Final answer:
To calculate the area under the normal distribution curve between z=-2.44 and z=1.35, we subtract the area to the left of z=-2.44 from the area to the left of z=1.35, found using a Z-table.
Step-by-step explanation:
To find the area under the standard normal distribution curve between z=-2.44 and z=1.35, we use a Z-table which shows the area under the curve to the left of each z-score. First, find the area to the left of z=-2.44, then find the area to the left of z=1.35. Since the Z-table only provides the area to the left, for negative z-scores, we use the symmetry of the standard normal distribution to understand that the area to the left of z=-2.44 is the same as the area to the right of z=2.44. Once we have both areas, the area between the two z-scores is the difference between the area to the left of z=1.35 and the area to the left of z=-2.44.
For example, if the Z-table indicates an area of 0.9938 to the left of z=1.35 and an area of 0.0072 to the left of z=-2.44 (equivalent to 1 - the area to the right of z=2.44), we calculate the area between these scores as:
0.9938 - 0.0072 = 0.9866
This computation results in an area under the curve of 0.9866, representing the probability that a value lies between z=-2.44 and z=1.35 on the standard normal distribution.