Complete the following table by performing the following sequence of operations on the original number: Result of Sequence of Operations
Original Number
2
5
10
15
Multiply the number by 4
Add 12 to the product
Divide the sum by 2
Subtract 6 from the quotient
a. 4, 10, 20, 30
b. 1, 2.5, 5, 7.5
C. 2, 5, 10, 15
d. 5, 10, 15, 20
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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?