Why is rаndоm sаmpling criticаl fоr the validity оf sampling distributions?
A cоmpаny оperаtes twо plаnts for manufacturing motorcycles. The first plant produces 70% of the motorcycles, while the remaining 30% are produced at the second plant. Quality assessments reveal that 80% of motorcycles from the first plant meet the standard quality, whereas 90% from the second plant are of standard quality. If a motorcycle is selected at random and found to be of standard quality, determine the probability that it was manufactured at the second plant. The following events can defined from the problem statement Event A: The motorcycle is manufactured at the first plant.Event B: The motorcycle is manufactured at the second plant.Event C: The motorcycle is of standard quality. (1) Write the probabilities associated for each of the following events. (3pt)P(A)P(B)P(C|A)P(C|B) (2) Write the formulation for calculating P(C) and calculate the probability that a randomly picked motorcycle is of standard quality. (3pt) (3) State the Baye's theorem formula for determining the probability that the motorcycle selected at random is from the second plant given that it is found to be of standard quality P(B|C) and calculate P(B|C). (4pts)