Certainly! Let's solve this step-by-step.
Step 1: Calculate the total sample size.
We need to sum up the number of adults who chose each source of news in the sample:
[tex]\[
62\ (\text{Newspapers}) + 86\ (\text{Internet}) + 165\ (\text{Television}) + 24\ (\text{Radio}) + 38\ (\text{Other}) = 375
\][/tex]
So, the total sample size is 375 adults.
Step 2: Determine the proportion of adults in the sample whose main source of news is television.
From the sample, we know that 165 adults mentioned television as their main source. To find the proportion, we divide this number by the total sample size:
[tex]\[
\frac{165\ (\text{Television})}{375\ (\text{Total Sample Size})} = 0.44
\][/tex]
So, the proportion of adults in the sample whose main source of news is television is 0.44.
Step 3: Use this proportion to predict the number of adults in the whole population of Palm City whose main source of news is television.
We know the total population of Palm City is 36,000 adults. We can predict the number of television viewers by multiplying the total number of adults by the proportion of television viewers:
[tex]\[
0.44 \times 36000 = 15840
\][/tex]
After rounding to the nearest whole number, the predicted number of adults in Palm City whose main source of news is television is 15,840.
