that $X$ has the following Rayleigh pdf. $$ f(x)=\left\{\begin{array}{11} \left(x / \theta^{2} ight) e^{-x^{2} Aleft(2 \theta^{2} ight)} & x>0 0 & \text { otherwise } \end{array} ight. $$ (a) If $\theta=95$, find the probability that the vibratory stress is between 93 and 296 (b) If $\theta=95$, then $70 %$ of the time the vibratory stress is greater than what value? SP.VS. 879