Question

the total area under the standard normal curve to the left of z = -0.22 or to the right of z = 1.17 is

Answer 1

Solution:

Find the total area under the standard normal curve to the left of z = -0.22 or to the right of z = 1.17.

That is:

P( Z < -0.22 or Z > 1.17) =..........?

P( Z < -0.22 or Z > 1.17) = P( Z < -0.22) + P(Z > 1.17)

P( Z < -0.22 or Z > 1.17) = P( Z < -0.22) + [ 1 - P(Z < 1.17) ]

Look in z table for z = -0.2 and 0.02 as well as for  z = 1.1 and 0.07  and find corresponding area.

P( Z< -0.22) = 0.4129

and

P( Z< 1.17) = 0.8790

thus

P( Z < -0.22 or Z > 1.17) = P( Z < -0.22) + [ 1 - P(Z < 1.17) ]

P( Z < -0.22 or Z > 1.17) = 0.4129 + [ 1 - 0.8790 ]

P( Z < -0.22 or Z > 1.17) =  0.4129 + 0.1210

P( Z < -0.22 or Z > 1.17) = 0.5339

Thus the total area under the standard normal curve to the left of z = -0.22 or to the right of z = 1.17 is 0.5339