Question

1. joe earned a 78, 82, and 95 on his last three quizzes. what is the minimum grade he needs on his next quiz to have a mean of 87? a. 87 b. 89 c. 93 d. 97

Explanation:

Step1: Recall mean formula

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $n$ is the number of data - points and $\sum_{i = 1}^{n}x_{i}$ is the sum of the data - points. Here, $n = 4$ (three quizzes plus the next one) and $\bar{x}=87$. Let the score of the next quiz be $x$. The sum of the first three scores is $78 + 82+95=255$.

Step2: Set up the equation for the mean

We have $87=\frac{78 + 82+95+x}{4}$, which simplifies to $87=\frac{255 + x}{4}$.

Step3: Solve the equation for $x$

Multiply both sides of the equation by 4: $87\times4=255 + x$. So, $348=255 + x$. Then subtract 255 from both sides: $x=348 - 255=93$.

Answer:

C. 93