Final answer:
The area under the normal curve between z=0 and z=1 is less than the area under the normal curve between z=1 and z=2.
Step-by-step explanation:
The area under the normal curve between z=0 and z=1 is less than the area under the normal curve between z=1 and z=2.
To understand why, we need to refer to the standard normal distribution and the z-table. The z-table shows that the area to the left of a z-score of 0 is 0.5, and the area to the left of a z-score of 1 is 0.8413. Therefore, the area between z=0 and z=1 is 0.8413 - 0.5 = 0.3413.
Similarly, the area between z=1 and z=2 can be calculated by subtracting the area to the left of z=1 from the area to the left of z=2. Using the z-table, we find that the area to the left of z=2 is 0.9772. So, the area between z=1 and z=2 is 0.9772 - 0.8413 = 0.1359.