Final answer:
To determine the z-values that bound the middle 83% of the standard normal curve, calculate the areas in the tails (8.5% each) and find the corresponding z-scores for 8.5% and 91.5%, which are approximately -1.405 and 1.405, respectively.
Step-by-step explanation:
To find the z-values that bound the middle 83% of the area under the standard normal curve, we start by determining the area in each tail outside of the middle 83%. Since the total area under the curve is 100%, each tail will have half of the remaining 17%, which is 8.5%. Using a standard normal distribution table or calculator, we need to find the z-scores corresponding to the area to the left of 8.5% and to the left of 91.5% (100% - 8.5%).
For the lower z-value, we use the value 0.085 in a z-table or an inverse normal function to find the corresponding z-score, which is typically around -1.405. For the upper z-value, we use the value 0.915 to find the corresponding z-score, which is typically around 1.405.
Therefore, the z-values c and d that bound the middle 83% of the area under the standard normal curve are approximately -1.405 and 1.405, when rounded to four decimal points.