5. Park Rangers wanted to estimate the total number of wild mustangs in Central Oregon. They tagged 30 wild mustangs and sent them back to the herd. They recorded the mustang population once a month for the next three months as shown below.
Month 1 Month 2 Month 3
tagged mustangs in sample 8 10 15
total mustangs in sample 100 150 200
c. The rangers combined the three months into one large sample so they could consider a sample of 100 + 150 + 200 = 450 mustangs. Estimate the size of the wild mustang population.
To estimate the size of the wild mustang population, we can use the concept of proportion.
First, we need to find the proportion of tagged mustangs in each monthly sample. This can be calculated by dividing the number of tagged mustangs by the total number of mustangs in each respective sample.
For Month 1: 8 tagged mustangs / 100 total mustangs = 0.08
For Month 2: 10 tagged mustangs / 150 total mustangs = 0.0667 (approximately)
For Month 3: 15 tagged mustangs / 200 total mustangs = 0.075
Next, we need to calculate the average proportion across the three months. This can be done by adding up the proportions and dividing by the number of months.
Average Proportion = (0.08 + 0.0667 + 0.075) / 3 ≈ 0.0739
Now, we can use the average proportion to estimate the size of the wild mustang population. Since we have a combined sample size of 450 mustangs, we can set up a proportion:
Tagged Mustangs / Total Mustangs = Average Proportion
Using this equation, we can solve for the total number of mustangs:
Tagged Mustangs / 450 = 0.0739
Tagged Mustangs = 450 * 0.0739 = 33.255
Therefore, the estimated size of the wild mustang population in Central Oregon would be approximately 33.255 mustangs.