at a health club, 60% of the members are men and 40% of the members are women. the average age of the men is…

at a health club, 60% of the members are men and 40% of the members are women. the average age of the men is 32 years. the average age of the women is 28 years. what is the average age of all the members of the health club? enter your answer as a decimal in the box. years

at a health club, 60% of the members are men and 40% of the members are women. the average age of the men is 32 years. the average age of the women is 28 years. what is the average age of all the members of the health club? enter your answer as a decimal in the box. years

Answer

Explanation:

Step1: Set up the weighted - average formula

Let the proportion of men be $p_m = 0.6$, the average age of men be $\bar{x}_m=32$, the proportion of women be $p_w = 0.4$, and the average age of women be $\bar{x}_w = 28$. The formula for the weighted average $\bar{x}$ is $\bar{x}=p_m\bar{x}_m + p_w\bar{x}_w$.

Step2: Substitute the values into the formula

$\bar{x}=0.6\times32+0.4\times28$. First, calculate $0.6\times32 = 19.2$ and $0.4\times28=11.2$. Then, $\bar{x}=19.2 + 11.2$.

Step3: Calculate the final result

$\bar{x}=30.4$.

Answer:

$30.4$