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

Answer:

46.75 minutes

Step-by-step 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:

$z=\frac{X- \mu}{\sigma}$

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

$0.675=\frac{X- 40}{10}\\X= 40+6.75=46.75\ minutes$