Final answer:
Using the 68-95-99.7 rule, 84% of the time, it will take Claudia less than 53 minutes to drive to work.
This is because 68% of her drive times are within one standard deviation of the mean, and 53 minutes is one standard deviation above the mean.
Step-by-step explanation:
To determine what percentage of the time it will take Claudia less than 53 minutes to drive to work, we will use the 68-95-99.7 rule (also known as the empirical rule).
This rule applies to normally distributed data and tells us that approximately 68% of the data falls within one standard deviation (±1σ) of the mean, 95% within two standard deviations (±2σ), and 99.7% within three standard deviations (±3σ).
Claudia's mean commute time is 48 minutes with a standard deviation of 5 minutes. Thus, taking one standard deviation above the mean gives us 48 + 5 = 53 minutes.
According to the empirical rule, 68% of her commute times are between 43 minutes (48 - 5) and 53 minutes.
Since the distribution is symmetric, half of that percentage (34%) will fall below the mean, and 34% will fall above the mean but still within one standard deviation.
Therefore, to find the percentage of the time it will take her less than 53 minutes, we add the 34% to the 50% of times that are below the mean.
In total, 84% (50% + 34%) of the time, it will take Claudia less than 53 minutes to drive to work.
The answer, as a whole number, is 84%.