Rihanna planned a rectangular courtyard for a park and made a scale drawing using inches as the unit of measurement. she originally planned for the length of the actual courtyard to be 54 feet, but she decided to change it to 72 feet. if the length of the courtyard is 18 inches in her scale drawing, which statement about the change of scale is true?

a one inch represented 1 foot in the first scale, but now 1 inch represents 4 feet in the second scale.
b one inch represented 4 feet in the first scale, but now 1 inch represents 3 feet in the second scale.
c one inch represented 54 feet in the first scale, but now 1 inch represents 72 feet in the second scale.
d one inch represented 3 feet in the first scale, but now 1 inch now represents 4 feet in the second scale.

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?