91Ó°ÊÓ

We are given data of speed of $35$cheetahs.

Mean $\overline{x}=59.53mph$

Standard deviation $s=4.27mph$

Because the distribution of cheetah speed is essentially bell-shaped, it is possible to use the empirical approach to estimate the percentages of observations that lie within one, two, and $3$ standard deviations to any side of the mean.

We are given data of speed of $35$cheetahs.

Mean $\overline{x}=59.53mph$

Standard deviation $4.27mph$

We estimate that of the data are one standard deviation to each side of the mean, $68\%$whereas two standard deviations to either side of the mean are $95\%$and $3$standard deviations to any of the two side of the mean, $99.7\%$using the empirical rule.

We are given data of speed of $35$cheetahs.

Mean$\overline{x}=59.53mph$

Standard deviation $s=4.27mph$

Referring to Table , we found that $25$of the $35$observations, or $71.7\%$. are within $1$standard deviation to any side of the mean; $32$of the $35$observations, or $90\%$, are within $2$standard deviations to any side of the mean; and $35$of the $35$observations, or $100\%$, are within $3$standard deviations to any side of the mean.

We are given data of speed of $35$cheetahs.

Mean $\overline{x}=59.53mph$

Standard deviation $s=4.27mph$

Comparing the percentages obtained in parts (b) and (c)

$68\%,95\%,99.7\%$vs $71.7\%,95\%,100\%$

We can see that the empirical rule yields great approximations of the actual percentages in this example.
This result is unsurprising, given that cheetahs' speed distribution is nearly bell-shaped.