A new movie opened the other day. So far, 500,000 people have seen it. The producers of the movie needed to know if the people liked it. A random sample of 8,000 people leaving showings of the movie were asked if they liked the movie. Of those interviewed, 4,200 enjoyed the movie. Predict the total number of people who have enjoyed the movie.
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To predict the total number of people who have enjoyed the movie based on the survey results, we can use the concept of sampling and proportions. We have a random sample of 8,000 people who were asked if they liked the movie, and out of those interviewed, 4,200 enjoyed it.
To calculate the proportion of people who enjoyed the movie in the sample, we can divide the number of people who enjoyed it (4,200) by the total sample size (8,000):
Proportion of people who enjoyed the movie in the sample = 4,200 / 8,000 = 0.525
Now, we can use this proportion to estimate the number of people who enjoyed the movie in the entire population. Since we are given that 500,000 people have seen the movie in total, we can multiply this number by the proportion from the sample to get our prediction:
Total number of people who enjoyed the movie = 500,000 * 0.525 = 262,500
Therefore, based on the given information, we can predict that approximately 262,500 people have enjoyed the movie.
4200/8000 = x/500,000
Solve for x.