Answer to Question #264176 in Statistics and Probability for talie

Question #264176

Suppose that Z ∼ N(0, 1), find


(a) P(Z = −0.93)


(b) P(Z > −0.93)


(c) P(Z < 0.25)


(d) P(−2.13 ≤ Z ≤ 1.93)

1
Expert's answer
2021-11-11T18:47:15-0500

We will use the standard normal tables to find these probabilities.

a.

"p(Z=-0.93)=0"

This probability is equal to zero because it is related to finding the area under a point(-0.93) which is zero.

b.

"p(Z\\gt-0.93)=1-p(Z\\lt-0.93)=1-0.1762= 0.8238"


c.

"p(Z\\lt0.25)=0.5987"


d.

"p(-2.13\\leqslant Z\\leqslant1.93)=\\phi(1.93)-\\phi(-2.13)=0.9732-0.0166= 0.9566"


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