Find the following probabilities:
a) Pr{Z < 0.33}
b) Pr{Z ≥ −0.33}
c) Pr{−2.06 < Z < 2.06}
d) Pr{−2.06 < Z < 0.0}
e) Pr{−4.00 < Z < 0.0}
f) Pr{Z < −1.75 or Z > 1.75} (you want the probability that Z
is outside the range −1.75 to 1.75) g) Pr{−1.75 < Z <
1.75}
Solution:
Since you have posted a question with multiple sub-parts, we will solve first four sub-parts for you.
a) We have to find P( z < 0.33 ) = ............?
Using excel , =NORMSDIST(0.33)
P( z < 0.33 ) = 0.6293
b) We have to find P( Z > -0.33 ) = ............ ?
We know P( Z > z ) = 1- P( Z < z )
So, P( Z > -0.33 ) = 1- P( Z < -0.33 )
Using excel , =1-NORMSDIST(-0.33)
P( Z > -0.33 ) = 0.6293
c) P( -2.06 < Z < 2.06 ) = ..........?
Above probability can be written as,
P( -2.06 < Z < 2.06 ) = P( Z < 2.06 ) - P( Z < -2.06)
Using excel , =NORMSDIST(2.06)-NORMSDIST(-2.06)
P( -2.06 < Z < 2.06 ) = 0.9606
d) P( -2.06 < Z < 0.0 ) = ..........?
Above probability can be written as,
P( -2.06 < Z < 0.0 ) = P( Z < 0 ) - P( Z < -2.06)
Using excel , =NORMSDIST(0)-NORMSDIST(-2.06)
P( -2.06 < Z < 0.0 ) = 0.4803
Done
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