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Question: Find the lowest control limit for a normally distributed curve with a mean of 15 and a standard deviation of 2.5.


A ) 12.5
B ) 10
C ) 7.5
D ) 22.5

Steps to derive

1 Mean μ = 15 and standard deviation σ = 2.5.

2 The control limits for 1 standard deviation are
μ - σ and μ + σ. That is 12.5 and 17.5.

3 The control limits for 2 standard deviations are
μ - 2σ and μ + 2σ. That is 10 and 20.

4 The control limits for 3 standard deviations are
μ - 3σ and μ + 3σ. That is 7.5 and 22.5.

5 So, the lowest control limit is 7.5.



Hence the right answer is Option C

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