A major cab company in Chicago has computed its mean fare from O\'Hare Airport t

Question

A major cab company in Chicago has computed its mean fare from O'Hare Airport to the Drake Hotel to be $28.66, with a standard deviation of $4.07. Based on this information, complete the following statements about the distribution of the company's fares from O'Hare Airport to the Drake Hotel. (a) According to Chebyshev's theorem, at least between 18.485 dollars and 38.835. of the fares lie (b) According to Chebyshev's theorem, at least between 20.52 dollars and 36.80 of the fares lie (c) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately of the fares lie between 20.52 dollars and 36.80. (d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 68% of the fares lie between 0 dollars and 0 dollars.

Explanation / Answer

Answer to the question is as follows:

a. So, these points are -2.411 and +2.5 deviation less than and more than mean

Hence, (1/2)*(1-1/2.411^2) + (1/2)*(1-1/2.5^2) = 83.4%

b.20.52 and 36.80 are 2 deviations less and more than mean. And hence,
1-1/2^2= 75% of the fares lie between these 2 points

c. For bell curve these points , which are 2 deviation away from mean:

According to the empirical rule, approx 95% of the fares lie between $20.52 and $36.80

d. 68% lie between 1 deviation. Hence, 28.66-4.07 to 28.66+4.07 = 24.59 to 32.73

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