Question

1. Determine the following probabilities and for each item, provide a sketch of the associated areas (3 points each).

a. P(z > 1.69)

b. P(z < -2.03)

c. P(z > -0.50)

d. P(-0.39 < z < 0)

e. P(0.75 < z < 2.01)

Answer 1

a)

= P(Z > 1.690   ) = P( Z <   -1.690   ) =    0.0455   (answer)

excel formula for probability from z score is =NORMSDIST(Z)

b)

=P(Z < -2.030   ) =   0.0212   (answer)

excel formula for probability from z score is =NORMSDIST(Z)

c)

= P(Z > -0.50 ) = P( Z <   0.500   ) =    0.6915   (answer)

d)

P (    -0.390   < Z <    0.000   )                       
= P ( Z <    0.000   ) - P ( Z <   -0.390   ) =    0.5000   -    0.3483   =    0.1517   (answer)

.

e)

P (    0.750   < Z <    2.010   )                           
= P ( Z <    2.010   ) - P ( Z <   0.750   ) =    0.9778   -    0.7734   =    0.2044   (answer)