Many typical household cleaners contain toxic chemicals. 2-Butoxyethanol is found in multipurpose cleaners and is a very powerful solvent. The EPA has a safety standard for this chemical when used in the workplace, but cleaning at home in a confined area can cause levels to rise well above this standard. The mean percent of 2-butoxyethanol in Rain-X Glass Cleaner is 3.11 Suppose the distribution is approximately normal and the standard deviation is 1%, and a random bottle of Rain-X Glass Cleaner is selected.
a. What is the probability that the percentage of 2-butoxyethanol is less than 2.5?
b. What is the probability that the percentage of 2-butoxyethanol is between 2.2 and 3.5?
c. Suppose the EPA has established a limit of 5% 2-butoxyethanol in all consumer products. What is the probability that a bottle exceeds this limit?
In many U.S. families, both parents work outside the home, while children spend time at daycare centers or are cared for by other relatives. The mean amount of time fathers spend with their child(ren) is 7.3 hours per week.12 Suppose this time distribution is approximately normal with standard deviation 0.75 hour, and suppose a father is randomly selected.
a. What is the probability that the father spends at least 8 hours with his child in a given week?
b. What is the probability that the father spends between 6 and 7 hours with his child in a given week?
c. If the child sees his or her father for less than 6 hours per week, the parental bond is weakened. What is the probability that this special bond will be weakened in a given week?
d. What is the probability that the father will spend at least 9 hours with his child in each of five randomly selected weeks?