A manufacturer must test that his bolts are 5.00cm long when they come off the assembly line. He must recalibrate his machines if the bolts are too long or too short. After sampling 121 randomly...

A manufacturer must test that his bolts are 5.00cm long when they come off the assembly line. He must recalibrate his machines if the bolts are too long or too short. After sampling 121 randomly selected bolts off the assembly line, he calculates the sample mean to be 4.87cm. He knows that the population standard deviation is 0.76cm. Assuming a level of significance of 0.05, is there sufficient evidence to show that the manufacturer needs to recalibrate the machines?