Question

Use the Empirical Rule. The mean speed of a sample of vehicles along a stretch of highway is 63 miles per hour, with a standard deviation of 4 miles per hour. Estimate the percent of vehicles whose speeds are between 55 miles per hour and 71 miles per hour. (Assume the data set has a bell-shaped distribution.) Approximately % of vehicles travel between 55 miles per hour and 71 miles per hour.

Please give answer and work to show how you got the answer.

Answer 1

Answer

We have mean = 63 and standard deviation = 4

First, we have to find how many standard deviation away from the mean, the given value of 55 and 71 are located

Mean + 2(standard deviation) = 63 + (2*4) = 63 + 8 = 71

Mean - 2(standard deviation) = 63 - (2*4) = 63 - 8 = 55

So, it is clear that 55 is two standard deviation below the mean and 71 is two standard deviation above the mean

Using the empirical formula, we know that exactly 95% of the data values fall within 2 standard deviation from the mean.

So, we can say that approximately 95% of vehicles travel between 55 miles per hour and 71 miles per hour.