Answer to Question #221197 in Statistics and Probability for haris

Question

A Bearing Manufacturing Company manufactures bearings with diameter of 12ିସ

ାଷ mm with a standard

deviation equal to 2mm. Bearing above USL are regarded as Scrap while below LSL as Rework. Find

 Percentage of bearings that can be scrapped

 Percentage of bearings that can be reworked

 Total Percentage of bearings non-conforming

 Total Percentage inside the limits

 If the company manufactures half million bearings then how many bearings are conforming to

specifications.

Note: Use normal probability figure for your ease.

Answer 1

Let $X=$ diameter of bearing: $X\sim N(\mu, \sigma^2)$

Given $\mu=12\ mm, \sigma=2\ mm$

a)

$P(X>\mu+1\sigma)=P(X\leq\mu+1\sigma)$

$=P(Z\leq\dfrac{\mu+\sigma-\mu}{\sigma})=P(Z\leq1)\approx0.158655$

$15.8655\%$  of bearings can be scrapped

b)

$P(X<\mu-1\sigma)=P(Z<\dfrac{\mu-\sigma-\mu}{\sigma})$

$=P(Z<-1)\approx0.158655$

$15.8655\%$  of bearings can be reworked

c)

$15.8655+15.8655=31.731$

$31.7310\%$  of bearings are non-conforming.

d)

$100-31.731=68.269$

$68.2690\%$  of bearings are inside the limits.

e)

$0.682690(500000)=341345$

$341345$ bearings among $500000$ are conforming to specifications.