Answer Happy

please help with 2 a and b and 3 d
2. Retail stores experience their heaviest volume of transactions that include returns on December 26th and December 27th each year. The distribution for the Number of Items Returned (X) by Macys customers who do a return transaction on those days last year is given in the table below. It has mean: μ = 2.61 and variance o² 1.80. Number of Items Returned Probability 1 0.25 2 0.28 3 0.2 0.17 0.08 0.02 5 6 (a) Is this population distribution left skewed, symmetric, or right skewed? How do you know? (b) In what percent of returns did retail workers see three or more items in the return?

3. Consider the tree data set in R, trees. You can access the data by running data(trees) and then typing “trees” as you would any other variable you've set. (a) Construct histograms and qqnorm plots for all three of the quantitative variables recorded on the 31 trees. For which of the three variables do we have the strongest evidence that the population of values may not be well approximated by a normal random variable? (b) Construct 97% t confidence intervals “by hand" for the Girth and Height data and explain why that is a reasonable approach. Summaries of the variables are given below and you should use an r function to find the relevant critical value for your margin of error. > mean (trees$Girth); sd(trees$Girth); length (trees$Girth) [1] 13.24839 [1] 3.138139 [1] 31 > mean(trees$Height); sd(trees$Height); length (trees$Height) [1] 76 [1] 6.371813 [1] 31 (c) Construct the same confidence intervals that you constructed in (b) above using the t.test() function in R. Confirm that you get very similar endpoints. (d) How would our process change if we wanted to construct and interpret 90% t CIs for Girth and Height? Compare it to the 97% t CIs constructed in (b).