OneNote File Edit View Insert Format Notebooks Tools Window Help K A ABC Q 8 Fri 6 May 9:07 PM ... OneNote Home Insert Draw View Co LE Share P AI OF N N N NN Text Lasso Insert Eraser Pen Marker Highlighter Ink 2 mm 3 mm 5 mm 6.5 mm 8 mm Mode Select Space Colour Problem 2 [21 Points] An automated process fills one bag after another with potatoes. Although each filled bag should weigh 1 kilogram, in fact, because of the differing shapes and weights of each Q potato, each bag weight, X, is anywhere from 0.8 kilogram to 1.3 kilogram, with Uniform Density. (a) [2 Points] What's the chance that the bag weight more than 1.1 kilogram? (b) [2 Points] What is the mean weight and standard deviation of a bag of potatoes? (c) [4 Points] Our canteen brought 24 bags of potatoes to prepare dinner. Let Y be the number of bags weight more than 1.1 kilogram (among 24 bags). So what's the distribution of Y? And please write out the parameter of this distribution. (d) [2 Points] Can we apply the approximation method for Y? Which method should be used? (e) [4 Points] Please calculate the probability that only 5 bags weight more than 1.1 kilogram (among 24 bags). (You can use exact method or approximation method). (f) [4 Points] Please calculate the probability that at most 15 bags weight more than 1. 1 kilogram (among 24 bags) by using the approximation method in part (d). (g) [3 Points] If it saves $2 dollars for each bags weight more than 1.1 kilogram, what's the expectation and variance of dollars we can save among 24 bags? LS 162 MAY 6 City E