Download A major cab company in Chicago has computed its

A major cab company in Chicago has computed its mean fare from O'Hare Airport to the
Drake Hotel to be $29.58, with a standard deviation of $3.21. 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 84%
of the fares lie between __ dollars and ____ dollars (round answer 2 decimal places)
B)According to Chebyshev's theorem, at least ____% of the fares lie between 23.16
dollars and 36 dollars (round answer 2 decimal places) C) Suppose that the distribustion
is bell shaped. According to the empirical rule, approxametley ____% of the fares lie
between 23.16 dollars and 36 dollars (round answer 2 decimal places) D) Suppose that
the distribustion is bell shaped. According to the empirical rule, approxametley 68% of
the fares lie between __ dollars and ____ dollars
According to Chebyshev’s theorem, at least 1 - (1/k^2) of the measurements will
fall within (Mean - k*SD, Mean + k*SD).
Here it is given that, Mean = $29.58 and SD = $3.21.
A) Substituting 1 - (1/k^2) = 0.84, we get
(1/k^2) = 1 – 0.84 = 0.16
i.e., k^2 = 1/0.16 = 6.25
i.e., k = √6.25 = 2.5
Therefore, according to Chebyshev’s theorem, at least 84% of the measurements will fall
within (Mean – 2.5*SD, Mean + 2.5*SD) = ($29.58 – 2.5*$3.21, ($29.58 + 2.5*$3.21)
=($21.56, $37.61)
Thus, according to Chebyshev's theorem, at least 84% of the fares lie between $21.56
dollars and $37.61 dollars
B) Here,
Mean - k*SD = $23.16 and Mean + k*SD = $36
Consider,
Mean + k*SD = $36
That is, $29.58 + k*$3.21 = $36
That is, k = ($36 - $29.58)/$3.21 = 2
Therefore, 1 - (1/k^2) = 1 – (1/2^2) = 1 – (1/4) = 1 – 0.25 = 0.75
Thus, according to Chebyshev's theorem, at least 75% of the fares lie between 23.16
dollars and 36 dollars
The empirical rule states that for a normal distribution:

68% of the data will fall within 1 standard deviation of the mean

95% of the data will fall within 2 standard deviations of the mean

Almost all (99.7%) of the data will fall within 3 standard deviations of the mean
C) By empirical rule 95% of the data will fall within 2 standard deviations of the mean.
Here the interval ($23.16, $36) = ($29.58 - 2*$3.21, $29.58 + 2*$3.21)
= (Mean – 2 *SD, Mean + 2*SD)
Thus, according to the empirical rule, approxametley 95% of the fares lie between 23.16
dollars and 36 dollars.
D) According to the empirical rule, approxametley 68% of the fares will fall within 1
standard deviation of the mean,
That is, approxametley 68% of the fares will fall in the interval
(Mean – SD, Mean +SD) = ($29.58 - $3.21, $29.58 + $3.21) = (26.37, 32.79)
Thus, according to the empirical rule, approxametley 68% of the fares lie between 26.37
dollars and 32.79 dollars