Decide which of the variables described is likely to have a normal or near-normal distribution.

3)

a. The amount of change held by a teacher at the end of each
day for a year
b. The amount of property taxes paid by homeowners in a
new "affordable housing" subdivision

3)

_______
A) a
B) b
C) both a and b
D) neither a nor b
I believe that the answer is C (both a and b) is this correct?

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D) neither a or b

To determine whether a variable is likely to have a normal or near-normal distribution, we can consider a few factors. These factors include the type of data, the population size, and the process that generates the data.

a) The amount of change held by a teacher at the end of each day for a year:
This variable is likely to have a normal or near-normal distribution. Assuming there is a large number of teachers and each teacher's change is independent of others, we can expect the distribution to be approximately normal. This is because the amount of change held by a teacher is likely to follow a random process influenced by various factors. These factors can include the number of transactions, the amount of change provided to each teacher, and any randomness involved. As the number of teachers and the number of transactions increase, the central limit theorem suggests that the distribution of the amount of change held by a teacher will approach a normal distribution.

b) The amount of property taxes paid by homeowners in a new "affordable housing" subdivision:
This variable is also likely to have a normal or near-normal distribution. Property taxes are typically calculated based on various factors such as the assessed value of the property, local tax rates, and other factors specific to the subdivision. These factors tend to have a random or uncorrelated effect on the amount paid by homeowners. If there is a significant number of homeowners in the subdivision, the central limit theorem suggests that the distribution of property taxes paid will approach a normal distribution.

Therefore, the correct answer is C) both a and b.