Question

Use Table A to find the value z of a standard Normal variable that satisfies each of the following conditions. (Use the value of z from Table A that comes closest to satisfying the condition.) In each case, sketch a standard Normal curve with your value of z marked on the axis. (Round your answers to two decimal places.)

(a) The point z with 60% of the observations falling below it

(b) The point z with 17% of the observations falling above it

(c) z < −0.86

(d) z > −0.86

(e) z < 1.95

(f) −0.86 < z < 1.95

Answer 1

a) From the standard normal table the value that is closest to the area that has 60% observation falling below it = 0.25

b) The point z with 17% of the observations falling above it or 100-17 = 83% of the observations falling below it

From the standard normal table the value that is closest to the area that has 83% observation falling below it = 0.95

c) P(z < -0.86) = 0.19

d) P(z > -0.86) = 1-P(z< -0.86)

= 1- 0.19 = 0.81

e) P(z < 1.95) = 0.97

f) P(-0.86 < z< 1.95) = P(z<1.95) - P(z<-0.86)

= 0.97 - 0.19 = 0.78