When Tallulah commutes to work, the amount of time it takes her to arrive is normally distributed with a mean of 48 minutes and a standard deviation of 4 minutes. Using the empirical rule, what percentage of her commutes will be between 36 and 60 minutes?
According to the empirical rule, for a normal distribution:
- About 68% of the data falls within one standard deviation of the mean.
- About 95% of the data falls within two standard deviations of the mean.
- About 99.7% of the data falls within three standard deviations of the mean.
In this case, Tallulah's commute time is normally distributed with a mean of 48 minutes and a standard deviation of 4 minutes.
To find the percentage of her commutes between 36 and 60 minutes, we need to find the z-scores for these values:
For 36 minutes: z = (36 - 48) / 4 = -3
For 60 minutes: z = (60 - 48) / 4 = 3
Using a standard normal distribution table or calculator, we find that the percentage of data between -3 and 3 standard deviations is about 99.7%.
Therefore, approximately 99.7% of Tallulah's commutes will be between 36 and 60 minutes.