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## Homework Statement

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)

## Homework Equations

## 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?