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 = -2.4 and z = 1.5

b. z = -1.5 and z = -0.25

c. z = 1.68 and z = 2.8

d. z = -2.36 and z = 1.01

Answer 1

a) P(-2.4<=z<=1.5) = P(z<=1.5) - P(z<= -2.4) = P(z<=1.5) - (1- P(z<=2.4)) = 0.93319 - (1-0.99180) = 0.9250

(From the standard normal distribution tables)

b) P(-1.5 <= z<= -0.25) = P(z<= -0.25) - P(z<= -1.5)

= (1- P(z<=0.25)) - (1- P(z<=1.5))

= P(z<=1.5) - P(z<=0.25) = 0.93319 - 0.59871 = 0.3345

c) P(1.68 <= z<= 2.8) = P(z<=2.8) - P(z<= 1.68) = 0.99744 - 0.95352 = 0.0439

d) P(-2.36 <=z <= 1.01) = P(z<=1.01) - (1- P(z<=2.36) = 0.84375 - (1-0.99086) = 0.8346

Note: All final valyes are rounded to 4 decimal