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 data set has 10 values). complete parts (a) through (d) below

c. would you expect the distribution to be symmetric, left - skewed, or right - skewed? explain

a. the distribution would probably be right - skewed because there is a clear minimum last digit of 0 but no obvious maximum last digit.

b. the distribution would probably be left - skewed because the number of street addresses that end in each digit increases as the digits increase

c. the distribution would probably be left - skewed because there are so many long streets, and therefore many more addresses with a last digit closer to 9 than to 0

d. the distribution would probably be symmetric because there are no obvious factors to indicate that any single digit would occur as the last digit more frequently than any other

d. would you expect the variation of the distribution to be small, moderate, or large? explain

a. the variation would probably be small because there are only 10 possible last digits

b. the variation would probably be moderate because there are no obvious factors that would make it small or large

c. the variation would probably be large because any one of the 10 digits is an equally - likely last digit

d. the variation would probably be small because most of the street addresses end in a digit close to 9

Explanation:

Part (c)

To determine the skewness, we analyze the last digits (0 - 9) of street addresses. There's no inherent reason for one digit to be more frequent than another (e.g., no bias towards higher or lower digits). A symmetric distribution occurs when values are evenly distributed around a center, and here, no factor suggests a digit is more frequent, so the distribution should be symmetric. Option D correctly states this as there are no obvious factors making one digit more frequent. Options A, B, and C suggest skewness, which isn't supported as digits 0 - 9 are equally likely in a random street address context.

For variation, we consider the range of possible last digits (0 - 9, 10 values). Since there are only 10 possible last digits, the number of people with addresses ending in each digit won't vary drastically (e.g., counts for each digit should be relatively close). Option A explains this—with only 10 possible digits, the variation (spread in counts) should be small. Option B claims moderate variation without reason, C claims large (untrue as digits are equally likely), and D's reasoning (most end near 9) is unfounded.

Answer:

D. The distribution would probably be symmetric because there are no obvious factors to indicate that any single digit would occur as the last digit more frequently than any other

Part (d)