The amount of caffeine in a cup of coffee varies considerably, even if it is brewed by the same person, using the same brewing method and ingredients. Suppose the amount of caffeine in an eight-ounce cup of Maxwell House coffee is approximately normally distributed with mean 120 mg and standard deviation 7.75 mg.27
a. What is the probability that a randomly selected cup of Maxwell House coffee will have less than 110 mg of caffeine?
b. What is the probability that a randomly selected cup of Maxwell House coffee will have between 115 and 130 mg of caffeine?
c. A recent article in a medical journal suggests that an eight-ounce cup of coffee with more than 140 mg of caffeine could cause a person’s heart to race. What is the probability that a randomly selected cup will have more than 140 mg of caffeine?
The quality of a kitchen knife is often measured by the sharpness and total lifetime of the blade. One test for sharpness involves mounting the knife with the blade vertical and lowering a specially designed pack of paper onto the blade. The sharpness is measured by the depth of the cut. A greater depth indicates a sharper knife. Suppose the depth of the cut for a randomly selected knife has a normal distribution with mean 92 mm and standard deviation 21 mm.
a. What is the probability that a randomly selected kitchen knife has a sharpness measure less than 75 mm?
b. A kitchen knife with a sharpness measure of at least 100 mm qualifies as a steak knife. What proportion of kitchen knives are steak knives?
c. The Kitchen Gadgets Association would like to set a maximum sharpness for butter knives. Find a value c such that 15% of all knives have sharpness less than c.
d. Suppose a randomly selected kitchen knife has sharpness greater than 90 mm. What is the probability that it has sharpness greater than 100 mm?