1. The SAT scores of high school seniors have a distribution that 
is approximately normal with mean 500 and standard deviation 100.

a) Choose one senior at random.  What is the probability that his 
or her score is higher than 500?  Higher than 600?

b) Now choose a random sample of 4 seniors.  What is the probability 
that the average of their scores is higher than 500?  
Higher than 600?


2. Juan makes a measurement in a chem lab and records the result in 
his lab report.  The standard deviation of students' lab measurements 
is 10 mg.  Juan repeats the measurement 3 times and records the average 
of his 3 measurements.

a)  What is the standard deviation of Juan's average result?  
(That is, if Juan kept on making 3 measurements and averaging them, 
what would be the standard deviation of all the averages?)

b) How many times must Juan repeat the measurement to reduce the 
standard deviation of the average to 5?