200 people were sampled and the following table shows the number of people with a certain average electric energy usage based upon the type of home an individual lives in:
Electric Usage (in kWh)
Type of Dwelling < 5,000 5,000 – 7,000 7,000 – 11,000 11,000 – 15,000 Total
Single Family 15 35 65 25 140
Multi-Family 25 15 15 5 60
Total 40 50 80 30 200
a) What is the probability of selecting someone who uses between 7,000 and 11,000 kWh?
b) What is the probability of randomly selecting someone who uses less than 5,000 kWh and who lives in a multi-family dwelling?
c) What is the probability of selecting someone who lives in a single family dwelling or uses between 5,000 and 7,000 kWh?
There is no table.
To answer the questions, we need to use the information provided in the table. The table shows the number of people with a certain average electric energy usage based on the type of home.
a) To find the probability of selecting someone who uses between 7,000 and 11,000 kWh, we need to add up the number of people in that range and divide it by the total number of people sampled.
According to the table, the number of people with average electric usage between 7,000 and 11,000 kWh is 80. The total number of people sampled is 200.
So, the probability is calculated by dividing 80 by 200:
Probability = 80/200 = 0.4 (or 40%)
Therefore, the probability of selecting someone who uses between 7,000 and 11,000 kWh is 40%.
b) To find the probability of randomly selecting someone who uses less than 5,000 kWh and lives in a multi-family dwelling, we need to find the number of people in that category and divide it by the total number of people sampled.
According to the table, the number of people with average electric usage less than 5,000 kWh and living in a multi-family dwelling is 25.
So, the probability is calculated by dividing 25 by 200:
Probability = 25/200 = 0.125 (or 12.5%)
Therefore, the probability of randomly selecting someone who uses less than 5,000 kWh and lives in a multi-family dwelling is 12.5%.
c) To find the probability of selecting someone who lives in a single-family dwelling or uses between 5,000 and 7,000 kWh, we need to find the sum of the number of people in these two categories and divide it by the total number of people sampled.
According to the table, the number of people who live in a single-family dwelling is 140 and the number of people with average electric usage between 5,000 and 7,000 kWh is 50.
So, the probability is calculated by adding 140 and 50, and then dividing the sum by 200:
Probability = (140 + 50)/200 = 190/200 = 0.95 (or 95%)
Therefore, the probability of selecting someone who lives in a single-family dwelling or uses between 5,000 and 7,000 kWh is 95%.