Given that z is a standard normal random variable, compute the following probabilities: a. P(z ≤ −1) b. P(z > .95) c. P(z ≥ −1.5) d. P(−.5 ≤ z ≤ 1.75) e. P(1 < z ≤ 3)

Step-by-step explanation:

Given that Z is a standard normal variate.

We are to calculate the probabilities as given

F(z) represents the cumulative probability i.e. P(Z<z)

a. P(z ≤ −1)

=F(-1)

= 0.158655

b. P(z > .95)

= 1-F(0.95)

= 0.1711

c. P(z ≥ −1.5)

= 1-F(-1.5)

= 0.9332

d. P(−.5 ≤ z ≤ 1.75)

=F(1.75)-F(-0.5)

= 0.6514

e. P(1 < z ≤ 3)

=F(3)-F(1)

=0.1573