Shannon has three different recipes for chocolate chip cookies. If she wants to make 4 dozen cookies from Batch A, she needs to use 2 cups of chocolate chips. If she wants to make 3 dozen cookies from Batch B, she needs to use 3 cups of chocolate chips. If she wants to make 3 dozen cookies from Batch C, she needs to use 1.5 cups of chocolate chips. Calculate each unit rate and then select the true statements below.

Batch C would use 6 cups of chocolate chips to make 12 dozen cookies.

Batch B uses 1 cup of chocolate chips per 1 dozen cookies.

Batch C uses less cups of chocolate chips per dozen than Batch A.

Batch A and Batch C have the same number of cups of chocolate chips per cookie.

Batch A and Batch B have the same number of cups of chocolate chips per cookie.

Batch B uses less cups of chocolate chips per dozen than Batch C.

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?