Question 1156965
z=(x-mean)/sd
a. this is (85-75)/20=z and want z<0.5.  prob is 0.6915
b. This is a z between -0.5 and +0.5. probability is 0.3829
c. this is a z> -1.5 with probability 0.9332
d.80% is the area between z=-1.282 and +1.282 
1.282=(x-mean)sd and -1.282=(x-mean)/sd
25.64=x-mean or $100.64 top end 
and $49.36 bottom end.   ($49.36, $100.64)

1.645 =(x-mean)/sd
32.90=x-mean and -32.90=(x-mean)
($42.10, $107.90)