A soft-drink machine is regulated so that the amount of drink dispensed is approximately normally distributed with standard deviation equal to 0.15 deciliter. Find a 95 % confidence level for the mean of all drinks dispensed by this machine if a random sample of 36 drinks has an average content of 2.25 deciliters.

The 95 % confidence level for the mean of all drinks dispensed by this machine is between 2.2010 deciliters and 2.2990 deciliters.

Step-by-step explanation:

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of .

So it is z with a pvalue of , so

Now, find M as such

In which is the standard deviation of the population and n is the size of the sample.

The lower end of the interval is the mean subtracted by M. So it is 2.25 - 0.049 = 2.2010 deciliters

The upper end of the interval is the mean added to M. So it is 2.25 + 0.049 = 2.2990 deciliters

The 95 % confidence level for the mean of all drinks dispensed by this machine is between 2.2010 deciliters and 2.2990 deciliters.

i think asking google will you get the answer to that question

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4