Final answer:
The z-value with an area of 0.0188 to its left can be found using a z-table or an invNorm function on a calculator, and it is approximately -2.09 after rounding to two decimal places.
Step-by-step explanation:
The student is asking for the z-value which corresponds to the point on a standard normal distribution curve that has 0.0188 of the area to its left. This is a task that typically involves using a z-table or statistical software to look up the value. To find this z-value, one would locate the area closest to 0.0188 in the z-table which provides the cumulative probabilities of a standard normal distribution. Once the area is found, the corresponding z-value can be read off the chart. Many statistical calculators and computer programs also provide a function such as invNorm which will compute this value directly. For instance, if using a TI-83 or similar calculator, the student would use the command invNorm(0.0188), which will return a z-value around -2.09 based on the standard normal distribution.