Question

Answer the following questions about the standard normal random variable Z. (Use 4 decimal places in your answers to parts a. through f.) a. What is P(-1.46 < Z < 0.63)?(No Response) b. What is P(0 < Z < 1.31)?(No Response) c. What is P(Z > -1.62)?(No Response) d. What is P(Z < -2.6)?(No Response) e. What is P(Z < 2.63)?(No Response) f. What is P(-2.58 < Z < -1.1)?

Answer 1

a) 0.6636

b) 0.0951

c) 0,9474

d) 0.0047

e) 0.9957

f) 0.1308

Explanation:

We look in tables z values and then we see carefully aereas inside normal curve

a) P[- 1.46 < z < 0.63 ] point 1.46 from table 0.0721 this s th area from value -1.46 to the left . And the value z = 0.63 corresond to the area 0.7357 which includes the area between 1.46 to the left tail, then we have to subtarct and get 0.6636 .

P[- 1.46 < z < 0.63 ] = 0.6636 66.36 %

b) P [ 0 < z < 1.31 ] we just need the area for point 1.31 that is 0.0951

P [ 0 < z < 1.31 ] = 0.0951 9.51 %

c) P [z > - 1.62 ] = 1 - 0.0526

P [z > - 1.62 ] = 0,9474 94.74 %

d) P[z < - 2.6 ] = 0.0047 0.47 %

e) P [ z < 2.63 ] = 1 - 0.0043

P [ z < 2.63 ] = 0.9957 99.57 %

f) P [ -2.58 < z < -1.1 ] = 0.1357 - 0.0049 =

P [ -2.58 < z < -1.1 ] = 0.1308 13.08 %