Question

A company manufactured a 16-oz box of cereal. Boxes are randomly weighted to ensure the correct amount. If the discrepancy in weight is more than 0.15 oz, the production is stopped. What is the range of acceptable values for production to continue?

Answer 1

Answer:

The acceptable range will be : 15.85 oz to 16.15 oz

Step-by-step explanation:

Let the weight of the box be = x

As given,

If the discrepancy in weight is more than 0.15 oz, the production is stopped.

And if the discrepancy in weight is less than 0.15 oz then the production will continue.

We can express this as : If $|x-16| \leq 0.15$ ; the production continues

$|z| \leq a$ or we can say

$-a\leq z\leq a$

Now, z = x-16, and a=0.15, then the value becomes,

$-0.15 \leq x-16 \leq 0.15$

Solving for x:

We get the final range as :

$-0.15+16 \leq x-16+16 \leq 0.15+16$

$15.85\leq x \leq 16.15$

Therefore, the answer is : $15.85\leq x \leq 16.15$

Answer 2

It should be noted that the range that's acceptable will be 15.85 oz and 16.15 oz.

How to calculate the range.

From the information, the discrepancy in weight is about 0.15 oz. The lowest weight will be:

= 16 - 0.15 = 15.85 oz

The highest weight will be:

= 16 + 0.15 = 16.15 oz.

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