1. A new movie open the other day. So far 500,000 people have seen. The producers of the movie need to know if the people liked it. A random sample of 8000 people were asked as they were leaving the theater if they like the movie. Of those interviewed 4200 enjoyed the movie. Predict the total number of people who have enjoyed the movie?

261,500
262,645
262,500***
263,000

I agree with that answer.

To predict the total number of people who have enjoyed the movie, we can use a simple proportional relationship between the sampled individuals and the total population.

First, we calculate the proportion of people who enjoyed the movie in the sample:

Proportion of people who enjoyed the movie = Number of people who enjoyed the movie in the sample / Total number of people in the sample

Proportion of people who enjoyed the movie = 4200 / 8000

Next, we use this proportion to estimate the total number of people who enjoyed the movie:

Estimated total number of people who enjoyed the movie = Proportion of people who enjoyed the movie * Total number of people who have seen the movie

Estimated total number of people who enjoyed the movie = (4200 / 8000) * 500,000

Estimated total number of people who enjoyed the movie ≈ 262,500

Therefore, the predicted total number of people who have enjoyed the movie is 262,500.