The cheetah 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 is capable of speeds above 72 mph. The accompanying table contains a sample of the top speeds of 35 cheetahs.

The sample mean and sample standard deviation of these speeds are 59.53 mph and 4.19 mph, respectively. A histogram of the speeds is bell-shaped.Complete parts

(a) through

(d) below.

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).

Top Speeds of Cheetahs (mph) 52.1 52.6 54.2 54.9 55.3 55.8 56.1 56.6 57.3 57.5 57.7 57.9 57.9 58.1 58.3 58.8 59.1 59.4 59.6 59.7 59.9 60.1 60.2 60.5 60.7 60.9 61.4 61.7 62.3 62.6 63.7 64.6 65.2 66.4 74.3 In each of Exercises 3.140–3.143, the quantitative data set under consideration has roughly a bell-shaped distribution. For each exercise,

a. construct a graph similar to Fig. 3.8 on page 140.

b. apply Property 1 of the empirical rule to make pertinent statements about the observations in the sample.

c. repeat part

(b) for Property 2 of the empirical rule.

d. repeat part

(b) for Property 3 of the empirical rule.

Model your solutions after those in Example 3.18 on page 143.