Question

a student has scores of 80%, 69%, 90%, and 72% on four exams. what grade does the student need on the next exam to have an overall mean of 80%? state your answer as a percent rounded to the nearest whole number, but do not include the % symbol in your answer.

Explanation:

Step1: Recall the formula for the mean

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Here, $n = 5$ (since there will be 5 exams in total after the next one), and $\bar{x}=80$. Let the score on the fifth exam be $x$. The sum of the first four scores is $80 + 69+90 + 72=311$.

Step2: Set up the equation for the mean

Using the mean formula $\frac{311 + x}{5}=80$. Multiply both sides by 5: $311+x = 80\times5$. So, $311+x=400$.

Step3: Solve for $x$

Subtract 311 from both sides: $x=400 - 311$. Then $x = 89$.

Answer:

89