10.57 Hard Hats A manufacturer of hard safety hats for construction workers is concerned about the mean and the variation of the forces helmets transmit to wearers when subjected to a standard external force. The manufacturer desires the mean force transmitted by helmets to be 363 kg (or less), well under the legal 454 kg limit, and or to be less than 18.1. A random sample of n = 40 helmets was tested, and the sample mean and variance were found to be equal to 374 kg and 350 kg, respectively.

a. If =363 and or = 18.1, is it likely that any helmet, subjected to the standard external force, will transmit a force to a wearer in excess of 454 kg? Explain.

b. Do the data provide sufficient evidence to indicate that when the helmets are subjected to the standard external force, the mean force transmitted by the helmets exceeds 454 kg?