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StatisticsQ&A LibraryIn a random sample of social robots obtained through a Web search, 28 werebuilt with wheels. The number of wheels on cach of the 28 robots is listed here:4,3,33,6,4,2,2,2,1,3,3,3,3,4,4,3,2,8,2,2,3,43,3,4,2a Generate a histogram for the sample data set. Is the distribution of number of wheelsmound-shaped and symmetrie?b. Find the mean and standard deviation for the sample data set.c. Form the interval, &t 2s.d. According to Chebychev's Rule, what proportion of sample observations will fallwithin the interval, part e?e. According to the Empirical Rule, what proportion of sample observations will fallwithin the interval, part c?f. Determine the actual proportion of sample observations that fall within the interval,part e. Even though the histogram, part a, is not perfectly symmetric, does theEmpirical Rule provide a good estimate of the proportion?Question

Asked Feb 11, 2020

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Part D&E&F

Step 1

(Here even though 28 ROBOTS mentioned in question, there are only 27 data points. So considering there are only 27 robots* and performing the calculations.

d)

Given data set of number of wheels each of 27 robots have

According to Chebyshev's rule

for any k > 1, at least (1-1/k^{2} )of the data lies within k standard deviations of the mean.

Here the interval in part c is given with in two standard deviations. So k = 2 we get (1 - 1/4) = 0.75.

So we say at least 75% of the data lie with in two standard deviations of the mean.

Step 2

e)

According to Empirical rule

With in one,two and three standard deviations of the mean 68%,95% and 99.7% of the data lie respectively.

The g...

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