Question

Use the Empirical Rule. The mean speed of a sample of vehicles along a stretch of highway is 67 miles per​ hour, with a standard deviation of 3miles per hour. Estimate the percent of vehicles whose speeds are between 64miles per hour and 70miles per hour.​ (Assume the data set has a​ bell-shaped distribution.)

Answer 1

Mean = 67 miles/hr

Standard deviation, = 3 miles/hr

According to the emirical rule 68% of the data lie between one standard deviation of the mean , i.e,

P( - < X <  +) = 0.68

P( 67-3 < X < 67+3) = 0.68

P( 64 < X < 70) = 0.68

Thus, there are 68% of vehicles whose speeds are between 64miles per hour and 70miles per hour