Question

The time it takes Claudia to drive to work is normally distributed with a mean of 48 minutes and a standard deviation of 5 minutes. What percentage of the time will it take her less than 53 minutes to drive to work?

Answer 1

To find the percentage of the time it will take Claudia less than 53 minutes to drive to work, we calculate the z-score and use a standard normal distribution table or technology to find the corresponding area.

Step-by-step explanation:

To find the percentage of the time it will take Claudia less than 53 minutes to drive to work, we need to calculate the area under the normal distribution curve to the left of 53 minutes.

First, we calculate the z-score using the formula: z = (x - mean) / standard deviation. In this case, z = (53 - 48) / 5 = 1.

Next, we use a standard normal distribution table or technology to find the area to the left of a z-score of 1. This area represents the percentage of the time it will take Claudia less than 53 minutes to drive to work. From the table or technology, we find that the area is approximately 0.8413, or 84.13%. Therefore, Claudia will take less than 53 minutes to drive to work approximately 84.13% of the time.