Final answer:
The z-score closest to representing the 80th percentile is 0.84, as it corresponds closely to an area of 0.7995 under the normal curve. The first quartile is another term for the 25th percentile or lower quartile.
Step-by-step explanation:
To find the 80th percentile in a normally distributed dataset, we need to know what z-score corresponds to that percentile. The 80th percentile means that 80% of the data lies below that point, and 20% lies above it. Looking at the given options, we want the z-score that is closest to representing this area under the normal curve.
Using a standard z-table, we find that a z-score of 0.84 corresponds closely to the 80th percentile (the exact value is about 0.7995). Z-scores of 0.85 and above (1.28; 1.34) will represent higher percentiles, hence z-score of 0.84 is the most accurate option given for the 80th percentile.
The first quartile, also known as the 25th percentile or the lower quartile, is the value below which 25% of the data can be found. It is found at the z-score corresponding to 0.25 on the z-table.