Question

Standard Normal distribution.

With regards to a standard normal distribution complete the following: (a) Find P(Z > 0), the proportion of the standard normal distribution above the z-score of 0. (b) Find P(Z <-0.75), the proportion of the standard normal distribution below the Z-score of -0.75 (c) Find P(-1.15<z <2.04). (d) Find P(Z > -1.25). (e) Find the Z-score corresponding to Pso, the 90th percentile value.

Answer 1

Solution :-

a)

P ( Z > 0 ) = 1 - P ( Z < 0 )

= 1 - 0.5

P ( Z > 0 ) = 0.5

b)

P ( Z < -0.75 ) = 0.2266

c)

P (-1.15 < Z < 2.04 ) = P ( Z < 2.04 ) - P ( Z < -1.15 )

= 0.9793 - 0.1251

P (-1.15 < Z < 2.04 ) = 0.8542.

d)

P ( Z > - 1.25 ) = 1 - P ( Z < - 1.25 )

= 1 - 0.1056

P ( Z > - 1.25 ) = 0.8944.

e)

The Z - Distribution of the 90 % is,

P ( Z < z ) = 90 %

P ( Z < z ) = 0.90

P ( Z < 1.28 ) = 0.90

z = 1.28

z Score Corresponding to P90 is 1.28.