There are 3,000 people at a concert. You survey a random sample of 200 people and find that for 35 of them this is the first concert they have ever attenede. Estimate how many total people are attending their first concert that night
Let x be the estimated number of the 3000 people who are attending their first concert.
35/200 = x/3000
To isolate x, multiply both sides by 3000:
3000(35/200) = 3000(x/3000)
525 = x
To estimate the total number of people attending their first concert that night, we can use the concept of a representative sample.
Step 1: Calculate the proportion of people in the sample who attended their first concert.
Proportion = Number of people in the sample who attended their first concert / Total number of people in the sample
Proportion = 35 / 200 = 0.175
Step 2: Apply the proportion to the total number of people attending the concert.
Estimated number of people attending their first concert = Proportion * Total number of people at the concert
Estimated number of people attending their first concert = 0.175 * 3000 = 525
Therefore, we can estimate that approximately 525 people are attending their first concert that night.