Question

Residents in a city are charged for water usage every three months. The water bill is computed from a common fee, along with the amount of water the customers use. The last water bills for 40 neighborhood residents are displayed in the histogram below.

A histogram titled Neighborhood Monthly water bill has monthly water bill (dollars) on the x-axis and frequency on the y-axis. 100 to 125, 1; 125 to 150, 2; 150 to 175, 5; 175 to 200, 10; 200 to 225, 13; 225 to 250, 8.

Which of these correctly describes the shape of the distribution of water bills?

uniform
skewed left
skewed right
roughly symmetric

Answer 1

The distribution of the water bills, as shown in the histogram, is a right-skewed distribution, because it has more low values and the tail extends to the right.

Step-by-step explanation:

To determine the shape of the distribution of water bills based on the histogram provided, we will describe the characteristics of the distribution. The histogram shows the following frequency counts for each water bill range: $100 to $125 has 1 resident, $125 to $150 has 2 residents, $150 to $175 has 5 residents, $175 to $200 has 10 residents, $200 to $225 has 13 residents, and $225 to $250 has 8 residents.

Observing the frequency counts, we see that the histogram does not represent a uniform distribution as the frequencies are not the same across all intervals. It also does not represent a symmetric distribution, since it does not appear to have mirror images on either side of a central point. Rather, the distribution has a higher frequency in the middle ranges, and it tapers off towards both the lower and higher ends, with the tail on the right side being slightly less pronounced than the left. This description matches that of a right-skewed distribution. Hence, the correct answer is that the shape of the distribution of water bills is skewed right because more low values are present and the tail of the histogram extends to the right.