According to a recent survey, high school girls average 100 text messages daily (The Boston Globe, April 21, 2010). Assume the population standard deviation is 20 text messages. Suppose a random sample of 50 high school girls is taken.
a. What is the probability that the sample mean is more than 105?
b. What is the probability that the sample mean is less than 95?
c. What is the probability that the sample mean is between 95 and 105?