What is the probability that a random variable with a standard normal distributi

Question

What is the probability that a random variable with a standard normal distribution takes a value between 0.6 and 2.2? What is the probability that a random variable with a normal distribution with mu = 4.1 and sigma =0.25 takes a value between 3.5 and 4.5? What is the probability that a random variable with a chi-square distribution with 28 degrees of freedom takes a value between 16.928 and 18.939? What is the probability that a random variable with a t-distribution with 22 degrees of freedom takes a value between -1.717 and 2.819?

Explanation / Answer

a).

P( 0.6<z<2.2)

=P( z <2.2) – P( z <0.6)

= 0.9861 - 0.7257

= 0.2604

b).

z value for 3.5, z=(3.5-4.1)/0.25 =-2.4

z value for 4.5, z=(4.5-4.1)/0.25 =1.6

P( 3.5<x<4.5) =P( -2.4<z<1.6)

=P( z < 1.6) – P( z < -2.4)

= 0.9452 - 0.0082

=0.937

c).

P( chi square <18.939) –P( chi square < 16.928)

=0.10-0.05

=0.05

d).

P( t <2.819) – P( t<-1.717)

=0.995 -0.05

=0.945

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