Two methods are proposed to measure the effectiveness of a brand of sunscreen. Method A: Survey adults visiting a beach on a busy weekend. Ask each adult which brand of sunscreen they are using, and assess their arms for sun exposure.

Method B: Volunteers are randomly assigned to one of two brands of sunscreen. Each volunteer is asked to report back at the end of the day, and their arms are assessed for sun exposure.

Which statement is a correct interpretation of these methods?

Both methods are experiments because sun exposure is assessed in both methods.
Both methods are observational studies because neither method attempts to influence responses.
Method A is an experiment because it compares many brands of sunscreen, while method B is an observational study.
Method B is an experiment because it randomly assigns volunteers a sunscreen, while method A is an observational study.

Amachine that produces a special type of transistor (a component of computers) has a 2% defective rate. the production is considered a random process where each transistor is independent of the others. (a) what is the probability that the 10th transistor produced is the first with a defect? (b) what is the probability that the machine produces no defective transistors in a batch of 100? (c) on average, how many transistors would you expect to be produced before the first with a defect? what is the standard deviation? (d) another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. on average how many transistors would you expect to be produced with this machine before the first with a defect? what is the standard deviation? (e) based on your answers to parts (c) and (d), how does increasing the probability of an event a↵ect the mean and standard deviation of the wait time until success?