The fill volume of an automated filling machine used for filling cans of carbonated beverage is normally distributed. Suppose, that the mean of the filling operation can be adjusted easily, but the standard deviation remains at 0.4 fluid ounce. (a) At what value should the mean be set so that 99.9% of all cans exceed 12 fluid ounces

At a value of 12.3 the mean should be set so that 99.9% of all cans exceed 12 fluid ounces.

Step-by-step explanation:

Let us assume that X is a normal rando variable with a mean value and standard deviation .

Hence, random variable Z will be introduced as follows.

(a) Set the value and the equation will be written down as follows.

According  to the tables,

Thus, we can conclude that at a value of 12.3 the mean should be set so that 99.9% of all cans exceed 12 fluid ounces.

options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒

or  

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.