Peter writes a blog covering news from his local area. He placed a survey on his blog asking whether users desired a change to his blog’s design. A total of 240 users took the survey on a day when the website had 2,975 visitors. Peter found that 55% of those surveyed were in favor of changing the design. Assuming a 90% confidence level, which statement holds true? HINT: It's not B. A. As the sample size is too small, the margin of error cannot be trusted.
B. As the sample size is too small, the margin of error is 0.053.
C. As the sample size is appropriately large, the margin of error is 0.063.
D. As the sample size is appropriately large, the margin of error is 0.053.

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?