. The data listed here are the weights (in pounds) of 27 packages of ground beef in a supermarket meat display: 1.08 .99 .97 1.18 141 1.28 .83 1.06 1.14 1.38 A .96 1.08 .87 .89 .89 96 1.12 1.12 .93 1.24 .89 .98 1.14 92 1.18 1.17 (6 points) . Find the mean and standard deviation of the data set. . Find the percentage of measurements in the intervals x + 5, x *+ 2s, and x * 3s. Show all work, including the number of data points in each interval, the interval, written in the form (lower, upper), and the percentages. . How do the percentages obtained in part C compare with those given by the Empirical Rule? Explain. . To estimate the amount of lumber in a tract of timber, an owner decided to count the number of trees with diameters exceeding 12 inches in randomly selected 50-by-50 foot squares. Seventy 50-by-50 foot squares were chosen via a simple random sample of all squares in the tract, and the selected trees were counted in each tract. The data are listed here: 7 8 7 10 4 8 6 8 9 10 9 6 4 9 10 9 8 8 7 9 3 9 5 9 9 8 7 5 8 8 10 2 7 4 8 5 10 7 7 7 9 6 8 8 8 7 8 9 6 8 6 11 9 11 7 7 11 7 9 13 10 8 8 5 9 9 8 5 9 8 (6 points) . Calculate the sample mean as an estimate of 4, the mean number of timber trees for all 50-by-50-foot squares in the tract. . Calculate the sample standard deviation (s) for the data. Construct intervals, calculate the percentage of squares falling into each of the three intervals, and compare with the corresponding percentages given by the empirical rule. . Create a normal quantile plot in your graphing calculator and sketch the plot here. Note: You don't have to know how to make a normal quantile plot by hand. However, you do need to have a general idea of how they're made, and you need to be able to use these plots to judge whether a distribution appears to be normal. . In the population, are the numbers of trees per 50-by-50-foot square normally distributed? Justify your answer. 3. The randNorm function in the graphing calculator was used to generate the following numbers with a mean of 75 and standard deviation of 5. Use the Copyright @ 2021 Apex Learning. See Terms of Use for further information. Images of the TI-84 calculator are used with the permission of Texas Instruments Incorporated. Copyright @ 2011 Texas Instruments Incorporated. AP Statistics Practice: Checking for Normalcy Page 2 of 2 empirical rule, a histogram, and a normal quantile plot to determine if this data could have come from a normal distribution. Explain clearly how each of these tools provide evidence for your conclusion. (Note: It isn't necessary to sketch the histogram or guantile plot, but do describe what they looked like when you made them on your calculator.) 66 66 67 68 68 68 70 70 70 71 71 71 72 73 73 73 73 73 74 75 75 75 76 76 76 77 77 77 77 77 77 77 78 78 78 78 78 79 79 79 80 81 81 82 82 84 84 84 85 86 (6 points) 4. You have the following data set of ages of students in a community college chemistry class. (7 points) Create a normal probability plot to determine whether these age data are normally distributed. Offer supporting evidence for your conclusion. (You don't need to draw the plot, but do describe what you see when you make the plot on your calculator.) Given what you know about this data, describe the shape of the distribution of ages and comment on the existence of outliers. In this instance, it may be useful to construct a histogram or box-and-whisker plot to find outliers and support your