Question

probability Q7 (4 marks) a) Creat a standard normal probability distribution plot for z-value for the range of (-3, 3) with increament of 0.5. b) Find the z value (to two decimal places) that cuts off an area in the upper tail section of the standard normal curve with probability of: 0.45 1) 0.0252) 0.053 ) 0.0054) 0.01 A) Answer Z-score probability -3 0.004431848 -2.5 0.0175283 -2 0.053990967 -1.5 0.129517596 -1 0.241970725 -0.5 0.352065327 0 0.39894228 0.5 0.352065327 1 0.241970725 1.5 0.129517596 2 0.053990967 2.5 0.0175283 3 0.004431848 B) Answer Fam F -3 -2 -1 0 1 2 3 4

Answer 1

Solution :

1)

P(Z > z) = 0.025

P(Z < z) = 1 - 0.025 = 0.975

P(Z < 1.960 = 0.975

z = 1.96

2)

P(Z > z) = 0.05

1 - P(Z < z) = 0.05

P(Z < z) = 0.95

P(Z < 1.65) = 0.95

z = 1.65

3)

P(Z > z) = 0.005

P(Z < z) = 1 - 0.005 = 0.995

P(Z < 2.8) = 0.995

4)

P(Z > z) = 0.01

P(Z < z) = 1 - 0.01 = 0.99

P(Z < 2.33) = 0.99

z = 2.33