Question

Find each of the following probabilities. Provide your answers to 4 decimal places.

P(0 ≤ z ≤ 1.5)   

P(z ≥ 2)   

P(z ≤ 1.5)    

P( -1 ≤ z ≤ 1)   

P( z ≥ - 1)

Answer 1

Solution:

1) P(0 ≤ z ≤ 1.5)

Use the rule P(a ≤ Z ≤ b) = F(b) - F(a)

P(0 ≤ z ≤ 1.5) = F(1.5)-F(0)

=0.9332-0.5000

=0.4332

2) P(z ≥ 2)   

Use the rule

P(Z ≥ a) = 1 - F(a)

P(z ≥ 2) =1-F(2)

=1-0.9772

=0.0228

3) P(z ≤ 1.5)  

Use the rule

P(Z ≤ a)= F(a) (when a is positive)

  P(z ≤ 1.5) = F(1.5)

=0.9332

4)  P( -1 ≤ z ≤ 1)

Use the rule

P(-a ≤ Z ≤ a) = 2*F(a) - 1

P( -1 ≤ z ≤ 1) = 2*F(1)-1

=2*0.8413-1

=0.6826

5) P( z ≥ - 1)

Use the rule

P(Z ≥ -a)= 1 -F(-a)

=1-F(-1)

=1-0.1587

=0.8413