Question 24.3: It has been observed from a sample of 200 bearing bushes tha...

\text { Given } \quad \mu=30.010 mm \quad \hat{\sigma}=0.008 mm .

X_{1}=30.02 mm \quad X_{2}=30.00 mm .

\text { Step I Standard variables } Z_{1} \text { and } Z_{2} .

From Eq. 24.7,

Z_{1}=\frac{X_{1}-\mu}{\hat{\sigma}} .               (24.7).

Z_{1}=\frac{X_{1}-\mu}{\hat{\sigma}}=\frac{30.02-30.01}{0.008}=+1.25 .

Z_{2}=\frac{X_{2}-\mu}{\hat{\sigma}}=\frac{30.00-30.01}{0.008}=-1.25 .

Step II Area below normal curve from Z_{1} \text { to } Z_{2}
As shown in Fig. 24.12, the shaded area below the curve represents the percentage of acceptable bushes. From Table 24.6,

Table 24.6 Areas under normal curve from 0 to Z

Shaded area = 2 (area between Z = 0 and Z = 1.25)
= 2 (0.3944) = 0.7888

Step III Percentage of rejected bushes
% of rejected bushes = (1 – 0.7888) × 100 = 21.12%