Question

z probability
0.00 0.5000
1.00 0.8413
2.00 0.9772
3.00 0.9987
0.16
0.68
0.82
0.84
mark this and return
save and exit

Explanation:

Step1: Identify area bounds

The shaded area is between $z=0$ and $z=2$.

Step2: Get cumulative probabilities

From the table: $P(Z \leq 2) = 0.9772$, $P(Z \leq 0) = 0.5000$

Step3: Calculate shaded area

Subtract the two probabilities: $P(0 \leq Z \leq 2) = P(Z \leq 2) - P(Z \leq 0)$
Expression: $0.9772 - 0.5000 = 0.4772$
Wait, correction: Recheck the curve—shaded area is $z=-1$ to $z=2$.

Step1 (Revised): Correct bounds

Shaded area: $z=-1$ to $z=2$.

Step2 (Revised): Use symmetry for $z=-1$

By standard normal symmetry, $P(Z \leq -1) = 1 - P(Z \leq 1) = 1 - 0.8413 = 0.1587$

Step3 (Revised): Compute target area

$P(-1 \leq Z \leq 2) = P(Z \leq 2) - P(Z \leq -1)$
Expression: $0.9772 - 0.1587 = 0.8185 \approx 0.82$

Answer:

0.82