Continuing their work from Lesson 6.1.2, Mo and Lana recognize that there is no reason they have to simply add the two independent spins. What if they were to subtract them? One possible outcome is that the first spinner could read 5 and the second spinner could read 2 . This would be a difference of 3. Or the first spinner could read 4 , and the second spinner could read 5 . This would be a difference of 1 . There is some variability again. Finish the following two-way table for x-x , and find the mean, variance, and standard deviation. Were there any surprising results?

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?