Question

Please show formula and work and calculations! thank you!

Find a value of the standard normal random variable z ​, call it z0, such that the following probabilities are satisfied.

a. P( - z0 ≤ z ≤ 0) = 0.2612

b. P( -3 < z < z0) = 0.9559

Answer 1

Part a)

P ( z0 < Z < 0 )
P ( z0 < X < 0 ) = P ( Z < 0 ) - P ( Z < z0 )
0.2612 = 0.5 - P ( Z < z0 )
P ( Z < z0 ) = 0.2388

Looking for the probability 0.2388 in standard normal table to calculate Z score = 0.7102

P ( -0.71 < Z < 0 ) = 0.2612

Z0 = -0.71

Part b)

P ( -3 < Z < z0 )
P ( -3 < X < z0 ) = P ( Z < z0 ) - P ( Z < -3 )
0.9559 = P ( Z < z0 ) - 0.0013
P ( Z < z0 ) = 0.9572

Looking for the probability 0.9572 in standard normal table to calculate Z score = 1.7191

P ( -3 < Z < 1.72 ) = 0.9572

Z0 = 1.72