Question

# Find the following probabilities: a) Pr{Z < 0.33} b) Pr{Z ≥ −0.33} c) Pr{−2.06 < Z...

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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