17. Hard Hats A manufacturer of hard safety hats for construction workers wants the mean force transmitted by helmets to be 3200 newtons (or less), well under the legal 4000-newton limit, and  to be less than 160. A random sample of n540 helmets was tested, and the sample mean and variance were found to be equal to 3300 newtons and 37,600 newtons2 respectively.

a. If m 53200 and  5160, is it likely that any helmet, subjected to the standard external force, will transmit a force to a wearer in excess of 4000 newtons?

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 3200 newtons?