1 Ten members Three juniors and seven seniors from the science club qualify for a national com people per school can attend the event. The coach decides to put the 10 members' names o paper, put the slips in a hat, and pull out five names, one at a time. Those five students will g competition. Let X represent the number of juniors selected to attend the competition. Have the conditions for a binomial setting been met for this scenario? Yes, all four conditions in BINS have been met. O No, we do not know how many people overall will go to the national competition. No, there is no way to find out the probability of choosing just one student to attend. No, the names were pulled and not replaced in the hat, so the independence condition is​

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?