For one binomial experiment, n1 = 75 binomial trials produced r1 = 45 successes. for a second independent binomial experiment, n2 = 100 binomial trials produced r2 = 70 successes. at the 5% level of significance, test the claim that the probabilities of success for the two binomial experiments differ. compute the pooled probability of success for the two experiments. (round your answer to three decimal places.

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?