Ketchup A fast-food restaurant has just installed a new automatic ketchup dispenser for use in preparing its burgers. The amount of ketchup dispensed by the machine follows a Normal distribution with mean 1.05 ounces and standard deviation 0.08 ounce.

(a) If the restaurant’s goal is to put between 1 and 1.2 ounces of ketchup on each burger, what percent of the time will this happen? Show your work.

(b) Suppose that the manager adjusts the machine’s settings so that the mean amount of ketchup dispensed is 1.1 ounces. How much does the machine’s standard deviation have to be reduced to ensure that at least 99% of the restaurant’s burgers have between 1 and 1.2 ounces of ketchup on them?