4. Andy has 60 orange trees in his grove that are in 6 rows of 10 trees. He wants to
know how many oranges he will harvest
this season but does not have time to
count the number of oranges on each
tree. Does the method described produce
a representative sample of the trees in
the grove?

a. Assign a number to
each tree and pull 8 numbers from a hat.

b. Select 10 trees from the same row

c. Select 3 consecutive trees

d. Randomly select 6 trees

e. Select the trees in each corner

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?