5. [-16 Points] DETAILS Suppose X has a normal distribution with mean 1.77 and standard deviation...

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5. [-16 Points] DETAILS Suppose X has a normal distribution with mean 1.77 and standard deviation 4. The pnorm(), dnorm() and qnorm() functions should be useful in the following. a) What is the expected value of 2X - 4? b) What is the variance of 2X-4? c) Calculate the probability X > 2.00 d) Calculate the probability that X < 1.5 e) Calculate the probability that 1.6 < x < 2.2 f) If the probability that X > t = 0.01 then what is t? g) Copy your R script for the above into the text box here. 5. [-16 Points] DETAILS Suppose X has a normal distribution with mean 1.77 and standard deviation 4. The pnorm(), dnorm() and qnorm() functions should be useful in the following. a) What is the expected value of 2X - 4? b) What is the variance of 2X-4? c) Calculate the probability X > 2.00 d) Calculate the probability that X < 1.5 e) Calculate the probability that 1.6 < x < 2.2 f) If the probability that X > t = 0.01 then what is t? g) Copy your R script for the above into the text box here.