Question

1. Directions: Determine each of the following areas and show these graphically. Use probability notation in your final answer. NOTE: Use graphing paper to graph.

1. To the left of z = 1.96 5. Below z = -1.96       9. 1.27≥z≥-2.1

2. At most z = 2.58 6. z≥1       10. z=-0.58

3. At least z = 1.96 7. z≤-1.5

4. To the right of z = 0.33 8. -0.92≤z≤1.75

Answer 1

1.

$$P(Z<1.96)=0.975002$$

2.

$$P(Z\le2.58)=0.995060$$

3.

$$P(Z\ge1.96)=1-P(Z<1.96)$$

$$=0.024998$$

4.

$$P(Z>0.33)=1-P(Z\le0.33)$$

$$=0.370700$$

5.

$$P(Z<-1.96)=0.024998$$

6.

$$P(Z\ge1)=1-P(Z<1)$$

$$=0.158655$$

7.

$$P(Z\le-1.5)=0.066807$$

8.

$$P(-0.92\le Z\le1.75)$$

$$=P(Z\le1.75)-P(Z<-0.92)$$

$$=0.9599408-0.1787864$$

$$=0.781154$$

9.

$$P(-2.1\le Z\le1.27)$$

$$=P(Z\le1.27)-P(Z<-2.1)$$

$$=0.8979577-0.0178644$$

$$=0.880093$$

10.

$$P(Z=-0.58)=0$$