A marketing firm wants to know how many people in District 6 have tried Popeyes' and Chick-fil-A's chicken sandwiches. Of the 10,000 people in District 6, 1500 are vegetarians or vegans and have never tried either sandwich, 5000 have tried both, and the rest have tried one or the other. What is the population proportion for people who have tried both sandwiches?
-0.50
-0.45
-0.30
-0.15
You clearly state that 5000 of the 10,000 have tried both.
The you ask what proportion have tried both sandwiches
obviously that would be 5000/10000 or 1/2
as a percentage it would be 50%, as a decimal .5
The rest of the data in your question appears to be just "white noise"
To find the population proportion of people who have tried both sandwiches, we need to subtract the proportion of people who have tried either sandwich individually from the total population.
Let's calculate the proportions:
Population in District 6: 10,000
Vegetarians/Vegans: 1,500
People who have never tried either sandwich: 1,500
People who have tried both sandwiches: 5,000
Now, let's calculate the proportion of people who have tried either sandwich individually:
P(people who have tried Popeyes' sandwich) = (Total population - Vegetarians/Vegans - Never tried either) / Total population
= (10,000 - 1,500 - 1,500) / 10,000
= 7,000 / 10,000
= 0.7
P(people who have tried Chick-fil-A's sandwich) = (Total population - Vegetarians/Vegans - Never tried either) / Total population
= (10,000 - 1,500 - 1,500) / 10,000
= 7,000 / 10,000
= 0.7
Since the proportions for Popeyes' and Chick-fil-A's sandwiches are the same, we can conclude that the proportion for people who have tried both sandwiches is:
P(people who have tried both sandwiches) = P(people who have tried Popeyes' sandwich) + P(people who have tried Chick-fil-A's sandwich) - 1
= 0.7 + 0.7 - 1
= 1.4 - 1
= 0.4
Therefore, the population proportion for people who have tried both sandwiches is 0.4.
None of the given answer choices (-0.50, -0.45, -0.30, -0.15) match the correct proportion.
To find the population proportion for people who have tried both sandwiches, we need to determine the number of people who have tried both sandwiches, divided by the total population.
Let's break down the given information:
- Total population in District 6: 10,000
- Number of vegetarians or vegans who haven't tried either sandwich: 1,500
- Number of people who have tried both sandwiches: 5,000
To calculate the population proportion of people who have tried both sandwiches, subtract the number of people who haven't tried either sandwich from the total population, and then divide the result by the total population:
Total number of people who have tried both sandwiches = Total population - Number of vegetarians or vegans who haven't tried either sandwich
= 10,000 - 1,500
= 8,500
Population proportion of people who have tried both sandwiches = Number of people who have tried both sandwiches / Total population
= 5,000 / 10,000
= 0.5
Therefore, the correct population proportion for people who have tried both sandwiches is 0.5 or 50%.