Answer to Question #301757 in Statistics and Probability for Bhie

Question

solve for the proportion of the area of the following probability notations then sketch the normal curve shading the required region of each given notation

1. P (-2 < z <1)

2. P (z > 3)

3. P (z < -2)

4. P (z > -1.5)

5. P (z = -1)

Answer 1

1.

$$P (-2 < z <1)=P(z<1)-P(z\le -2)$$

$$\approx0.84134-0.02275\approx0.8186$$

2.

$$P (z>3)=1-P(z\le3)$$

$$\approx0.00135$$

3.

$$P ( z <-2)\approx0.02275$$

4.

$$P (z>-1.5)=1-P(z\le-1.5)$$

$$\approx0.9332$$

5.

$$P (z=-1)=0$$