At a local restaurant, the amount of time that customers have to wait for their food is normally distributed with a mean of 46 minutes and a standard deviation of 3 minutes. Using the empirical rule, what percentage of customers have to wait between 40 minutes and 52 minutes?
According to the empirical rule, approximately 68% of data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.
In this case, the interval 40 minutes to 52 minutes is within two standard deviations of the mean. Since 52 minutes is 2 standard deviations above the mean (46 + 2(3) = 52) and 40 minutes is 2 standard deviations below the mean (46 - 2(3) = 40), we can expect approximately 95% of customers to have to wait between 40 minutes and 52 minutes.