Tyshara wants to go ice-skating. She checks the prices at the two closest skating rinks online. Skate-A-While charges a skate rental fee of $2 and $2.50 for each hour of ice-skating. Rink-for-Skate charges a skate rental fee of $3.50

and $2 for each hour of ice-skating,
How many hours would Tyshara have to skate for the costs to be the same?
2
If she wants to skate for 2 hours, which place is cheaper?

A. the cost will be the same at 2 hours, so Tyshara could go to either one since they would cost the same amount.

B. the costs will be the same at 3 hours, so Tyshara should go to Rink-for-Skate

C. The costs will be the same at 2 hours, so Tyshara should go to skate-a-while

D. the costs will be the same at 3 hours, so Tyshara should go to skate-a-while

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?