Chapter 2 Assignment (20pts) Name:............ Date: ...... . . .... The Normal Distribution The 68-95-99.7 Empirical Rule About 68% of the data points fall within 1 standard deviation of the mean About 95% of the data points fall within 2 standard deviation of the mean About 99.7% of the data points fall within 3 standard deviations of the mean 1. Assume that a set test scores is normally distributed with a mean of 60 and a standard deviation of 12. Use the 68-95-99.7 rule to find the following. Sketch the curve to show your work. Just numbers will not be graded. a. Percentages of scores greater than 60 b. Percentage of scores less than 72 c. Percentage of scores greater than 48 d. Percentage of scores between 48 and 72 e. Percentage of scores between 24 and 96 2. When designing the placement of a CD player in a new model car, engineers must consider the forward grip reach of the driver. Women have forward grip reaches that are normally distributed with a mean of 28.0 inches and a standard deviation of 1.4 inches. Use the 68-95-99.7 rule to find the indicated quantity: a. Find the percentage of women with forward grip reaches between 25.2 inches and 29.4 inches b. Find the percentage of women with forward grip reaches less than 30.8 inches c. Find the percentage of women with forward grip reaches between 26.6 inches and 28.0 inches d. Suppose that 500 women were studied. How many of them are with forward grip reaches between 26.6 inches and 28.0 inches