How much does a wild mountain lion weigh? Bill Montana went into the mountains of Idaho and captured 12 random mountain lions. Their weights, in pounds, were the following:93.0, 109.4, 88.2, 114.5, 83.0, 103.2, 110.7, 128.9, 62.8, 97.9, 94.7, 92.5Mountain lion weights in Idaho are known to be normally distributed with an unknown mean of ???? pounds and an unknown standard deviation ???? pounds.a) Calculate the sample mean for this data.b) Calculate the sample standard deviation for this data.c) Calculate the maximum likelihood estimate for????2using this data.d) Calculate an unbiased estimate for????2using this data.e) Calculate the sample median for this data.f) Suppose W has a t distribution with 11 degrees of freedom. If P(W > t) = .08 then what is t?g) Suppose W has a t distribution with 11 degrees of freedom. If P(W < t) = .08 then what is t?h) Calculate the 90th percentile of a standard normal distribution.i) Compute an 80% confidence interval for ???? using your answers above.,j) Compute an 80% prediction interval for ???? using your answers above.,k) Copy your R script or other comments for the above into the text box here.