Questions: The following data represent the monthly phone use, in minutes, of a customer enrolled in a fraud prevention program for the past 20 months. The phone company decides to use the upper fence as the cutoff point for the number of minutes at which the customer should be contacted. What is the cutoff point? 454 328 396 379 427 535 339 353 406 451 361 392 380 423 416 311 478 441 513 463 The cutoff point is minutes. (Round to the nearest minute.)

The following data represent the monthly phone use, in minutes, of a customer enrolled in a fraud prevention program for the past 20 months. The phone company decides to use the upper fence as the cutoff point for the number of minutes at which the customer should be contacted. What is the cutoff point?

454 328 396 379 427 535 339 353 406 451 361 392 380 423 416 311 478 441 513 463

The cutoff point is minutes. (Round to the nearest minute.)

Transcript text: The following data represent the monthly phone use, in minutes, of a customer enrolled in a fraud prevention program for the past 20 months. The phone company decides to use the upper fence as the cutoff point for the number of minutes at which the customer should be contacted. What is the cutoff point? 454 328 396 379 427 535 339 353 406 451 361 392 380 423 416 311 478 441 513 463 The cutoff point is $\square$ minutes. (Round to the nearest minute.)

Solution

Solution Steps

Step 1: Sort the Data

The sorted dataset is: [311, 328, 339, 353, 361, 379, 380, 392, 396, 406, 416, 423, 427, 441, 451, 454, 463, 478, 513, 535].

Step 2: Calculate Quartiles

The first quartile (Q1) is calculated as the median of the lower half of the dataset, resulting in 379. The third quartile (Q3) is calculated as the median of the upper half of the dataset, resulting in 454.

Step 3: Compute the Interquartile Range (IQR)

The interquartile range (IQR) is the difference between Q3 and Q1, which is $IQR = Q3 - Q1 = 75$.

Step 4: Calculate the Upper Fence

The upper fence is calculated by adding $1.5 imes IQR$ to Q3, resulting in $Upper Fence = Q3 + 1.5 imes IQR = 566.5$.