Elongation (in percent) of steel plates treated with aluminium are random with probability density function (Give your answers to 3 decimal places accurately) sa- 20

Using integrals, directly calculate the variance of the Weibull distribution with shape α and scale µ

Let T represent the lifetime in years of a part which follows a Weibull distribution with shape 2 and scale 5. (a) What is E(T )? Make sure to simplify the gamma function in terms of pi.(b)  What is V(T )? Make sure to simplify the gamma function in terms of pi.

Exercise 2: Finding the Area Under the Curve In Major League Baseball, the average fastball pitch is 90 miles per hour, μ = 90, with a standard deviation of 3 miles per hour, σ = 3. A pitcher’s fastball is 96 miles per hour. Is he among the fastest 1 percent of pitchers?     A pitcher’s fastball is 95 miles per hour. Is he among the fastest 2.5 percent of pitchers?     A pitcher’s fastball is 85 miles per hour. Is he among the slowest 2.5 percent of pitchers?     A pitcher’s fastball is 80 miles per hour. Is he among the slowest 1 percent of pitchers?   Use Assignment05_Data.xlsx to solve these problems. Or, you may use the Area Under the Curve Table and a handheld calculator. The key part of your solution is used the correct z-value. Remember: z-values can be positive or negative. The Area Under the Curve Table only shows positive z-values. Because the normal curve is symmetrical, the probability of negative z-values are the same has their corresponding…