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LAB 5: Computing Probabilities for Normal Distribution Before you begin this lab, make sure that the Analysis ToolPak Add-in feature is loaded on your computer. To do this with your home PCs, click on the Data option to see if Data Analysis is an option at the far right of the screen. If Data Analysis does not appear, click on the Office Button at the far top left of the screen and then click on Excel Options at the bottom of the menu. Then click on Add-ins and Analysis ToolPak. Click on Go and check Analysis ToolPak. Then click OK. Once it loads, click on Data at the top of the main screen and you should see Data Analysis as an option at the far right. In the lab classroom, it is ready for you to use whenever you use Microsoft Excel. Purpose: In this lab, we will use Excel to compute probabilities for a normal distribution. (Note: Excel finds cumulative probabilities, which can be shown as the area under the curve from negative infinity to a specified z value.) Finding probabilities for a normal distribution For this lab we will be using the dataset BODYTEMP.xls which includes body temperatures of 106 healthy adults. Let’s assume that body temperatures are normally distributed. In order to use Excel to find normal probabilities, we will need to use the following steps. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Double click on the Connect to the Internet icon on the desktop. Click on Authenticate for Network Access. Fill in your username and password. Click Submit and then click on The University Portal, WINGS. Click on the website address and type in http://www.wright.edu/cosm/departments/math/resources/student/stt160lab.html. Click on BODYTEMP.xls to open the dataset. In the File Download dialog box click on Save. When the Save As dialog box opens, click Save. Close the Download dialog box. (The default save location will be the lab computer’s hard drive. Your file will be automatically deleted once the lab computer is restarted. To keep your work, we recommend that you save your file to a flash drive or Skydrive through your RaiderMail.) To open Excel, click on the Start Menu, Productivity Apps, Office 2010 and Excel 2010. Open the data set BODYTEMP.XLS which was saved on your lab computers hard drive by going to the File tab and selecting Open. In the Open dialog box, find the BODYTEMP.XLS file and double click on the BODYTEMP.XLS file. Sort the data by highlighting the body temps data and then clicking on Home, Sort and Filter (under the Editing clipboard) and then select “Sort Smallest to Largest”. 11. Let’s now find the mean and standard deviation of the body temperature data. Click on B2 and type Mean= and then click on B3 and type Standard Deviation=. To find the mean, click on C2 and enter a formula similar to what you learned in lab 1 and hit enter. To find the standard deviation, click on C3 and enter a formula similar to what you learned in lab1 and hit enter. We will need these values when finding a normal probability in Excel. 12. Let’s find the probability that an adult has a temperature less than 99 degrees. To do this, click on B4 in your BODYTEMP worksheet and type in P(X<99degrees) =. Click on C4 and then select Formulas on the ribbon followed by More Functions, Statistical, NORM.DIST (Do NOT choose NORM.S.DIST for this step.) In the Functions Arguments dialog box, type in the X value (which in this case represents 99), and the mean and standard deviation you found above. Then type 1 for the cumulative blank and click on OK. The probability will be placed in C4. 13. Be aware that the normal probabilities that Excel gives you are cumulative probabilities. So the probability in C4 represents the probability that an adult has a temperature less than 99 degrees. If you want a non-cumulative probability, you will need to perform calculations to obtain it. 14. Also be aware that since we have a continuous normal distribution, the P(X<99 degrees) is the same as the P(X≤99 degrees). Use the ideas from this lab to answer the following questions. 1. Use your sorted body temperatures to compute by hand the proportion of temperatures that are less than 99 degrees. To do this, count the number of times a body temperature was less than 99 degrees and divide by the sample size. Compare your answer to the probability found by using Excel in step 12. 2. Use your sorted body temperatures to compute by hand the proportion of temperatures that are greater than or equal to 99 degrees. 3. Use Excel to find the probability that an adult has a temperature of greater than or equal to 99 degrees. To do this, click on B5 and type in P(X≥99degrees)=. Then click on C5 and type in =1-C4. Explain why are we subtracting these two values and not following the directions from step 12? Compare your answer to the sample proportion found in #2. 4. Save your Excel worksheet to your H drive. 5. Click on a blank cell of the worksheet so that the entire sheet is active. Then select Page Layout on the ribbon and in the Scale To Fit section, change width and height to 1 page. Click on File tab and choose Print to make sure your data and work look correct. Then print out a copy of your body temperature worksheet. Be sure to include the following in your lab report: A. Cover sheet with a summary of the lab you did. It should be one to two paragraphs. B. Answer all the questions stated above on the answer sheets provided to get full credit. C. Attach the body temperature worksheet you were asked to print.