Use the Empirical Rule. The mean speed of a sample of vehicles along a stretch of highway is miles per hour, with a standard de
viation of miles per hour. Estimate the percent of vehicles whose speeds are between miles per hour and miles per hour. (Assume the data set has a bell-shaped distribution.) Approximately % of vehicles travel between 61 miles per hour and 71 miles per hour.
We observe that the mean of the sample is (61+71)/2 = 66 mph which means the standard deviation of the sample is 5 because 66-5=61 and 66+5=71. The Empirical Rule states that for data observed in a normal distribution, 68% of data will fall within one standard deviation of the mean. Therefore, approximately 68% of vehicles travel between 61 miles per hour and 71 miles per hour.
