The upper and lower specifications for metal head plates are 5 ±0.1 cm. A sample of the metal head plates in 25 undergraduates yields a mean of 5.05. What is the population standard deviation if the population capability index is 1.666?
A) 0.01
B) 0.02
C) 0.03
D) 0.04
E) 0.05

Question

Quizplus · Accepted Answer

The population capability index is defined as:$$C_p = \frac{USL - LSL}{6\sigma}$$where USL is the upper specification limit, LSL is the lower specification limit, and $\sigma$ is the population standard deviation.Substituting the given values into the equation, we get:$$1.666 = \frac{5.1 - 4.9}{6\sigma}$$Solving for $\sigma$, we get:$$\sigma = \frac{0.2}{6(1.666)} = 0.01$$

The Upper and Lower Specifications for Metal Head Plates Are