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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