Question 1120173
z=(x-mean)/sd
a. (63-64)/1=-1/3 and for 65, it would be +1/3
Probability between those two values is 0.2611
b. The sampling distribution of samples of size 25 is normally distributed with mean 64 inches and sd 3/sqrt(25) or 0.6 inches.  The sampling distribution of a given sample of size n has a sd of sigma/sqrt(n)
c. For 66 inches, the SD is +2/3, and that is divided by sqrt of 25 or 5, so the z score is (x-mean)/sigma/sqrt(n) which is (x-mean)*sqrt(n)/sigma, which is 2*5/3 or 3.33
d. This probability would be 0.0004
e  which would be unusual.
f.  This would be between-5/3 and +5/3 sd, since the sd of the sampling distribution is 0.6.  The probability is 0.9044.