Final answer:
To find the area under the standard normal curve to the left of z=0.21, refer to a Z-table and look up the cumulative probability associated with z=0.21. This value will be the area under the curve to the left of the given z-score, rounded to four decimal places.
Step-by-step explanation:
The student has asked to find the area under the standard normal curve to the left of z=0.21.
To find this area, also known as the cumulative probability, you will need to refer to a Z-table or use statistical software or a calculator with statistical functions. The table consists of z-scores in the leftmost column and the top row, and the intersection of the row and column corresponding to the z-score gives the area under the curve to the left of that z-score.
Using a Z-table, locate the area for the z-score of 0.21. The area to the left of z=0.21 corresponds to the cumulative probability that a value is less than this particular z-score on the standard normal distribution. For a z-score of approximately 0.21, the area you find in the Z-table will be slightly over 0.5, as 0.5 represents the area to the left of z=0 (the mean of the distribution).
Example of Using the Z-Table
The area to the left of the z-score of -0.40 is 0.3446. However, the exact area for z=0.21 can vary and needs to be looked up for precision. The student must use the Z-table to find the corresponding area value for z=0.21 and round the result to four decimal places if necessary.