(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The number of hours spent in a library per week by arts and science students in a college is normally distributed with mean 12 hours and standard deviation 5 hours for arts students and mean 15 hours and standard deviation 4 hours for science students. A random sample of four arts students and six science students is chosen. Assuming that X is the mean number if hours spent by these 10 students in a week. Calculate Var(X)

2. Relevant equations

3. The attempt at a solution

Let X_A and X_S be the random variable of number of hours spent by arts and science students respectively.

X=(4X_A+6X_S)/(10)

Var(X)=Var((4X_A+6X_S)/(10))

=1/100 (16 Var(X_A)+36 Var(X_s))

=1/100 (16 x 25 + 36 x 16)

=9.76

Am i correct?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Find the Variance of this distribution

**Physics Forums | Science Articles, Homework Help, Discussion**