Question

Consider a process with mean equal to 10 and standard deviation 3, following a normal distribution. With USL=16 and LSL=4, the probability of defects is

0.317

0.0455

0.0027

0.0001

Answer 1

Mean = 10 units

Standard deviation = 3 units

USL = 16 units

Z-score corresponding to USL = (USL - Mean) / Standard deviation

= (16 - 10) / 3

= 2

The probability of a value to the left of the Z-score of 2.0 from a standard normal distribution table = 0.97725

LSL = 4 units

Z-score corresponding to LSL = (LSL - Mean) / Standard deviation

= (4 - 10) / 3

= -2

The probability of a value to the left of the Z-score of -2.0 from a standard normal distribution table = 0.02275

The probability of a value lying within the specification limits = 0.97725 - 0.02275

= 0.9545

The probability of defects is the probability of a value lying outside the specification limits, i.e. [1 - The probability of a value lying within the specification limits]

= 1 - 0.9545

= 0.0455

Hence the correct answer is option B.