Question

An automatic filling machine is used to fill 1-liter bottles of cola. The machine's output is approximately normal with a mean of 1.0 liter and a standard deviation of 0.02 liters. Output mean is monitored daily by using 100 samples, each with 25 observations. Determine three sigma upper and lower control limits. Select one: a. UCL = 1.012; LCL = 0.988 О b. UCL = 1.006; LCL = 0.994 O c. UCL = 1.02; LCL = 0.98 d. none of the listed e. UCL = 1.06; LCL=0.94

Answer 1

mean  - 1 liter

standard deviation $\sigma$ = 0.02 liters

output mean iis taken using the  -

sample = 100

observation = 25

therefore 4 times of observatioon is taken

N = 4

as 3 $\sigma$ standard deviation is needed there fore z value is taken for 97% of confidence i.e 2.17

upper control limit = mean + z * $\sigma$ / observation (N)

= 1 + 2.17 * 0.02 / 4 = 1.01085 = 1.02

lower control limit = mean - z * $\sigma$ / observation (N)

=   1 -  2.17 * 0.02 / 4 = 0.98915 = 0.98  

answer = c) UCL = 1.02 , LCL = 0.98