Question

Given the following pairs of z-values, find the area under the normal curve between each pair of z-values. Refer to the table in Appendix B.1. (Round the final answers to 4 decimal places.)    

a. z = -0.3 and z = 2

b. z = -2.25 and z = -0.6

c. z = 1.45 and z = 2.71

d. z = -2.52 and z = 1.61

Answer 1

Part a)

P ( -0.3 < Z < 2 ) = P ( Z < 2 ) - P ( Z < -0.3 )
P ( -0.3 < Z < 2 ) = 0.9772 - 0.3821
P ( -0.3 < Z < 2 ) = 0.5952

Part b)

P ( -2.25 < Z < -0.6 ) = P ( Z < -0.6 ) - P ( Z < -2.25 )
P ( -2.25 < Z < -0.6 ) = 0.2743 - 0.0122
P ( -2.25 < Z < -0.6 ) = 0.262

Part c)

P ( 1.45 < Z < 2.71 ) = P ( Z < 2.71 ) - P ( Z < 1.45 )
P ( 1.45 < Z < 2.71 ) = 0.9966 - 0.9265
P ( 1.45 < Z < 2.71 ) = 0.0702

Part d)

P ( -2.52 < Z < 1.61 ) = P ( Z < 1.61 ) - P ( Z < -2.52 )
P ( -2.52 < Z < 1.61 ) = 0.9463 - 0.0059
P ( -2.52 < Z < 1.61 ) = 0.9404