Answer:
a. Since we know the mean and median of the wingspans, we can assume that the data is approximately normally distributed. We also know the range, which is the difference between the maximum and minimum values. From this information, we can set up two equations:
Mean = (Wingspan1 + Wingspan2 + Wingspan3)/3 = 6 1/4
Median = 6
We can use the second equation to eliminate one of the variables. If the median is 6, then the middle value must be 6 as well. Let's assume that Wingspan2 = 6. Then we have:
(Wingspan1 + 6 + Wingspan3)/3 = 6 1/4
Multiplying both sides by 3 and simplifying:
Wingspan1 + Wingspan3 = 18 3/4
We also know that the range is 1 3/4, so:
Wingspan3 - Wingspan1 = 1 3/4
Solving for Wingspan3 in terms of Wingspan1:
Wingspan3 = Wingspan1 + 1 3/4
Substituting this into the previous equation:
Wingspan1 + (Wingspan1 + 1 3/4) = 18 3/4
2Wingspan1 + 1 3/4 = 18 3/4
2Wingspan1 = 17
Wingspan1 = 8 1/2
Therefore, Wingspan3 = 10 1/4. So the three bald eagles have wingspans of 8 1/2 feet, 6 feet, and 10 1/4 feet.
b. Since the mean and median of the weights are the same, we can assume that the data is exactly normally distributed. We also know the range, which is the difference between the maximum and minimum values. From this information, we can set up two equations:
Mean = (Weight1 + Weight2 + Weight3)/3 = 12.75
Median = 12.75
We can use the second equation to eliminate one of the variables. If the median is 12.75, then the middle value must be 12.75 as well. Let's assume that Weight2 = 12.75. Then we have:
(Weight1 + 12.75 + Weight3)/3 = 12.75
Multiplying both sides by 3 and simplifying:
Weight1 + Weight3 = 38.25
We also know that the range is 5 pounds, so:
Weight3 - Weight1 = 5
Solving for Weight3 in terms of Weight1:
Weight3 = Weight1 + 5
Substituting this into the previous equation:
Weight1 + (Weight1 + 5) = 38.25
2Weight1 + 5 = 38.25
2Weight1 = 33.25
Weight1 = 16.625
Therefore, Weight3 = 21.625. So the three bald eagles have weights of 16.625 pounds, 12.75 pounds, and 21.625 pounds.