Question

a ride - sharing company has computed its mean fare to be $37.00, with a standard deviation of $4.10. suppose that the fares are normally distributed. complete the following statements. (a) approximately 99.7% of the companys rides have fares between $24.70 and $49.30. (b) approximately 68% of the companys rides have fares between $ and $.

Explanation:

Step1: Recall the empirical rule for normal distribution

For a normal - distributed data, about 68% of the data lies within 1 standard deviation of the mean, about 95% lies within 2 standard deviations of the mean, and about 99.7% lies within 3 standard deviations of the mean. The formula for the interval around the mean is $\mu\pm k\sigma$, where $\mu$ is the mean, $\sigma$ is the standard deviation, and $k$ is the number of standard - deviations.

Step2: Calculate the interval for 68%

Given $\mu = 37.00$ and $\sigma=4.10$. For 68% of the data (since it is within 1 standard deviation of the mean), the lower bound is $\mu-\sigma=37.00 - 4.10=32.90$ and the upper bound is $\mu+\sigma=37.00 + 4.10 = 41.10$.

Step3: Calculate the interval for 99.7%

For 99.7% of the data (within 3 standard deviations of the mean), the lower bound is $\mu - 3\sigma=37.00-3\times4.10=37.00 - 12.30 = 24.70$ and the upper bound is $\mu+3\sigma=37.00 + 3\times4.10=37.00+12.30 = 49.30$.

Answer:

(a) 24.70, 49.30
(b) 32.90, 41.10