Question 3 Determine the area under the standard normal curv

Question 3

Determine the area under the standard normal curve that lies between (a) Z = - 0.05 and Z = 0.05, (b) Z = - 1.91 and Z = 0, and Z = - 0.47 and Z = - 0.21.

(a) The area that lies between Z= - 0.05 and Z = 0.05 is?

       (Round to four decimal places as needed)

(b) The area that lies between z = - 1.91 and Z = 0 is?

       (Round to four decimal places as needed)

(c) The area that lies between Z = - 0.47 and Z =- 0.21 is?

       (Round to four decimal places as needed)

Solution

(A) area that lies between Z= - 0.05 and Z = 0.05 is = P(-0.05 <= Z <= 0.05)

                        = P(Z <= 0.05) - P(Z <= -0.05) = P(Z <= 0.05) - [1 - P(Z <= 0.05)] = 0.5199 - 1 + 0.5199 = 0.0398

(B) area that lies between z = - 1.91 and Z = 0 is = P(-1.91 <= Z <= 0) = P(Z<= 0) - P(Z<= -1.91)

                                               = 0.5 -[1 - 0.9719] = 0.4719

(C) area that lies between z = - 0.47 and Z = 0.21 is = P(-0.47 <= Z <= 0.21) = P(Z<= 0.21) - P(Z<= -0.47)

                                               = 0.5832 -[1 - 0.6808] = 0.264