Recall that in a random sample of social robots obtained through a Web search, 28 were built with wheels. The number of wheels on each of the 28 robots is listed in the accompanying table. For Information: Refer to the International Conference on Social Robotics (Vol. 6414, 2010) study on the current trend in the design of social robots, Exercise 2.3.

a. Generate a histogram for the sample data set. Is the distribution of number of wheels mound-shaped and symmetric?
b. Find the mean and standard deviation for the sample data set.
c. Form the interval, ± 2s.
d. According to Chebychev's rule, what proportion of sample observations will fall within the interval, part c?
e. According to the Empirical Rule, what proportion of sample observations will fall within the interval, part c?
f. Determine the actual proportion of sample observations that fall within the interval, part c. Even though the histogram, part a, is not perfectly symmetric, does the Empirical Rule provide a good estimate of the proportion?

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