In each case, consider what you know about the distribution and them explain why you would expect it to be or not to be norally distributed.

a. The wealth of the parents of students attending your school
b. The value that a group of fourth-grade students would give for the length of a segment that they measured with a ruler
c. The SAT and ACT examination sores in mathematics for students who were in your high school graduation class
d. The weights of all incoming freshman students at your school

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To determine whether a distribution is expected to be normally distributed or not, consider the characteristics and nature of the variables involved in each case.

a. Wealth of parents of students attending your school:
In this case, you would likely not expect the distribution to be normally distributed. Wealth tends to follow a skewed distribution, with the majority of individuals having lower wealth and a smaller number having higher wealth. This is commonly referred to as a long-tailed distribution or a distribution with positive skewness.

b. Value that a group of fourth-grade students would give for the length of a segment they measured with a ruler:
For this case, you would expect the distribution to be normally distributed, assuming the measurements are made accurately. The length of a segment measured by a group of fourth-grade students is likely to be influenced by random errors, such as slight variations in placement and reading of the ruler. These random errors tend to follow a normal distribution.

c. SAT and ACT examination scores in mathematics for students in your high school graduation class:
In this case, you would expect the distribution to be normally distributed. Standardized tests, like the SAT and ACT, are designed to measure a wide range of abilities and knowledge levels. The test scores tend to have a symmetric distribution around a mean, forming a bell-shaped curve. This is the underlying assumption of these tests.

d. Weights of incoming freshman students at your school:
The distribution of weights is expected to be normally distributed. The weights of humans in a given population tend to follow a bell-shaped curve. While there may be slight deviations due to factors like gender and different body types, overall, a large sample of weights will approximate a normal distribution.

It's important to note that the above expectations are based on general trends and assumptions. Actual data may deviate from these expectations due to various factors, such as sample size, biases, or specific characteristics of the population under consideration. Therefore, it is always essential to verify the assumptions by analyzing the data itself.