(b) Find the area under the standard normal curve between $z=0.31$ and $z=1.88$.

Step 1 ：The problem is asking for the area under the standard normal curve between $z=0.31$ and $z=1.88$.

Step 2 ：The area under the standard normal curve between two points can be found by calculating the definite integral of the standard normal distribution function between those two points. The standard normal distribution function is given by $f(z) = \frac{1}{\sqrt{2\pi}}e^{-\frac{1}{2}z^2}$.

Step 3 ：However, in practice, we usually use Z-tables or software to find these areas, as the integral of the standard normal distribution function cannot be expressed in terms of elementary functions.

Step 4 ：Using a Z-table or software, we find that the area under the standard normal curve between $z=0.31$ and $z=1.88$ is approximately 0.3482.

Step 5 ：This means that approximately 34.82% of the data falls between these two z-scores in a standard normal distribution.

Step 6 ：Final Answer: The area under the standard normal curve between $z=0.31$ and $z=1.88$ is approximately \(\boxed{0.3482}\).