The commute times during rush hour traffic on a local interstate have a mean of 25 minutes and a standard deviation of 5 minutes. Repeated studies of this section of interstate are considered normally distributed. What percent of commuters drive between 20 - 25 minutes to work daily?
A) 16%
B) 32%
C) 34%
D) 50%
My answer choice is C
correct
To find the percentage of commuters who drive between 20 and 25 minutes to work daily, we need to calculate the z-scores for both durations and then find the corresponding area under the normal curve.
First, let's calculate the z-score for 20 minutes:
z = (x - mean) / standard deviation
z = (20 - 25) / 5
z = -1
Next, let's calculate the z-score for 25 minutes:
z = (x - mean) / standard deviation
z = (25 - 25) / 5
z = 0
Now, we need to find the area between these two z-scores using a standard normal distribution table or a calculator.
Looking up the z-score of -1 and 0 in a standard normal distribution table, we find the following areas:
z = -1: 0.1587 (From the table)
z = 0: 0.5
To find the area between these two z-scores, we subtract the smaller area from the larger area:
Area between -1 and 0 = 0.5 - 0.1587 = 0.3413
Converting this value to a percentage, we get:
Percentage = 0.3413 * 100 = 34.13%
Therefore, the percentage of commuters who drive between 20 and 25 minutes to work daily is approximately 34%, which corresponds to answer choice C).