Question: Wasatch Wireless manufactures a deluxe cell phone model which can retain its battery charge for a population mean average of 20 hours with a population standard deviation of 4 hours. The continuous random variable, x, represents the length of time the charge lasts, and is found to be normally distributed. [COMMENTS & HINTS: When answering the following questions, draw a diagram of the distribution.]

a) What is the probability that the battery for a randomly selected cell phone manufactured by Wasatch Wireless retains its charge for at least 13 hours but less than 31 hours?

b) What is the probability that the battery for a randomly selected cell phone manufactured by Wasatch Wireless retains its charge for more than 27.5 hours?