(Refer to Solved Problem 2.) Here is solved problem 2 below:

Z value for 99.74% of sample means can be obtainted from the Normal distribution Z chart Use 0 to Z values on both sides of 0, that - / + sides. Each side will have 99.74 / 2 = 49.87%

The samples lie between -3 <= Z <= 3 ; Z = 3

a) UCL = Mean + Z x [ St Deviation / SQRT(N) ] = 1.0 + 3 x [ 0.01 / SQRT(25) ] = 1.006 ~ 1.01

LCL = Mean - Z x [ St Deviation / SQRT(N) ] = 1.0 - 3 x [ 0.01 / SQRT(25) ] = 0.994 ~ 0.99

b) sample means1.007, 1.002, .998, 1.003, .993, and .994

The process is not in control

1.007 falls above the UCL and 0.993 falls below LCL

c) sample means1.003, .999, .997, 1.001, 1.002, .998, and 1.004

The process is in control

All the sample means falls between the UCL and LCL.

The question is:

Suppose the process specifications are 9.65 and 10.35 minutes. Based on the data given, does it appear that the specifications are being met? If not, what should one look for?