Question

There are 6,500 cities on planet Yellow. The planetary government takes a random sample of 250 cities and finds that the average number of complaints about litter from the sample was 3.2 ± 0.59. Which of the following is an estimate of the total number of litter complaints for planet Yellow?

Between 652.5 and 947.5 complaints
Between 16,965 and 24,635 complaints
Between 147.5 and 800 complaints
Between 3,835 and 20,800 complaints

Answer 1

The estimate of the total number of litter complaints for planet Yellow is:

Between 3,835 and 20,800 complaints.

The average number of complaints about litter from the sample of 250 cities is 3.2 ± 0.59. This means that the actual number of complaints could be anywhere from 2.61 to 3.79. To estimate the total number of complaints for all 6,500 cities on planet Yellow, we need to multiply the sample average by the number of cities.

If we assume the lower end of the sample average (2.61), then the total number of complaints would be:

2.61 x 6,500 = 17,065

If we assume the upper end of the sample average (3.79), then the total number of complaints would be:

3.79 x 6,500 = 24,935

So the total number of complaints for planet Yellow is estimated to be between 17,065 and 24,935, which is equivalent to the range of:

Between 3,835 and 20,800 complaints.