Use the Empirical Rule to Solve the Problem Note: the Sample Mean and Sample Standard Deviation of These

Use the empirical rule to solve the problem.
-Consider the following sample of exam scores, arranged in increasing order:
$\begin{array} { c c c c c c } 22 & 35 & 44 & 55 & 67 & 70 \\78 & 81 & 81 & 82 & 84 & 88 \\88 & 89 & 90 & 90 & 91 & 92 \\92 & 93 & 93 & 94 & 94 & 95 \\95 & 96 & 96 & 97 & 99 & 100\end{array}$
Note: The sample mean and sample standard deviation of these weights are, respectively, 82.4 and 19.5.

A) (i) Use the Empirical rule to estimate the percentages of the observations that lie within 3 standard
Deviation(s) to either side of the mean.
(ii) Use the data to obtain the exact percentages of the observations that lie within 3 standard
Deviation(s) to either side of the mean. (i) Assuming that the scores have a roughly bell-shaped distribution, approximately 99.7% of the observations should lie within 19.5 points of the mean 82.4 or within the interval from 23.4
To 141.4;
(ii) 29 of the 30 observations (96.7%) lie between 23.4 and 141.4.
B) (i) Assuming that the scores have a roughly bell-shaped distribution, approximately 99.7% of the observations should lie within 19.5 points of the mean 82.4 or within the interval from 23.9
To 140.9;
(ii) 27 of the 30 observations 90% lie between 23.9 and 140.9.
C) (i) Assuming that the scores have a roughly bell-shaped distribution, approximately 99.7% of the observations should lie within 19.5 points of the mean 82.4 or within the interval from 22.7
To 142.7;
(ii) 30 of the 30 observations 100% lie between 22.7 to 142.7.
D) (i) Assuming that the scores have a roughly bell-shaped distribution, approximately 99.7% of the observations should lie within 19.5 points of the mean 82.4 or within the interval from 23.9
To 140.9;
(ii) 29 of the 30 observations (96.7%) lie between 23.9 and 140.9.