Question

Consider a random sample of 200 one-way commute distances (in miles) from Radcliffe College to a student’s primary place of residence. The sample mean is 10.33 miles and the sample standard deviation is 3.77 miles. What percent of students sampled live between 0.81 and 19.85 miles from Radcliffe College? Suppose a student lived 25 miles from Radcliffe College. Would this commute distance be considered an outlier?

Answer 1

Given information:

Since we do not anything about the distribution of commute miles so we need to use Chebyshev's theorem.

For that first we need to find k. We have

Solving first equation

Now,

So according to Chebyshev's theorem at least 84.32% of students sampled live between 0.81 and 19.85 miles from Radcliffe College.

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Now

Solving first equation

Now,

So according to Chebyshev's theorem at least 93.39% of students sampled live between and 25 miles from Radcliffe College. That is 25 miles is not outlier.