A production process that is in control has a mean of 80 an

A production process that is in control has a mean () of 80 and a standard deviation () of 10.

a. Determine the upper and the lower control limits for sample sizes of 25.

b. Five samples had means of 81, 84, 75, 83, and 79. Construct an X bar chart and explain whether or not the process is in control.

mu =80 and sigma =10

Sample size = 25

rt of n = 5

Hence std error for the sample = 10/5 = 2

Lower control limit = Mean - 3(std error)

= 74

Upper control limit = Mean+3(std error)

= 86

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b) First find out the sample mean

Sample mean = 402/5

= 80.4

As 80.4 lies within upper and lower limits the process is in control.