I am stuck on two of the practice problems. I've tried everything I can think of, but I'm just completely lost.
Could I get some directions/hints for these two problems?
First problem: "The batteries produced in a manufacturing plant have a mean time to failure of 28 months with a standard deviation of 3 months. A simple random sample of 100 batteries is taken and it is recorded how long it takes for each battery to fail. What is the level L so there is only a 13% chance that the sample mean time to failure falls above L?"
I think this is a z-score problem possibly, but I've tried setting it up using the z-score 1.13, which represents the left tail 87%, and setting up a (mean-x)/std dev=z, Iusing the sample std dev (.3) and I get 27.66 which is apparently wrong.
Second problem: "Pharmaceutical companies advertise for the birth control pill an efficacy of 99.5% in preventing pregnancy. However, under typical use, the real efficacy is only about 98%. That is, 2% of women taking the pill for a year will experience an unplanned pregnancy that year.
A gynecologist looks back at a random sample of 100 medical records from patients who had been prescribed the pill one year before. What is the probability that the proportion of the women in the sample that experienced an unplanned pregnancy is more than 0.03?"
I sort of tried the same as above, and a ton of other things, but none of it has worked at all and now I'm not even sure I understand the problem anymore.