Exit polling has been a controversial practice in recent elections, since early release of the resulting information appears to affect whether or not those who have not yet voted do so. Suppose that 90% of all registered Wisconsin voters favor banning the release of information from exit polls in presidential elections until after the polls in Wisconsin close. A random sample of 250 Wisconsin voters are selected (You can assume that the responses of those surveyed are independent). Let X be the number of people in the 250 who favor the ban. Required:
a. What is the probability that more than 23 favor the ban?
b. What is the probability that at least 23 favor the ban?
c. What are the mean value and standard deviation of the number who favor the ban in a sample of size 25?
d. Is it probable that fewer than 23 in the sample favor the ban with the assertion that 90% populace favors the ban?

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?