Final answer:
The area under the standard normal curve between z=-0.1 and z=0.1 is found by subtracting the area to the left of z=-0.1 from the area to the left of z=0.1, using a z-table or calculator. The closest matching answer from the provided options would be chosen, but there is a discrepancy with the calculated area of 0.0796 not matching any given options.
Step-by-step explanation:
The student asked to find the area under a standard normal curve that lies between z=-0.1 and z=0.1. To do this, one must use a z-table, which outlines the area under the curve to the left of a given z-value. The standard normal distribution is symmetric around z=0, and most z-tables give the cumulative area to the left of z.
To find the area between z=-0.1 and z=0.1, we calculate the area to the left of z=0.1 and subtract the area to the left of z=-0.1. Using a standard normal probability table or the invNorm function on a scientific calculator, we can find these values.
After finding the corresponding areas for z=0.1 and z=-0.1, the difference gives the area between those two points under the curve. In this case, it is approximately 0.0796. However, none of the options provided in the question (a. 0.0398, b. 0.0250, c. 0.0080, d. 0.0198) match this area. The closest available option to the computed area would typically be selected, but there's a clear discrepancy that should be addressed.