# Sums of Independent Random Variables

## Homework Statement

The distribution of the IQ of a randomly selected student from a certain college is N(110,16). What is the probability that the average of the IQ's of 10 randomly selected students from this college is at least 112?

## Homework Equations

I think we need P(Sample Mean - 110 >= 2)

## The Attempt at a Solution

My solution was Probability = (112-110)/1.6 = 1.25; 1-I(1.25)= 1-.8944 =.1056

The answer in the book is .0571, so I know I'm going wrong somewhere.

Any ideas?