Question

The waiting time in line at an ice cream shop has a uniform distribution between 0 and 9 minutes. What is the 80th percentile of this distribution? (Recall: The 80th percentile divides the distribution into 2 parts so that 80% of area is to the left of 80th percentile) _______ minutes. A) 7.2 minutes

B) 7.6 minutes
C) 8.0 minutes
D) 8.4 minutes

Answer 1

To calculate the 80th percentile of a uniform distribution between 0 and 9 minutes, use the formula P = a + (b - a) * (percentile/100) resulting in 7.2 minutes.

Step-by-step explanation:

The waiting time at an ice cream shop has a uniform distribution between 0 and 9 minutes. To find the 80th percentile, which divides the distribution so that 80% is to the left (i.e., less waiting time), we use the formula for the uniform distribution percentile:

P = a + (b - a) \( imes\) (percentile/100)

where a is the minimum value, b is the maximum value, and percentile is the desired percentile.

Substituting the values:

P = 0 + (9 - 0) \( imes\) (80/100)

P = 0 + 9 \( imes\) 0.8

P = 7.2 minutes

So, the 80th percentile of this distribution is 7.2 minutes, which corresponds to option A).