When Harper commutes to work, the amount of time it takes her to arrive is normally distributed with a mean of 20 minutes and a standard deviation of 3.5 minutes. What percentage of her commutes will be shorter than 23 minutes, to the nearest tenth?

Answer 1

To find the percentage of Harper's commutes that will be shorter than 23 minutes, we can calculate the z-score for 23 minutes using the formula:

z = (X - μ) / σ

where:
X = 23 minutes
μ = mean (20 minutes)
σ = standard deviation (3.5 minutes)

z = (23 - 20) / 3.5 = 3 / 3.5 = 0.857

Next, we can look up the z-score of 0.857 in a standard normal distribution table to find the percentage of data below this value. From the table, we find that approximately 80.4% of the data falls below a z-score of 0.857.

Therefore, approximately 80.4% of Harper's commutes will be shorter than 23 minutes.