Question

Use the empirical rule. the mean speed of a sample of vehicles along a stretch of highway is 66 miles per​ hour, with a standard deviation of 4 miles per hour. estimate the percent of vehicles whose speeds are between 62 miles per hour and 70 miles per hour.​ (assume the data set has a​ bell-shaped distribution.)

Answer 1

I dont know this one i am very sorry

Answer 2

Answer: About 68%

Step-by-step explanation:

Given : The mean speed of a sample of vehicles along a stretch of highway is 66 miles per​ hour, with a standard deviation of 4 miles per hour.

i.e. $\mu=\text{ 66 miles per​ hour}$

$\sigma=\text{ 4 miles per hour}$

We assume the data set has a​ bell-shaped distribution (i.e. Normal distribution).

To find :  The percent of vehicles whose speeds are between 62 miles per hour and 70 miles per hour.

i.e . The percent of vehicles whose speeds are between $66-4$ miles per hour and $66+4$ miles per hour.

i.e . The percent of vehicles whose speeds are between $\mu-\sigma$ miles per hour and $\mu +\sigma$ miles per hour.

i.e. i.e . The percent of vehicles whose speeds are within one standard deviation from the mean.

According to the Empirical rule , about 68% of the population lies within one standard deviation of the mean.

It means , about 68% of vehicles lies within one standard deviation of the mean.

i.e . About 68% of vehicles whose speeds are between $\mu-\sigma$ miles per hour and $\mu +\sigma$ miles per hour.

i.e .  About 68% of vehicles whose speeds are between $66-4$ miles per hour and $66+4$ miles per hour.

⇒ About 68% of vehicles whose speeds are between 62 miles per hour and 70 miles per hour.