A packaging system fills boxes to an average weight of 16 ounces with a standard deviation of 0.3 ounce. It is reasonable to assume that the weights are normally distributed. Calculate the 1st, 2nd, and 3rd quartiles of the box weight.

Step-by-step explanation:

Given

---- the average

-- standard deviation

Required

The 1st to 3rd quartile

Since the distribution is normal, then:

i.e.

So, we have:

Rewrite Median as Q2

To solve for Q1 and Q3, we use the following formula

Multiply both sides by 2

Substitute

Also, we have:

----- quadrants are equidistant

Rewrite as:

Substitute:

Make Q3 the subject

Substitute in

Collect like terms

Divide by 2

Substitute in

-7/8

step-by-step explanation:

instead of subtracting you add the -6/8 and -1/8

shift 4 units up, and 1 unit left.

it will translate f(x) = 3^x to g(x) = 3^(x+1) + 4