Question

Given that z is a standard normal random variable, use the Excel to compute the following probabilities.

a) P(z > 0.5)
b) P(z ≤ −1)
c) P(1≤ Z ≤ 1.5)

d) P(0.5 ≤ z ≤ 1.25)

e) P(0 < z < 2.5)

Answer 1

Z~Normal(0,1)

a) P(z > 0.5)=1-p(z<0.5)

=1-0.6914

=0.3085

#value of z is obtained from Excell command is =NORM.S.DIST(B5,1)

b) P(z ≤ −1)=0.1587

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

=0.9332-0.8413=0.0918

# P(1≤ Z ≤ 1.5)=0.0918

d) P(0.5 ≤ z ≤ 1.25)= P( z ≤ 1.25)- P( z ≤ 0.5)

=0.8944-0.6915=0.2029

# P(0.5 ≤ z ≤ 1.25)=0.2029

e) P(0 < z < 2.5)=p(z<2.5)-p(z<0)

=0.9938-0.5=0.4938

#P(0 < z < 2.5)=0.4938