Problem #8: 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 probability density function (called the Rayleigh probability density function).
f(x)={(((x)/(\theta ^(2)))e^(-(x^(2))/(2\theta ^(2))),x>0),(0 otherwise ):}
(a) If
\theta =96
, find the probability that the vibratory stress is between 76 and 174 . (b) If
\theta =96
, then
86%
of the time the vibratory stress is greater than what value? Problem #8(a): Problem #8(b): Round your answer to 4 decimals. round your answer to
2
decimals