Question

1. Find z_0 such that 8% of the values of the standard normal curve lies to the right of z_0.

2. Find the z_0 value such that 98% of values of the standard normal curve lies between - z_0 and z_0.

Answer 1

1.

Find z_0 such that 8% of the values of the standard normal curve lies to the right of z_0.

P(Z>z_0) = 8/100 =0.08

P(Z>z_0) = 1-P(Z<z_0) =0.08

P(Z<z_0) =1-0.08 =0.92

From standard normal tables,

P(Z<1.41) = 0.9207

Therefore z_0 = 1.41

z_0 = 1.41

2.

Find the z_0 value such that 98% of values of the standard normal curve lies between - z_0 and z_0.

P(-z_0 < Z <z_0) = 98/100 =0.98

From the diagram it can be observed that,

P(Z<-z_0) = 1%=0.01

From standard normal tables,

P(Z<-2.33) =0.00990.01

Therefore,

-z_0 = -2.33

z_0=2.33