The average daily high temperature in February in Fort Collins is 47 degrees (weatherchannel.com). Assume that the daily high temperatures in Fort Collins in February follow a normal distribution. Use the given average as a population mean, with a population standard deviation of 6 degrees.
(a) What is the probability that one randomly selected day will have a high temperature between 42 and 52 degrees?
(b) What is the probability that a simple random sample of 4 days will provide a sample mean between 42 and 52 degrees?
(c) What is the probability that a simple random sample of 8 days will provide a sample mean between 42 and 52 degrees?