normal random variable P(0.68≤z≤2.70)

Question

find the probabilities for the standard normal random variable P(0.68≤z≤2.70)

Answer 1

Note:  There is no difference in this case between < and <= because the p(0.68 = z) and p(z = 2.70) in a continuous distribution is 0.

p(0.68 < z < 2.70)

p(z<2.70) - p(z<0.68)

1 - p(z>2.70) - (1 - p(z>0.68) )

1 - p(z>2.70) - 1 + p(z>0.68)

p(z>0.68) - p(z>2.70)

p(z<-0.68) - p(z<-2.70)

Using the z table here ( http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf ):

0.2483 - 0.0035

0.2448