College

Pete's grade on a test was within 5 points of his class average of 94. What is his range of grades on the test?

A. [tex]89 \leq g \leq 99[/tex]
B. [tex]g \leq 89[/tex] or [tex]g \geq 99[/tex]
C. [tex]g \ < \ 99[/tex] or [tex]g \ < \ 89[/tex]
D. [tex]g \geq 89[/tex] or [tex]g \geq 99[/tex]

Answer :

To find the range of Pete's grades, we know that his grade was within 5 points of the class average, which is 94.

1. Identify the Class Average:
The class average for the test is 94.

2. Determine the Range Margin:
Pete's grade can vary by up to 5 points above or below the class average.

3. Calculate the Lower Bound:
Subtract the margin from the class average to find the lowest possible grade Pete could have scored:
[tex]\[
94 - 5 = 89
\][/tex]

4. Calculate the Upper Bound:
Add the margin to the class average to find the highest possible grade Pete could have scored:
[tex]\[
94 + 5 = 99
\][/tex]

5. Establish Pete's Grade Range:
Since Pete's grade is within 5 points of the class average, his possible grades fall between the lower and upper bounds, inclusive. Therefore, the range of Pete's grades is:
[tex]\[
89 \leq g \leq 99
\][/tex]

By comparing this result to the given options, we find that the correct choice is:
- a) [tex]\(89 \leq g \leq 99\)[/tex]

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