The cheetah (Acinonyx jubatus) is the fastest land mammal and is highly specialized to run down prey. The cheetah often exceeds speeds of 60 miles per hour (mph) and, according to the online document "Cheetah Conservation in Southern Africa" (Trade & Environment Database (TED) Case Studies, Vol. 8, No. 2) by J. Urbaniak, the cheetah is capable of speeds up to 72 mph. The following table gives the top speeds, in miles per hour, arranged in increasing order, for a sample of 35 cheetahs.

The sample mean and sample standard deviation of these speeds are 59.53 mph and 4.27 mph, respectively. A histogram of the speeds is bell shaped. Modeling your solutions after those in Example 3.17 on pages 119-121, solve the following problems.
a. Is it reasonable to apply the empirical rule to estimate the percentages of observations that lie within one, two, and three standard deviations to either side of the mean?
b. Use the empirical rule to estimate the percentages of observations that lie within one, two, and three standard deviations to either side of the mean.
c. Use the data to obtain the exact percentages of observations that lie within one, two, and three standard deviations to either side of the mean.
d. Compare your answers in parts (b) and (c).

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52.4 52.6 54.7 54.8 55.4 55.5 55.9 56.5 57.3 57.5 57.6 57.857.8 58.1 58.3 58.7 59.0 59.2 59.659.7 59.8 60.1 60.2 60.6 60.7 60.961.3 61.6 62.3 62.6 63.4 65.0 65.2 66.0 75.3