Bottles filled by a certain machine are supposed to

Answer:

Step 1 of 2:

(a)

In this question, we are asked to find the mean volume of a random sample of  bottles is less than oz.

Bottles filled by a certain machine are supposed to contain 12 oz of liquid.

Fill volume has mean 12.01 oz and standard deviation 0.2 oz.

Let denote the fill volume in the 144 bottles.

We need to find

Now the sample size is , which is a large sample.

Then according to Central Limit Theorem,

Let  be a simple random sample from a population with mean

and variance .

Let

Hence  can be approximately normal distributed.

CLT specifies that , variance  and standard deviation

Hence our sample mean and standard deviation is,

 = 0.01667

Therefore the  score of 12 oz is

=

=

 =

From the z table, the area to the left of   is 0.2877.

Therefore = 0.2877, so only 28.77% of samples of size 144 will have fewer than 12 oz of fill volume.