Question

An executive drives from her home to her office in the city. The driving times are normally distributed with a mean of 35 minutes and a standard deviation of 8 minutes. How long will the longest 10 percent of the trips take?

Answer 1

To find the longest 10 percent of trips, we need to find the value that corresponds to the 90th percentile of the driving times distribution.

Step-by-step explanation:

To find the longest 10 percent of trips, we need to find the value that corresponds to the 90th percentile of the driving times distribution.

First, we need to standardize the value using the z-score formula: Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

Then, we can use a standard normal distribution table (also called a Z-table) or a statistical calculator to find the z-score that corresponds to the 90th percentile. Finally, we can solve for X using the formula X = Z σ + μ.