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.)

68% of vehicles have speeds are between 62 miles per hour and 70 miles per hour.

The empirical rule states that for a normal distribution, 68% of the distribution are within one standard deviation from the mean, 95% are within two standard deviation from the mean and 99.7% are within three standard deviations from the mean.

Given that:

Mean (μ) = 66, Standard deviation (σ) = 4

68% are within one standard deviation = μ ± σ = 66 ± 4 = (62, 70)

68% of vehicles have speeds are between 62 miles per hour and 70 miles per hour.

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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.

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 miles per hour and miles per hour.

i.e . The percent of vehicles whose speeds are between miles per hour and 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 miles per hour and miles per hour.

i.e .  About 68% of vehicles whose speeds are between miles per hour and miles per hour.

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

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