Question

Calculate the following probabilities using the standard normal distribution. (Round your answers to four decimal places.) (a) P(0.0 ≤ Z ≤ 1.8) (b) P(−0.1 ≤ Z ≤ 0.0) (c) P(0.0 ≤ Z ≤ 1.46) (d) P(0.3 ≤ Z ≤ 1.58) (e) P(−2.02 ≤ Z ≤ −1.72) (f) P(−0.02 ≤ Z ≤ 3.51) (g) P(Z ≥ 2.10) (h) P(Z ≤ 1.63) (i) P(Z ≥ 6) (j) P(Z ≥ −9)

Answer 1

solution

P(0.0 < Z <1.8 )

= P(Z <1.8 ) - P(Z < 0.0)

Using z table,  

= 0.9641 -0.5

=0.4641

probability=0.4641

(B)P(−0.1 ≤ Z ≤ 0.0)

P(Z <0.0 ) - P(Z < -0.1)

Using z table,  

= 0.5 -0.4602

=0.0398

probability=0.0398

(C)P(0.0 ≤ Z ≤ 1.46)

P(Z <1.46 ) - P(Z < 0.0)

Using z table,  

= 0.9279 -0.5

=0.4279

probability=0.4279

(D)P(0.3 ≤ Z ≤ 1.58)

P(Z <1.58 ) - P(Z < 0.3)

Using z table,  

= 0.9429 -0.6179

=0.3250

probability=0.3250

(E) P(−2.02 ≤ Z ≤ −1.72)

P(Z <-1.72 ) - P(Z < -2.02)

Using z table,  

= 0.0427 - 0.0217

=0.0210

probability=0.0210

(f)P(−0.02 ≤ Z ≤ 3.51)

P(Z <3.51 ) - P(Z < -0.02)

Using z table,  

=0.9998 - 0.4920

=0.5078

probability=0.5078

(g)P(Z ≥ 2.10) =1 - P(Z < 2.10) =1 -0.9821=0.0179

probability=0.0179

(h) P(Z ≤ 1.63) =0.9484

probability=0.9484

(i)P(Z ≥ 6) =1 - P(Z < 6) =1 -1=0

probability=0

(J)P(Z ≥ −9)=1 - P(Z < -9) =1 -0=1

probability=1