The price that watermelon farmers get for their watermelons has a normal distribution with unknown mean of u dollars per hundred pounds and known standard deviation o = $1.92 per hundred pounds. We wish to create a confidence interval for . We randomly select 20 watermelon farmers and measure the price per hundred pounds x; that each farmer gets for his/her watermelons. The sample mean was x = $6.88 per hundred pounds of watermelon and the sample standard deviation was s = $1.37 per hundred pounds. a)What is the critical value for a 95% confidence interval for u? b) Create a 95% confidence interval for u c) How long is the 95% confidence interval for u? d) How many observations would we need to guarantee that the 95% confidence interval above has a length of 0.8 or less? e) Create a 95% prediction interval for u using this data. f) Assuming o is not known, create a 95.0% confidence interval for a using this data. g. What is the length of the confidence interval for part f? h) Copy your R script for the above into the text box here