According to a 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. [You may find it useful to reference the z table.]
a. What is the probability that the sample mean is more than 105? (Round "z" value to 2 decimal places, and final answer to 4 decimal places.)
b. What is the probability that the sample mean is less than 95? (Round "z" value to 2 decimal places, and final answer to 4 decimal places.)
c. What is the probability that the sample mean is between 95 and 105? (Round "z" value to 2 decimal places, and final answer to 4 decimal places.)