3 In a factory the time it takes to assemble a given equipme

3. In a factory the time it takes to assemble a given equipment varies from worker to worker, but it is known that the distribution of assembly time is normal with a mean of 100 minutes and with a standard deviation of 10 minutes.

a) Compute the probability that an assembly time for a randomly chosen worker will be between 90 and 105 minutes

b) The management gives a bonus to 10% of workers with the shortest assembly time. What is the largest assembly time that qualifies the worker for a bonus?

c) Suppose that 20 workers are selected at random. What is the proba- bility that the number (out of 20 selected workers) who get a bonus will be greater or equal to 1 and less or equal to 3?

d) If the bonus is $500 per worker, what is the expected total amount in bonus that management should be prepared to pay to 20 randomly selected workers? What is the standard deviation of the total amount in bonus?

Solution