1. A survey of college women. A sample survey interviews an SRS of 280 college women. Suppose (as is roughly true) that 70% of all college women have been on a diet within the last 12 months. What is the probability that 75% or more of the women in the sample have been on a diet?
2. Plastic caps for motor oil containers. A machine fastens plastic screw-on caps onto containers of motor oil. If the machine applies more torque than the cap can withstand, the cap will break. Both the torque applied and the strength of the caps vary. The capping-machine torque has the Normal distribution with mean 7.0 inch-pounds and standard deviation 0.9 inch-pounds. The cap strength (the torque that would break the cap) has the Normal distribution with mean 10.1 inch- pounds and standard deviation 1.2 inch-pounds.
(a) Explain why it is reasonable to assume that the cap strength and the torque applied by the machine are independent.
(b) What is the probability that a cap will break while being fastened by the capping machine?