Question

An insurance company has an online help service for its customers. Customer queries that take more than 5 minutes to resolve are categorized as​ "unsatisfactory" experiences. To evaluate the quality of its​ service, the company takes 10 samples of 100 calls each while the process is under control.

p values (n = 100)

0.06

0.14

0.13

0.05

0.16

0.08

0.17

0.04

0.19

0.16

a. calculate the p̄ and S_p values and set up control limits so that future sample p values should fall within the control limits 99.7% of the time

The p̄ value is _____. (enter your response rounded to three decimal places.)

Answer 1

a)

The p- value is average(0.06,0.14,0.13,0.05,0.16,0.08,0.17,0.04,0.19,0.16) = 0.118

p value is sqrt((p-bar*(1-p-bar))/sample size) = sqrt((0.118*(1-0.118))/100) = 0.032260812 = 0.032 (Rounded to 3 decimal places)

As Z = 3 here,

The upper control limit is p-bar + z*Sp = 0.118+3*0.032 = 0.214
The upper control limit is p-bar - z*Sp = 0.118-3*0.032 = 0.022