The SteelCo company manufactures steel rods. The specification limits on the lengths of these rods are from 95.6 inches to 95.7 inches. The process that produces these rods currently yields lengths that are normally distributed with mean 95.66 inches and standard deviation 0.025 inch.
a. What is the probability that a single rod will be within specification limits?
b. What is the probability that at least 90 of 100 rods will be within specification limits?
c. SteelCo's best customer currently buys 200 of these rods each day and pays the company $20 apiece. However, it gets a $40 refund for each rod that doesn't meet specifications. What is SteelCo's current expected profit per day? How small would its standard deviation need to be before it would net an expected $3900 per day?