M9 Case Study

TheUSDA'sNationalAgricultural Statistics Services collects, summarizes, and distributes statistics on many elements of the agricultural industry. Annual reports are published nationally and by state.A dairy farmer provided this data set for the monthly mild production (in pounds) for 50 Holstein dairy cows.Refer to this chart to answer the questions which follow the chart.

Monthly Milk Production
2825	2072	2733	2069	2484
4285	2862	3353	1449	2029
1285	2982	2045	1677	1619
2597	3512	2444	1773	2284
1884	2359	2046	2364	2669
3109	2804	1658	2207	2159
2207	2882	1647	2051	2202
3223	2383	1732	2230	1147
2711	1874	1979	1319	2923
2281	1230	1665	1294	2936

Usewww.Statcrunch.comto execute the following tasks and submit the results in Canvas.The data in the chart is also availableas an Excel file to import.

1.A)Use the Stat toolto createthe Summary statistics for thechart data.Add the values to the chart provided in Canvas.

B)Create ahistogramto display the data in the chart. Set thestarting bin value as 1100 and enter a bin width that will generate between 5 and 10 classes.

C)Based on the shape alone, do you think it is appropriate to apply the Empirical Rule? Explain your answer.

D Use the results of the histogram in part B) to create a frequency distribution for the given data set. Copy and paste this provided chart to enter your results. If you have fewer than ten classes, just leave the lower lines of the cart empty.

2.A) Determine the monthly milk production values that correspond to z = -3, -2, -1, 0, 1, 2, 3.

B) Complete thedistributionin Canvas by inserting the values from part A)as class boundariesand determine the number of values within each interval

C)Use the results of part B) to determine the percentages of values within 1, 2, and 3 standard deviationsof the mean.

D)Based onthe resultsof part C)and theEmpirical Rule, do you think the data is approximately normally distributed? Explain your answer.

3.A)Select two values from the provided chart: one below the mean(a) and one above the mean (b). The selected values should NOT be one of the values entered into the chart in 2A). Let x represent a randomly selected value from the data chart. Explain why the random variable is a discrete random variable.

B)Translate each verbal statement into symbolic form

the empirical probability that the randomly selected value, x, is no more a.the empirical probability that the randomly selected value, x, is at least b.the empirical probability that the randomly selected value, x, is between a and b.

C) Explain the general process for finding an empirical probability.Determine the empirical probabilities described in part B) based on the chart provided at the start of the case study. Enter the probability, correct to two decimal places, into the chart in Canvas.

4.A)Let x represent a randomly selected number between the minimum and maximum values in #1; a and b represent the same values selected in #3.Explain why x represents a continuous random variable in this part of thecase study. B)Assume that the monthly milk production of Holstein cows is normally distributed, with the mean and standard deviation as determined in #1A).State the probabilities described in #3 in terms of z-scores and determine the probabilities. C)Select StatCalculatorsNormal. Then, setting the mean to 0 and standard deviation to 1,determine the probabilities for the statementsin part B). Enter the probability, correct to four decimal places, into the copied chart. Download the result and save as an image to your device. Embed the images as support for the submitted probabilities.D)It is very unlikely that the probabilities found in #4B) areexactly the sameas those found in #3. Explain why the probabilities are different.