Question

The time required for a citizen to complete the 2010 U.S. Census ""long"" form is normally distributed with a mean of 40 minutes and a standard deviation of 10 minutes. What is the third quartile (in minutes) for the time required to complete the form?

Answer 1

46.75 minutes

Explanation:

Mean time (μ) = 40 minutes

Standard deviation (σ) = 10 minutes

The third quartile is at the 75th percentile of a normal distribution. According to a z-score table, the corresponding z-score for the 75th percentile is z=0.675.

The z-score for any given time, 'X', is:

`z=(X- \mu)/(\sigma)`

The third quartile for the time required to complete the form is:

`0.675=(X- 40)/(10)\\X= 40+6.75=46.75\ minutes`