Ms. Finkel has suggested that if given sufficient resources, she could redesign the production process to reduce the percentage of 16-ounce boxes of Go Bananas! that fail to meet the standard weight of banana-flavored marshmallows when the process is working properly. To what level must Ms. Finkel reduce the percentage of 16-ounce boxes of Go Bananas! that fail to meet the standard weight of banana-flavored marshmallows when the process is working properly in order for her to reduce the probability at least five of the sampled boxes fail to meet the standard to .01 or less

To find the probability that the sample which fails to meet the required weight or the standard weight of the marshmallows having banana flavor if the process of production is working, such that probability for the weekly sample leads to shutdown of the production if the process of the production is running properly of 1 % of the probability that at least five boxes out of the twenty five sample fails to meet the standard weight which is less than one percent that is [tex]$p(x \geq 5) \leq 0.01$[/tex]

We know that for p = 0.8, [tex]$p(x \geq 5) = 0.0452$[/tex]

Now using binomial simulation, we can determine that [tex]$p(x \geq 5) \leq 0.01$[/tex] for p = 0.0452

So the production process is to be redesigned for reducing the percentage of boxes of the Go Bananas of 16 ounces which failed to meet the required weight of the marshmallows having banana flavor if the production process is working properly to 5.42 percent.