Let X ~ Normal (=3, 2 =16) and Z ~ Normal (0,1) use the Standard Normal Table in
ID: 3340592 • Letter: L
Question
Let X ~ Normal (=3, 2=16) and Z ~ Normal (0,1) use the Standard Normal Table in Appendix B or MS Excel to find each of the following:
a. P(Z = 1)
b. P(Z < 0)
c. P(Z 1)
d. P(|Z| < 1)
e. P(|Z| > 1.5)
f. P(|Z| > 2)
g. P(0.5 < Z < 1)
h. The point z such that P(Z z)=0.8
i. The point z such that P(Z z)=0.8
j. The point z such that P(-z Z z)=0.9
k. P(X = 1)
l. P(X < 0)
m. P(X 1)
n. P(|X| < 1)
o. P(|X| > 1.5)
p. P(|X| > 2)
q. P(0.5 < X < 1)
r. P(- < X < +)
s. P(- 2 < X < +2)
t. The point x such that P(X x)=0.8
Problem(1) Let X ~ Normal( = 3, 2 = 16) and Z ~ Normal (0, 1), use the Standard Normal Table in Appendix B or MS Excel to find each of the following: (a) P(Z = 1) (b) P(Z 2) (g) P(0.5Explanation / Answer
Solution- Z follows normal ( 0,1 )
(a) P(Z=1)
= 0 [ As in continous probability distribution, probability at a point is zero]
(b) P(z< 0)
= 0.5
(c) P( Z < 1)
= 0.8413
(d) P( |Z| < 1 )
= P( -1 < Z < 1)
= 0.6826
(e) P( |Z| > 1.5 )
= P( Z > 1.5) + P( Z < -1.5 )
= .066 +.066
= 0.133
(f) P( |Z| > 2 )
= P( Z > 2) + P( Z < -2 )
= 0.22 + 0.22
= 0.0455
Answers
TY!
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