Find the value of z if the area under a standard normal curve (a) to the right of z is 0.3622; (b) to the left of z is 0.1131; (c) between 0 and z, with z > 0, is 0.4838; (d) between - z and z, with z > 0, is 0.9500.

Probability of x for an area under standard normal curve is given as follows:

P (X) = P (z)

a] when P (X≥x) = 0.3622

The value of z will be:

1-0.3622=0.6378

The corresponding value in the z-table is:

z=0.34

b] P (X≤x) = 0.1131

The corresponding value in z-table is:

z=-1.21

c] P (0≤X≤x) = 0.4838

When P (x) = 0 then z=0.5

P (x) = 0.4838 then z=0.04

hence:

Z=0.5+0.04=0.54

D] P (X≤x) = 0.9500

the value of z>0 is z=1.66

Answer: z=1.66