**3. Correct. The
answer is false. **

The sample mean in standard units is Z=`X-m(`X)/s(`X) = (`X-67.0) /0.6

a) 66.8 in standard units = (65.8-67)/0.6=-2.0

67.3 in standard units =(67.3-67)/0.6=0.5

Proportion of samples with means between 65.8 and 67.3 in = (area under normal curve between z=-2.0 and z=0.5) = (area under normal curve between z=-2.0 and z=0) = (area under normal curve between z=0 and z=0.5)=0.4772+0.1915=0.6687

Then the expected number of samples =80(0.6687)=53

b) 65.4 in standard units = (65.4-67.0)=-2.67.

Proportion of samples with means less than 65.4 in.= (area under normal curve to the left of z=-2.67) = (area under normal curve to the left of z=0) - (area between z=-2.67 and z=0)=0.5-0.4962=0.0038

Then the expected number of samples =80(0.0038)=0.304 or zero.