Question

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.) 

SAMPLE 

$$ \begin{array}{cccccc} 1 & 2 & 3 & 4 & 5 & 6 \\ 79.2 & 83.2 & 79.6 & 78.9 & 80.8 & 79.7 \\ 80.3 & 78.7 & 79.6 & 79.2 & 79.6 & 80.6 \\ 80.0 & 81.0 & 83.9 & 79.7 & 80.4 & 78.7 \\ 78.4 & 80.4 & 80.3 & 79.4 & 80.6 & 80.0 \\ 81.0 & 80.1 & 80.8 & 80.6 & 78.8 & 81.1 \end{array} $$

 Expected process output ____ %

Answer 1

Here, specifications for the computer upgrades are 77 min and 81 min.

By way of observing data, one can say that among the 30 observations, eight observations are outside the specification. Therefore, favorable is 22 (i.e.30-8).

Therefore,

$$ \begin{aligned} P(77

Hence, as per the sample, \(73.3 \%\) of the process output can be expected to fall within the specifications. Therefore, the expected process output is \(73.3 \%\).

Answer 2

In the given data,

Out of the 30 observations, only 3 values(83.2,83.9,81.1) exceeds the tolerances or 3/30*100 = 10%. Thus, it seems that the tolerances are being met : approximately 90% of the output will be acceptable.

So, Expected process output = 90%

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