Question

Let Z be a standard normal random variable (mean = 0 and sd = 1) and calculate the following probabilities:

(a)    Pr(0 ≤ Z ≤ 2.49)


(b)    Pr(0 ≤ Z ≤ 1)


(c)    

Pr(−2.50 ≤ Z ≤ 0)

(d)    

Pr(−2.50 ≤ Z ≤ 2.50)

(e)    Pr(Z ≤ 1.52)

Answer 1

Let Z be a standard normal random variable.

Using standard normal z-table we find the following probabilities,

a) Pr(0 ≤ Z ≤ 2.49)

=Pr(Z ≤ 2.49) - Pr(Z ≤ 0)

= 0.9936 - 0.5000

= 0.4936

=> Pr(0 ≤ Z ≤ 2.49) = 0.4936

b) Pr(0 ≤ Z ≤ 1)

=Pr(Z ≤ 1) - Pr(Z ≤ 0)

= 0.8413 - 0.5000

= 0.3413

=> Pr(0 ≤ Z ≤ 1) = 0.3413

c) Pr(-2.50 ≤ Z ≤ 0)

= Pr(Z ≤ 0) - Pr(Z ≤ -2.50)

= 0.5000 - 0.0062

= 0.4938

=> Pr(-2.50 ≤ Z ≤ 0) = 0.4938

d) Pr(-2.50 ≤ Z ≤ 2.50)

= 2 * Pr(Z ≤ 2.50) - 1

= (2 * 0.9938) - 1

= 1.9876 - 1

= 0.9876

=> Pr(-2.50 ≤ Z ≤ 2.50) = 0.9876

e) Pr(Z ≤ 1.52) = 0.9357