Needing help understanding and solving this problem... I have several other like

Question

Needing help understanding and solving this problem... I have several other like it. Trying to find the expected process output.

Specifications for the computer upgrades are 77 minutes and 81 minutes. Estimate the percentage of process output that can be expected to fall within the specifications. (Round your answer to 1 decimal place. Omit the "%" sign in your response.)

Expected process output: %

SAMPLE 79.2 80. 79.6 78.9 80.4 79.7 79.778.779.6 78.7 79.6 80.6 80.0 81.080.2 79.7 80.4 80.5 78.4 80.4 80.3 79.4 78.8 80.0 81.0 80.1 80.8 80.6 78.8 81.1

Explanation / Answer

There can be two methods to calculate the above %.

Method 1 - Counting (more popular)

Looking at the data above, we see that there are 30 total points, and 1 point (last is outside the specifications limits.

The proportion within the specification limits is 29/30 = 0.9667 or 96.67%

Method 2 - Range method (more accurate)

R_bar = 1.83333

for n=5; d2= 2.326 (from standard 3-sigma table)

Estimate for process standard deviation = R_bar / d2 = 1.83333/2.326 = 0.7882
Estimate for process mean = mean of the sampling means = 79.8767

% of process output within the range [77, 81] = NORMDIST(81, 79.8767, 0.7882, TRUE) - NORMDIST(77, 79.8767, 0.7882, TRUE) = 92.28%

Observation 1 2 3 4 5 6 Average 1 79.2 80.1 79.6 78.9 80.4 79.7 2 79.7 78.7 79.6 78.7 79.6 80.6 3 80 81 80.2 79.7 80.4 80.5 4 78.4 80.4 80.3 79.4 78.8 80 5 81 80.1 80.8 80.6 78.8 81.1 Range 2.6 2.3 1.2 1.9 1.6 1.4 1.833333

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