# The humidity level, X, in Tropicana Field in Tampa at the time of a night game...

###### Question:

The humidity level, X, in Tropicana Field in Tampa at the time of a night game ranges from 40% to 100 %. (.40 to 1.00) The random variable X has cumulative distribution F with the following definition: F(x) 0 for x < 40, F(x)= 5(X-.4)(2-x) for .4 s x 1.0, F(x)=1 for x 2 1.0. a) What is the probability density function for X for .4 s xs 1.0? 1-5(x-4)(2-x) 5(2-x)+5(x-0.4) 5(2-x)-5(x-0.4) Odnorm(x,2,.4 b) What is the probability that X>0.5? c) What is the probability X < 0.5? ? d) What is the probability that X > 0.6? e) What is the probability that X> 0.8? f) What is the probability that X> 0.8 given the X> 0.6 g) Calculate the 60th percentile of X. h) What is the expected value of X? i) What is the expected value of X2? j) What is the variance of X?
k) What is the probability that X is more than 0.1 above its expected value?

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