You want to find Pr[-2 < <em>Z</em> < -1].
The table tells you that
• Pr[<em>Z</em> < 0] = 0.5000
• Pr[<em>Z</em> < 1.00] = 0.8412
• Pr[<em>Z</em> < 2.00] = 0.9772
• Pr[<em>Z</em> < 3.00] = 0.9987
We have
Pr[-2 < <em>Z</em> < -1] = Pr[<em>Z</em> < -1] - Pr[<em>Z</em> < -2]
(because the distribution of <em>Z</em> is continuous)
… = Pr[<em>Z</em> > 1] - Pr[<em>Z</em> > 2]
(by symmetry of the distribution about its mean)
… = (1 - Pr[<em>Z</em> < 1]) - (1 - Pr[<em>Z</em> < 2])
(by definition of complement)
… = Pr[<em>Z</em> < 2] - Pr[<em>Z</em> < 1]
… = 0.9772 - 0.8412
… = 0.1360 ≈ 0.14 … … … (B)