An automatic machine in a manufacturing process is operating properly if the length of an important subcomponent is normally distributed with a mean= 80 cm and a standard deviation= 2 cm. a) Find the probability that the length of one randomly selected unit is less than 79 cm. b) Find the probability that the average length of 10 randomly selected units is less than 79 cm. c) Find the probability that the average length of 30 randomly selected units is less than 79 cm. A retailer is looking to evaluate its customer service. Management has determined that if the retailer wants to stay competitive, then it will have to have at least a 90% satisfaction rate among its customers. Management will take corrective actions if the satisfaction rate falls below 90%. A survey of 1,200 customers showed that 1,068 were satisfied with their customer service. a)State the hypotheses to test if the retailer needs to improve its services. b)What is the value of the test statistic? c)Compute the critical value. d)Interpret the results at= 0.05