For a bell-shaped distribution, which Z score value would best approximate the 84th percentile?

In a bell-shaped distribution, also known as a normal distribution, the Z score represents how many standard deviations a data point is from the mean. The Z score corresponding to specific percentiles can be referenced using a Z table (standard normal distribution table), which provides the area (or cumulative probability) to the left of a given Z score.

To find the Z score that approximates the 84th percentile, we look for the Z score that has about 84% of the data to its left. The Z score that corresponds to 0.84 (which represents 84% cumulative probability) is approximately +1. This means that a score at the 84th percentile is one standard deviation above the mean in a normal distribution.

This understanding aligns with the properties of the normal distribution, where about 68% of the data lies within one standard deviation from the mean (34% on either side), and about 95% within two standard deviations. Therefore, since 84% is well beyond the mean, the Z score of +1 is the appropriate choice as it captures the point at which 84% of the population falls below.

Knowing that the other value options represent Z scores that are further from the mean or below it, they