Question

El Dorado Community College has a main campus in the suburbs and a downtown campus. The amount X spent on tuition by a randomly selected student at the main campus has mean 732.50 and standard deviation 103. The amount Y spent on tuition by a randomly selected student at the downtown campus has mean 825 and standard deviation 126.50. Suppose we randomly select one full-time student from each of the two campuses. Calculate and interpret the mean of the sum$\mathrm{S}=\mathrm{X}+\mathrm{Y}.$

Short answer

The Average mean of the main campus and downtown campus is$15570.50$

Step-by-step solution

Given information

The main campus mean $732.50$, standard deviation $103$

The downtown campus mean $825$,standard deviation $126.50$

$$\begin{gathered} {\mathrm{\mu }}_{\mathrm{X}}=732.50 \\ {\mathrm{\sigma }}_{\mathrm{X}}=103 \\ {\mathrm{\mu }}_{\mathrm{Y}}=825 \\ {\mathrm{\sigma }}_{\mathrm{Y}}=126.50 \end{gathered}$$

X = Amount spent on tuition by students on the main campus who were chosen at random.

Y= Amount spent on tuition by students on the downtown campus who were chosen at random.

Calculations

$$\begin{gathered} \mathrm{\mu }={\mathrm{\mu }}_{\mathrm{X}}+{\mathrm{\mu }}_{\mathrm{Y}} \\ =732.50+825 \\ =1557.50 \end{gathered}$$

There are two mean of two unique irregular factors ${\mathrm{\mu }}_{\mathrm{X}}=732.50$ and ${\mathrm{\mu }}_{\mathrm{Y}}=825$ so the mean of the two arbitrary variable will be the amount of their means. The aggregate sum spent on both the principal grounds and downtown grounds will be normal$15570.50$