A machine that fills bottles with a beverage has a fill volume whose mean is 20.01 ounces, with a standard deviation of 0.02 ounces. A case consists of 24 bottles randomly sampled from the output of the machine.

a. Find the mean of the total volume of the beverage in the case.

b. Find the standard deviation of the total volume of the beverage in the case.

c. Find the mean of the average volume per bottle of the beverage in the case.

d. Find the standard deviation of the volume per bottle of the beverage in the case.

e. How many bottles must be included in a case for the standard deviation of the average volume per bottle to be 0.0025 ounces?

Solution 8E

Step1 of 3:

We have machine and that fills bottles with a beverage has a fill volume whose mean is 20.01 ounces and standard deviation is 0.02 ounces. Let us consider a random variable X it consists of 24 bottles randomly sampled from the output of the machine.

That is

Here our goal is:

a).We need to Find the mean of the total volume of the beverage in the case.

b).We need to Find the standard deviation of the total volume of the beverage in the case.

c).We need to Find the mean of the average volume per bottle of the beverage in the case.

d).We need to Find the standard deviation of the volume per bottle of the beverage in the case.

e).We need to find How many bottles must be included in a case for the standard deviation of the average volume per bottle to be 0.0025 ounces?

Step2 of 3:

a).

The mean of the total volume of the beverage in the case is given by

=

= n

= 2420.01

= 480.24

Therefore, The mean of the total volume of the beverage in the case is 480.24.

b).

We have

Variance

= 0.0004

The standard deviation of the total volume of the beverage in the case is given by

=

=

...