$3.$ Electronics, Inc. buys electronic switches from Extel Corp for use in their own manufacturing process. In the negotiations for a contract, the companies have agreed that a shipment will be considered good quality if it contains no more than $3\%$ defective switches and will be considered a poor quality shipment if it contains $15\%$ or more defective switches.

Answer part $($a$)$ i and ii without using the smallest$-$sample$-$size calculation $($that will be used in $($b$))$The companies would like a plan with sample size $30$ or $35($convenient for their record$-$keeping$)$ for which the risk to Extel $($supplier$)$ is no more than $5\%$ and the risk to Electronics. $($purchaser$)$ is no more than $10\%.$

Can this be done with sample size $30?$ Explain $($For a $$Yes$,$ giving the plan $$ with the actually achieved $\backslash$alpha and $\backslash$beta $$ counts as an explanation. For a $$No$$ you need to say why no acceptance number can work with sample size $30)$

Can this be done with sample size $35?$ Explain $($give the plan $$ including actual $\backslash$alpha and $\backslash$beta $$ or explain shy no plan can work$)$