An electrical component for one of the main products your company produces is specified to have an electrical impedance of 2.15 ohms. However, the manufacturing process is not perfect and there is some variation on the actual impedance of these components. A recent statistical study indicated that in fact, the impedances are normally distributed with a mean impedance of 2.15 ohms and a standard deviation of 0.05 ohms. When the impedance exceeds 2.25 ohms, the product malfunctions so that component must be rejected and replaced by one whose impedance is within the acceptable limit. If you need 1350 usable components, how many components should you order

In this problem we have to calculate the proportion of products that are within specifications, according to the mean anda standard deviation of the process.

The limit value for the impedance X is 2.25 ohms. Products within specifications have an impedance smaller than 2.25 ohms.

The z-value to calculate the probability of X<2.25 is

[tex]z=\frac{X-\mu}{\sigma}=\frac{2.25-2.15}{0.05}=\frac{0.10}{0.05}=2[/tex]

Then we have that

[tex]P(X<2.25)=P(z<2)=0.97725[/tex]

It means than for every 1000 products, 977 are within specifications and 23 are not.

To manufacture 1350 usable components, we can calculate

[tex]N=\frac{1350}{0.977}= 1382[/tex]

To manufacture 1350 usable components you should order 1382 components.