Answer to Question #323830 in Statistics and Probability for Bless

Question

Given the Standard Normal distribution, find the following

(a) P(Z < 1.8)

(b) P(−1.1 < Z ≤ 1.8)

(c) P(−1.8 ≤ Z ≤−1.1)

(d) P(Z > −2.5)

(e) P(Z > −0.95)

(f) P(Z < −0.95)

(g) P(Z ≥ 2.18)

(h) P(Z > 10)

Answer 1

$a:P\left( Z<1.8 \right) =\varPhi \left( 1.8 \right) =0.9641\\b:P\left( -1.1<Z\leqslant 1.8 \right) =\varPhi \left( 1.8 \right) -\varPhi \left( -1.1 \right) =0.9641-0.1357=0.8284\\c:P\left( -1.8\leqslant Z\leqslant -1.1 \right) =\varPhi \left( -1.1 \right) -\varPhi \left( -1.8 \right) =0.1357-0.0359=0.0998\\d:P\left( Z>-2.5 \right) =1-\varPhi \left( -2.5 \right) =1-0.0062=0.9938\\e:P\left( Z>-0.95 \right) =1-\varPhi \left( -0.95 \right) =1-0.1711=0.8289\\f:P\left( Z<-0.95 \right) =0.1711\\g:P\left( Z\geqslant 2.18 \right) =1-\varPhi \left( 2.18 \right) =1-0.9854=0.0146\\h:P\left( Z>10 \right) =\varPhi \left( -10 \right) =7.62\cdot 10^{-24}$