In: Statistics and Probability
4. If Z is a standard normal random variable, that is Z ∼ N(0, 1), (a) what is P(Z 2 < 1)? (b) Find a number c such that P(Z < c) = 0.75 (c) Find a number d such that P(Z > d) = 0.83 (d) Find a number b such that P(−b < Z < b) = 0.95
a) P(Z < 1.000 ) = 0.8413 (answer)
b)Z value at 0.75 = 0.674 (excel formula =NORMSINV( 0.75 ) )
answer: 0.674
c)P(Z > d) = 0.83
P(Z≤d) = 1-0.83 = 0.17
Z value at 0.17 =
-0.954 (excel formula =NORMSINV(
0.17 ) )
answer: -0.954
d)proportion= 0.9500
proportion left 0.0500 is equally
distributed both left and right side of normal
curve
z value at 0.025 = ±
1.960 (excel formula =NORMSINV(
0.05 / 2 ) )
so, value of b = 1.96