Suppose Candidate A holds a yes or no vote of confidence and claims that he was at least supported by 65% of the voters. Candidate B suspects foul play and hires you to test the validity of the Candidate A’s claim. So you randomly sample 200 voters from the voting population. Let X be the number of yes votes obtained from a random sample of 200 out of the entire voting population. Calculate the expected value of X, if in fact, 65% of all voters supported Candidate A? g

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?

What is the arc length of the subtending arc for an angle of 72 degrees on a circle of radius 4? o a. 8a oc. 16 t d. 8

The computer that controls a bank's automatic teller machine crashes a mean of 0.6 times per day. what is the probability that, in any seven-day week, the computer will crash less than 5 times? round your answer to four decimal places