Assume that Z is a standard normal random variable Calculate

Assume that Z is a standard normal random variable. Calculate:

Please show step by step, Thank You

Assume that Z is a standard normal random variable. Calculate:

Solution

We get the probability values from the standard normal distribution table

(a)

P(Z>-2) =

1-P(Z<=-2)

=1-0.02275

= 0.97725

(b) P(1.7<Z<2.8)

=P(Z<2.8)-P(Z<1.7) =

1-P(Z>=2.8)-1+P(Z>1.7) =

P(Z>1.7)-P(Z>2.8) =

0.044565-0.002555 =

0.04201

(c) P(-1<Z<1.5) = P(Z<1.5)-P(Z<-1)

=1-P(Z>=1.5)-P(Z<-1)

=1-0.077807-0.158655

=0.774538