Question

Use the Empirical Rule. The mean speed of a sample of vehicles along a stretch of highway is 7171 miles per​ hour, with a standard deviation of 33 miles per hour. Estimate the percent of vehicles whose speeds are between 6868 miles per hour and 7474 miles per hour.​ (Assume the data set has a​ bell-shaped distribution.)

Answer 1

Mean = $\mu$ = 71

Standard deviation = $\sigma$ = 3

Empirical rule:

1) About 68% data lies in the 1 standard deviation from the mean.

that is in the interval $( \mu - 1*\sigma , \mu +1*\sigma ).$

2) About 95% data lies in the 2 standard deviations from the mean.

that is in the interval $( \mu - 2*\sigma , \mu +2*\sigma ).$

3) About 99.7% data lies in the 3 standard deviations from the mean.

that is in the interval $(\mu - 3*\sigma , \mu +3\sigma) .$

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$\mu - 1*\sigma \Rightarrow 71-1*3=68$

$\mu + 1*\sigma \Rightarrow 71+1*3=74$

Therefore the first rule is appropriate in this case.

68% of vehicles whose speeds are between 68 miles per hour and 74 miles per hour.​