Final answer:
The correct option regarding the proportions in the body of a normal distribution is that body proportions on the right side of a positive z-score are greater than 0.50, and on the left side, they are less than 0.50.
Step-by-step explanation:
The question asks about the proportions in the body of a normal distribution, which can be examined using z-scores. In a normal distribution, the mean is located at the center, and the distribution is symmetrical around the mean. This symmetry means that the proportion of the data within a certain number of standard deviations from the mean is the same on both sides of the mean.
Choosing the correct option from the provided choices, we should consider the fact that the total area under the normal distribution curve is 1 (or 100%). Half of this area is to the left of the mean, and the other half is to the right. Therefore, for any value of z (the z-score), the proportion of the body on the right of the z-score on the curve is less than 0.50 if z is positive, and greater than 0.50 if z is negative.
Similarly, the proportion on the left of the z-score is greater than 0.50 if z is positive, and less than 0.50 if z is negative. Consequently, the correct answer to the question is option (a): body proportions on the right side of the z-score are greater than 0.50; on the left side, they are less than 0.50.