Answer to Question #195369 in Statistics and Probability for Abel

Question

The manufacturer sells an article in lots of hundred and agree to pay the purchaser a penalty of no if five or more articles in a lot are defective. He knows from past experience that, on average, 2% of the articles are defective. It costs €2 to make each article, what should the selling price be if the manufacturers over all profit is to be 25%?

Answer 1

$\hat{p}=\dfrac{5}{100}=0.05$

On an average 2% of the article is defective-

$p=0.02$

Number of defective items $= 0.02\times 100=2$

Cost of the manufacturing of items $= 100\times 2=200$

Profit $= \dfrac{Sp-Cp}{Cp}\times 100$

$\Rightarrow25=\dfrac{Sp-200}{200}\times 100\\[9pt]\Rightarrow Sp-200=50\Rightarrow Sp=250$

Hence The selling price will be 250 .