Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

At Quickie Car Wash, the wash process is advertised to take less than 7 minutes.

ID: 422315 • Letter: A

Question

At Quickie Car Wash, the wash process is advertised to take less than 7 minutes. Consequently, management has set a target average of 380 seconds for the wash process. Suppose the average range for a sample of 9 cars is 9 seconds. Use Table below to establish control limits for sample means and ranges for the car wash process.

TABLE: FACTORS FOR CALCULATING THREE-SIGMA LIMITS FOR THE X-CHART AND R-CHART

Factor for UCL and LCL for x-Chart (A2)

Factor for LCL for
R-Chart (D3)

Factor for UCL for R-Chart (D4)

size of sample (n)

Factor for UCL and LCL for x-Chart (A2)

Factor for LCL for
R-Chart (D3)

Factor for UCL for R-Chart (D4)

2 1.880 0 3.267 3 1.023 0 2.575 4 0.729 0 2.282 5 0.577 0 2.115 6 0.483 0 2.004 7 0.419 0.076 1.924 8 0.373 0.136 1.864 9 0.337 0.184 1.816 10 0.308 0.223 1.777

Explanation / Answer

Mean of the sampling distribution = x_double_bar = 380 seconds
Range of the sampling distribution = R_bar = 9 seconds

n=9
A2 = 0.337
D3 = 0.184
D4 = 1.816

UCLx = x_double_bar + A2 * R_bar = 380 + 0.337*9 = 383.033 or 383 seconds
LCLx = x_double_bar - A2 * R_bar = 380 - 0.337*9 = 376.967 or 377 seconds

UCLr = D4 * R_bar = 1.816*9 = 16.344 or 16 seconds
LCLr = D3 * R_bar = 0.184*9 = 1.656 or 2 seconds

Hire Me For All Your Tutoring Needs
Integrity-first tutoring: clear explanations, guidance, and feedback.
Drop an Email at
drjack9650@gmail.com
Chat Now And Get Quote