Question

question #1 provide an approiate response. Write the next equation in the pattern
1+1=2
1+1+2=4
1+1+2+3=7
1+1+2+3+5=12
question #2
Decide which of the variables described is likely to have a normal or near normal distribution.
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 owners in a new "affordable housing' division
A)a B)b C)both a and b D)neither a or b

Answer 1

A is probably near normal (the teacher cant have negative cents in her pocket). On the property taxes, it is impossible to say. For instance, what if there are 15 units, 5 of the small house, 5 of the medium house size, and 5 of the largest house size. That will not give a normal distribution.

Answer 2

b) is likely to have a normal or near normal distribution.

If the amount of change held were normal, then there would be a well-defined mean associated with the distribution. Since it is impossible to even guess a ballpark value for what the mean may be, it is likely that the underlying distribution is not normal.

Likewise, in a new affordable housing subdivision, the prices and sizes of the properties are strictly controlled. Property tax goes as the size of the property. As much as the architects would like for each property to be exactly the same size, realistically, that won't happen. As a result, each property will be approximately the same size, with some variation. As a result, the property tax owed on each property will also be approximately the same (establishing the well-defined mean for the distribution) and the variations in property size will carry over to the variations in the property tax. Also, since the housing development will probably contain more than 25-30 new homes, central limit theorem tells us that even if the distribution underlying the variations in the property sizes is not normal, the resulting statistics will be well approximated by a normal distribution.