Question

1. The P(Z ≤ 1.74) is _______

2. The P(Z ≥ 0.64) is _______

3. The P(- 1.24 ≤ Z ≤ 2.72) is _______

4. The value of z such that P(Z ≤ z) = .2061 is ________

5. The value of z such that P(- z ≤ Z ≤ z) = .7960 is ________

6. The value of z that is exceeded 10% of the time is ________

Answer 1

solution

(A)P(Z ≤ 1.74) =0.9591

probability=0.9591

(B)P(z ≥0.64 ) =1 - P(z <0.64 )

Using z table,
= 1 -0.7389

= 0.2611   

probability = 0.2611

(C)

P(- 1.24 ≤ Z ≤ 2.72)

= P(Z <2.72 ) - P(Z <-1.24 )

Using z table,  

=   0.9967-0.1075

probability=0.8892

(D)

Using standard normal table,

P(Z ≤ z) =0.2061

= P(Z ≤ z) = 0.2061

= P(Z ≤-0.82 ) =0.2061

z = - 0.82 Using standard normal z table,

(E)
P(-z < Z < z) = 0..7960

P(Z < z) - P(Z < -z) = 0..7960

2 P(Z < z) - 1 = 0..7960

2 P(Z < z) = 1 + 0. .7960= 1.7960

P(Z < z) =1.7960 / 2 = 0.898

P(Z <1.27 ) = 0.898

z  ± 1.27 using z table

(F)

Using standard normal table,

P(Z > z) = 10%

= 1 - P(Z < z) = 0.10  

= P(Z < z) = 1 - 0.10

= P(Z < z ) = 0.90

= P(Z <1.28 ) = 0.90

z =1.28 ( using z table )