Question

Your first assignment at El Smello Perfume Co. is to determine the proper setting for filling the bottles. The company wishes to keep profits high by using as little perfume as possible, but a government regulation states that no more than 2.5% of the bottles may contain less than the stated volume on the bottle. If the bottles you are filling are stated to contain 100 mL, what is the minimum volume you should use for filling if the standard deviation in the fill level is /- 1.6 mL. (Hint: assume an infinite number of samples where the CI is x /- ts and t

Answer 1

Answer:

The answer is "96.864 ml".

Step-by-step explanation:

In this question, the formula of $\bold{CI = X \pm t \times s}$.

( where X is the mean, t is the coefficient, and s is the mean difference error)

As a result, only 2.5% of containers might include less than 100 ml of volume, its trust coefficient could indeed be used in accordance with 95%, which is $t=1.96$.  

And it can take $\pm \ 1.6 \ ml$ to have been the full value the standard infinite:  $\to CI = 100 \pm (1.96 \times 1.6)$

         $= 100 \pm (3.136)$

Consequently, if the standard error is  $\pm \ 1.6 \ ml$ , a similar amount should be used to fill  

$= 100 - 3.136 \\\\= 96.864 \ \ mL$