Calculate the mean and standard deviation of a normal distribution question horace was told that his math test score was 3 standard deviations above the mean. if test scores were approximate normal with = 81 and o = 6, what was horace's score? do not include units in your answer. for example, if you fo that the score was 81 points, you would enter 81. provide your answer below: feedback more instruction coment attribution • previous

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?