What percent of heights of adult males in the normally distributed general population

have z-scores between -1 and +1?

68.27% of the population is between z= -1 and z = 1. That is the fraction within "one sigma" of the mean, for any normal distribution.

To find the percentage of heights of adult males in the normally distributed general population that have z-scores between -1 and +1, we can utilize the properties of the standard normal distribution.

The standard normal distribution has a mean of 0 and a standard deviation of 1. A z-score measures how many standard deviations an observation is above or below the mean. In this case, we want to find the percentage of heights that fall within 1 standard deviation below the mean (-1) and 1 standard deviation above the mean (+1).

To find this percentage, we can refer to a standard normal distribution table or use statistical software. Let's use a standard normal distribution table.

1. Look up the area (percentage) associated with a z-score of -1 by finding the value closest to -1 in the left column of the table. The corresponding area to the right of this value is the percentage.
- A z-score of -1 corresponds to an area of 0.1587, which represents approximately 15.87% of the population.

2. Look up the area (percentage) associated with a z-score of +1 by finding the value closest to 1 in the left column of the table. The corresponding area to the left of this value is the percentage.
- A z-score of +1 corresponds to an area of 0.8413, which represents approximately 84.13% of the population.

To find the percentage of heights within this range:
Percentage = Area above z=-1 - Area above z=1 = 84.13% - 15.87% = 68.26%

Therefore, approximately 68.26% of heights of adult males in the normally distributed general population have z-scores between -1 and +1.