Question

consider the distribution of the numbers of people whose street address ends in 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 (the distribution has 10 values). complete parts (a) through (d) below

a. how many peaks would you expect for the distribution? explain.

a. there would probably be two peaks, one close to the least number, 0, and one close to the greatest number, 9, because those are the numbers that everyone picks for their address.

b. there would probably be one peak. many streets are long, and the addresses for people living on those streets are large numbers, so the peak would be at a number close to 9.

c. there would probably be no peaks. when all street addresses are considered, the distribution of the last digit tends to be uniform.

d. there would probably be many peaks corresponding to each of the last digits that are even numbers, because there are always more buildings on the even side of the street.

b. make a sketch of the distribution. choose the correct answer below

a. bar graph with equal height bars for each last digit

b. skewed graph

c. two - peaked graph

d. single - peaked graph

Explanation:

Part (a)

To determine the number of peaks in the distribution of the last digits of street addresses, we analyze the nature of street address numbering. Street addresses are typically assigned in a sequential manner (e.g., 1, 2, 3,... on one side and even numbers on the other, but across all streets, there's no inherent bias towards a particular last digit). So, the last digits (0 - 9) should be roughly equally likely, leading to a uniform distribution. A uniform distribution has no peaks (since all values occur with similar frequency).

• Option A is incorrect because there's no reason for peaks at 0 and 9 specifically—addresses aren't biased to end at 0 or 9.
• Option B is incorrect because addresses aren't all large numbers (many streets have small - numbered addresses too, and even for long streets, the last digit distribution should still be uniform).
• Option D is incorrect because there's no universal rule that there are more buildings on the even side (and even if there were, it wouldn't create "many peaks" corresponding to each even digit in a way that's consistent across all streets).
• Option C is correct as the last - digit distribution of all street addresses tends to be uniform, so no peaks.

Part (b)

Since the distribution of the last digits of street addresses is uniform (from part (a)), the graph should show all the bars (or the line, depending on the graph type) at approximately the same height. Looking at the options:

• Option A shows a uniform - height graph (all the "bars" or the line is flat), which matches a uniform distribution.
• Option B shows a skewed distribution (peaking at the left and tapering off), which is not uniform.
• Option C shows a bimodal distribution (two peaks), which is not uniform.
• Option D shows a unimodal (bell - shaped) distribution, which is not uniform.

Answer:

Part (a)

C. There would probably be no peaks. When all street addresses are considered, the distribution of the last digit tends to be uniform.

Part (b)

A. (The graph with the uniform height across the last digits 0 - 9)