Question 3 (4 marks) A sports store has three types of weights machines priced at $550, $750 and $990 and three types of
bench presses priced at $160, $220 and $350. The owner of the store wishes to mark down the prices of
the weights machines by 10% and mark up the prices of the bench presses by 10%.
a.
1mark
Show the prices of the weights machines and bench presses as a suitable matrix
1
b.
Show the scalar matrix that would mark down the weights machines by 10% and mark up the
bench presses by 10%.
1 mark
Mi

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?