Question

Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wherever appropriate. (Round your answers to four decimal places.)
(a) P(0 ≤ Z ≤ 2.33)
0.4875

Incorrect: Your answer is incorrect.

(b) P(0 ≤ Z ≤ 2)
0.4772

Correct: Your answer is correct.

(c)
P(−2.70 ≤ Z ≤ 0)

0.4981

Incorrect: Your answer is incorrect.

(d)
P(−2.70 ≤ Z ≤ 2.70)

0.9963

Incorrect: Your answer is incorrect.

(e) P(Z ≤ 1.93)
0.9545

Incorrect: Your answer is incorrect.

(f)
P(−1.45 ≤ Z)

0.9394

Incorrect: Your answer is incorrect.

(g)
P(−1.70 ≤ Z ≤ 2.00)

0.9485

Incorrect: Your answer is incorrect.

(h) P(1.93 ≤ Z ≤ 2.50)
0.0393

Incorrect: Your answer is incorrect.

(i) P(1.70 ≤ Z)
0.0287

Incorrect: Your answer is incorrect.

(j) P(|Z| ≤ 2.50)
0.9876

Correct: Your answer is correct.

Answer 1

Part a)

P ( 0 <= Z <= 2.33 ) = P ( Z < 2.33 ) - P ( Z < 0 )
P ( 0 <= Z <= 2.33 ) = 0.9901 - 0.5
P ( 0 <= Z <= 2.33 ) = 0.4901

part b)

P ( 0 <= Z <= 2 ) = P ( Z < 2 ) - P ( Z < 0 )
P ( 0 <= Z <= 2 ) = 0.9772 - 0.5
P ( 0 <= Z <= 2 ) = 0.4772

Part c)

P ( -2.7 <= Z <= 0 ) = P ( Z < 0 ) - P ( Z < -2.7 )
P ( -2.7 <= Z <= 0 ) = 0.5 - 0.0035
P ( -2.7 <= Z <= 0 ) = 0.4965

Part d)

P ( -2.7 <= Z <= 2.7 ) = P ( Z < 2.7 ) - P ( Z < -2.7 )
P ( -2.7 <= Z <= 2.7 ) = 0.9965 - 0.0035
P ( -2.7 <= Z <= 2.7 ) = 0.9931

Part e)

P ( Z <= 1.93 ) = 0.9732

Part f)

P ( Z >= -1.45 ) = 1 - P ( Z < -1.45 )
P ( Z >= -1.45 ) = 1 - 0.0735
P ( Z >= -1.45 ) = 0.9265

Part g)

P ( -1.7 <= Z <= 2 ) = P ( Z < 2 ) - P ( Z < -1.7 )
P ( -1.7 <= Z <= 2 ) = 0.9772 - 0.0446
P ( -1.7 <= Z <= 2 ) = 0.9327

Part h)

P ( 1.93 <= Z <= 2.5 ) = P ( Z < 2.5 ) - P ( Z < 1.93 )
P ( 1.93 <= Z <= 2.5 ) = 0.9938 - 0.9732
P ( 1.93 <= Z <= 2.5 ) = 0.0206

part i)

P ( Z >= 1.7 ) = 1 - P ( Z < 1.7 )
P ( Z >= 1.7 ) = 1 - 0.9554
P ( Z >= 1.7 ) = 0.0446

Part j)

P ( -2.5 <= Z <= 2.5 ) = P ( Z < 2.5 ) - P ( Z < -2.5 )
P ( -2.5 <= Z <= 2.5 ) = 0.9938 - 0.0062
P ( -2.5 <= Z <= 2.5 ) = 0.9876