Final answer:
To find the area under the standard normal curve, we can use the z-table to find the area to the left of a given z-score. By subtracting this area from 1, we can find the area to the right of a z-score. To find the area between two z-scores, we subtract the area to the left of the smaller z-score from the area to the left of the larger z-score.
Step-by-step explanation:
To find the area under the standard normal curve, we will use the z-table. The z-table provides the area to the left of a given z-score.
(a) To find the area outside the interval between z=0.57 and z=1.82, we will find the area to the left of each z-score and subtract. The area to the left of z=0.57 is 0.7157, and the area to the left of z=1.82 is 0.9656. Therefore, the area outside the interval is 1 - (0.9656 - 0.7157) = 0.7501.
(b) To find the area to the left of z=2.32, we locate the z-score on the z-table, which equals 0.9898.
(c) To find the area to the right of z=1.13, we subtract the area to the left of z from 1. The area to the left of z=1.13 is 0.8708, so the area to the right is 1 - 0.8708 = 0.1292.
(d) To find the area between z=-0.94 and z=-0.63, we subtract the area to the left of z=-0.63 from the area to the left of z=-0.94. The area to the left of z=-0.63 is 0.2650, and the area to the left of z=-0.94 is 0.1729. Therefore, the area between the two z-scores is 0.2650 - 0.1729 = 0.0921.