Question

Consider a standard normal distribution (a mean of zero and a standard deviation of 1.) What percentage of this distribution is found in each of the following regions?

Select the most apropriate answer from the drop down list.
Region: Z > -1.13   87 20 0 % (options are 87,20, or 0)

Region: Z < 0.18   81 71 57 % (options are 81,71, or 57)

Region: Z > 8   0 16 99 % (options are 0, 16, or 99)

Region: |Z| < 0.5   100 38 46 % (options are 100, 38 or 46)

Answer 1

a)

P(Z > -1.13) = P(Z < 1.13)

= 0.8708 (From Z table)

= 87%

b)

P(Z < 0.18 ) = 0.5714 (From Z table)

= 57%

c)

P(Z > 8) = 1 - P(Z <= 8)

= 1 - 1 (From Z table)

= 0

d)

P( | z | < 0.5) = P(-0.5 < Z < 0.5)

= P(Z < 0.5) - P(Z < -0.5)

= P(Z < 0.5) - ( 1 - P(Z < 0.5) )

= 0.6915 - ( 1 - 0.6915) (From Z table)

= 0.383

= 38%