Question

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?322 305 437 474430 335 368 332401 323 516 310361 437 464 488375 542 515 332the cutoff point is $square$ minutes.(round to the nearest minute.)

Explanation:

Step1: Sort data ascendingly

305, 310, 322, 323, 332, 332, 335, 361, 368, 375, 401, 430, 437, 437, 464, 474, 488, 515, 516, 542

Step2: Find median (Q2)

Split data into lower/upper halves.
Lower half: 305, 310, 322, 323, 332, 332, 335, 361, 368, 375
Upper half: 401, 430, 437, 437, 464, 474, 488, 515, 516, 542
Median $Q2 = \frac{375+401}{2} = 388$

Step3: Calculate Q1 (lower median)

$Q1 = \frac{332+332}{2} = 332$

Step4: Calculate Q3 (upper median)

$Q3 = \frac{464+474}{2} = 469$

Step5: Compute interquartile range (IQR)

$IQR = Q3 - Q1 = 469 - 332 = 137$

Step6: Calculate upper fence

Upper fence = $Q3 + 1.5 \times IQR$
$= 469 + 1.5 \times 137 = 469 + 205.5 = 674.5$

Step7: Round to nearest minute

$674.5 \approx 675$

Answer:

675 minutes