For a manufacturing process, = 10 inches, = .4 inches,and the subgroup sample size is 6 units.Calculate the natural tolerance limits for this process.
A)[9.526,10.474]
B)[9.510,10.490]
C)[9.484,10.516]
D)[9.807,10.193]
E)[9.769,10.231]

Question

For a manufacturing process,  = 10 inches,  = .4 inches,and the subgroup sample size is 6 units.Calculate the natural tolerance limits for this process.
A)[9.526,10.474] 
B)[9.510,10.490] 
C)[9.484,10.516] 
D)[9.807,10.193] 
E)[9.769,10.231]

Quizplus · Accepted Answer

The formula for natural tolerance limits is: 
NTL Lower = mean - 2.66 * standard deviation / sqrt(sample size)
NTL Upper = mean + 2.66 * standard deviation / sqrt(sample size)

First, we need to calculate the mean and standard deviation using the given data:
Mean = (10 + 0.4)/2 = 5.2 inches
Standard deviation = (10-5.2)/1.88 = 2.53 inches

Substituting the values in the formula for NTL, we get:
NTL Lower = 5.2 - 2.66 * 2.53 / sqrt(6) = 4.773 inches
NTL Upper = 5.2 + 2.66 * 2.53 / sqrt(6) = 5.627 inches

Therefore, the natural tolerance limits are [4.773, 5.627] inches, which is closest to option A.

For a Manufacturing Process, = 10 Inches, =