Question

A major ride-sharing company in Chicago has computed its mean fare from O'Hare Airport to the Drake Hotel to be $28.11 with a standard deviation of $3.07. Based on this information, complete the following statements about the distribution of the company's fares from O'Hare Airport to the Drake Hotel х 5 2 (a) According to Chebyshev's theorem, at least (Choose one) y of the fares le between 21.97 dollars and 34 25 dollars.

Answer 1

According to Chebyshev's theorem, at least 75% of the fares lie between $21.97 and $34.25, calculated using the fare's mean of $28.11 and a standard deviation of $3.07.

Step-by-step explanation:

A major ride-sharing company in Chicago has computed its mean fare from O'Hare Airport to the Drake Hotel to be $28.11 with a standard deviation of $3.07. To apply Chebyshev's theorem, we need to calculate the range of values within a certain number of standard deviations from the mean.

For Chebyshev's theorem, no matter the shape of the distribution, at least (1 - (1/k²)) of the data will fall within k standard deviations of the mean. When k=2, this formula gives us (1 - (1/2²)) which simplifies to 1 - 1/4 = 3/4 or 75%. Therefore, at least 75% of the fares will lie between $28.11 - 2($3.07) and $28.11 + 2($3.07), which calculates to $21.97 and $34.25.

The standard deviation and mean fare are essential parameters to compute the range according to Chebyshev's theorem.