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? Multiple Choice

a.47.50
b.44.75
c.46.75
d.52.50

Answer 1

Third quartile (Q₃) = 46.75 minutes.

Therefore, Option (c) is the correct answer.

Explanation:

Given: Mean (μ) = 40 minutes and S.D (σ) = 10 minutes

To find : Third quartile (Q₃) = ?

Sol: As the third quartile of normal distribution covers the 75% of the total area of the curve and first quartile covers the 25% of the total area of the curve. Then with the help of z score table, the value represented the third quartile of the normal distribution is:

Q₃ = μ + 0.675 σ

Now by substitution the value of mean and standard deviation,

Q₃ = 40 + 0.675 × (10)

Q₃ = 40 + 6.75

Q₃ = 46.75

Therefore, the third quartile (Q₃) = 46.75. So, option (c) is the correct answer.