A random sample of 48 days taken at a large hospital shows that an average of 38 patients were treated in the emergency room (ER) per day. The standard deviation of the population is 4.
a. Find the 95% confidence interval of the mean number of ER patients treated each day in the hospital
b. Find the 95% confidence interval of the mean number of ER patients treated each day in the hospital if the standard deviation is 8 instead of 4.