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. [tex]\mu=\text{ 66 miles per hour}[/tex]
[tex]\sigma=\text{ 4 miles per hour}[/tex]
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 [tex]66-4[/tex] miles per hour and [tex]66+4[/tex] miles per hour.
i.e . The percent of vehicles whose speeds are between [tex]\mu-\sigma[/tex] miles per hour and [tex]\mu +\sigma[/tex] 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 [tex]\mu-\sigma[/tex] miles per hour and [tex]\mu +\sigma[/tex] miles per hour.
i.e . About 68% of vehicles whose speeds are between [tex]66-4[/tex] miles per hour and [tex]66+4[/tex] miles per hour.
⇒ About 68% of vehicles whose speeds are between 62 miles per hour and 70 miles per hour.
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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