Let z denote a random variable having a standard normal dist

Let z denote a random variable having a standard normal distribution. Determine the following probabilities: p[ -2.50 z 1.75] p[ -2.0 z -0.5] p[z 1.57] use the z - able to find a number c such that: P[ Z C] = 0.617

Solution

a)

1) p(-2.50<z<1.75)

=p(z<1.75) - p(z<-2.50)

= 0.9599408-  0.006209665

=0.9537312

2) p(-2<z< -0.5)

=p(z< -0.5) - p(z< -2)

= 0.3085375-0.02275013

=0.2857874

3) p(z<1.57)

= 0.9417924

b)

1) p(z<c)= 0.617

value of c = -0.9660883

2) p(-2.50<z<c)=0.95

=p(z<c) - p(z<-2.50) = 0.95

p(z<c)-0.006209665= 0.95

p(z<c)= 0.9562097

thus c = 1.7083

3) p(z<c) = 0.8749

thus c= 1.149864