Question

The label on a package of bolts says each bolt has a diameter of 0.35 inch. To be in the package, the percent error of the diameter must be less than 5%. One bolt has a diameter of 0.33 inch. Should it go in the package?

Answer 1

Answer : The bolt should not go in the package.

Step-by-step explanation :

To calculate the percentage error, we use the equation:

`\%\text{ error}=\frac{|\text{Experimental value - Accepted value}|}{\text{Accepted value}}* 100`

We are given:

Experimental value of diameter of bolt = 0.33 inch

Accepted value of diameter of bolt = 0.35 inch

Putting values in above equation, we get:

`\%\text{ error}=(|0.33-0.35|)/(0.35)* 100\\\\\%\text{ error}=5.71\%`

As we are given that the percent error must be less than 5%.

As the percent error is 5.71% which is greater than 5%, that means the bolt cannot be in the package.

Hence, the bolt should not go in the package.

Answer 2

Answer: No

Step-by-step explanation:-

Labeled diameter on the bolt = 0.35 inch

The observed diameter of the bolt= 0.33 inch

`{\text {Percentage Error}}=|\frac{\text {labeled value}-{Observed value}}{\text {Observed value}}|* 100\%`

`{\text{Percentage Error}=|(0.35-0.33)/(0.33)|* 100\%=6.06\%`

For the bolt to be in the package, the percent error must be less than 5%. As the percent error is 6.06% which is greater than 5%, the bolt cannot be in the package.