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Name: ________________________________________ Date: ___________________________ Period: _______ AP Statistics FID Day #1 Assignment 28 Points The heights of young women vary approximately according to the Normal distribution with a mean (𝜇) of 64.5 inches and a standard deviation (𝜎) of 2.5 inches. The random variable measured is X = the height of a randomly selected young woman. In this assignment, you will use a random number generator (RNG) to sample from this distribution and then construct a distribution of the averages. 1. (2 points) Collect your sample using N(64.5, 2.5) distribution. On your calculator, clear your lists. Put your cursor over L1. Press Math PRB and choose “randNorm(.“ Complete the command: randNorm(64.5, 2.5, 100) and press enter. You will see 100 randomly selected heights appear in your list. Write down the first 10 heights that were given to you: _________, _________, _________, _________, _________, _________, _________,_________, _________, _________ 2. (4 points) Plot a histogram of your data using the graphing calculator. Adjust your window to the following parameters: Xmin = 57, Xmax = 72, Xscl = 2.5, Ymin = -10, Ymax = 45, Yscl = 5, Xres = 1. Show a sketch below. Use the trace button to label the values on your x- and y- axes. 3. (4 points) Describe the shape of your sample distribution. What are the appropriate measures of center and spread of your sample data? Provide the values. 4. (1 points) Approximately how many heights should be within 3 standard deviations of the mean (i.e. between 57 and 72)? 5. (1 points) Use the TRACE button to count the number of heights within 3 SD. 6. (1 points) Approximately how many heights should be within 2 standard deviations of the mean? 7. (1 points) Use the TRACE button to count the number of heights within 2 SD. 8. (4 points) Repeat step 1 30 times. Each time, record the mean, median, standard deviation, and the shape of the distribution. Organize your data in the table below: ̅ Sample Median s Symmetry 𝒙 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 9. (4 points) Graph a histogram of all of the sample means. Stay in the same window as defined in #2. Show a sketch with numerical labels. 10. (2 points) What is the sample mean of all of the sample means? How does this compare to the true mean (𝜇)? 11. (2 points) What is the sample standard deviation of all of the sample standard deviations? How does this compare to 𝜎 ? √𝑛 12. (2 points) What theorem does this lab describe? Explain.