Sums of Independent Random Variables

[WHB3]

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?

 

[WHB3]

No need to respond, guys. I have found the error of my ways. I forgot that the std Error equals the std deviation divided by the sqr. root of the sample size. Working with that would have brought me to the Probability = 1-I(1.58) = 1-1.9429 =.0571. Thanks, anyway!