the scores and their percent of the final grade for a statistics student are given. what is the students…

Explanation:

Step1: Recall weighted - mean formula

The formula for the weighted mean $\bar{x}=\sum_{i = 1}^{n}x_{i}w_{i}$, where $x_{i}$ is the score and $w_{i}$ is the weight (as a decimal). First, convert the percentages to decimals.

Step2: Convert percentages to decimals

Homework: $w_1 = 0.15$, Quiz 1: $w_2=0.15$, Quiz 2: $w_3 = 0.15$, Project: $w_4=0.25$, Final Exam: $w_5 = 0.30$. Scores are $x_1 = 84$, $x_2=81$, $x_3 = 91$, $x_4=95$, $x_5 = 90$.

Step3: Calculate the product of each score and its weight

$x_1w_1=84\times0.15 = 12.6$, $x_2w_2=81\times0.15=12.15$, $x_3w_3=91\times0.15 = 13.65$, $x_4w_4=95\times0.25=23.75$, $x_5w_5=90\times0.30 = 27$.

Step4: Sum up the products

$\bar{x}=12.6 + 12.15+13.65 + 23.75+27$ $\bar{x}=89.15$

Answer:

$89.15$