A certain zoo kept records of the relationships between the weight of a mother ostrich and the weight of her egg. Data for 3 birds is shown in the next table.
Os. 1 Os. 2 Os. 3
lb of mom 120lb 160lb 180lb
lb of egg 2.4lb 3.2lb 3.6lb
A. Est, the weight of an egg from a mother ostrich weighing 175lbs.
B. How much would you expect the egg to weigh from a mother ostrich weighing 190lbs?
a. e = .02(175) = 3.5
b. e = .02(190) = 3.8
To estimate the weight of an egg from a mother ostrich weighing 175 lbs, we can use the data provided in the table to find a correlation between the weight of the mother ostrich and the weight of the egg.
Based on the data given, we can see that there is a relationship between the weight of the mother ostrich and the weight of the egg. Specifically, as the weight of the mother ostrich increases, the weight of the egg also increases.
To estimate the weight of the egg from a mother ostrich weighing 175 lbs, we can use the concept of linear interpolation. This involves finding a linear equation that relates the weight of the mother ostrich to the weight of the egg and then substituting the given weight into the equation.
To find the equation, we need to calculate the slope (m) and the y-intercept (b) using the given data points.
Using the data from Os. 1 and Os. 2:
Weight of mother ostrich: 120 lbs, Weight of egg: 2.4 lbs
Weight of mother ostrich: 160 lbs, Weight of egg: 3.2 lbs
To calculate the slope (m):
m = (y2 - y1) / (x2 - x1) = (3.2 - 2.4) / (160 - 120) = 0.8 / 40 = 0.02
Now we can find the y- intercept (b) by using one of the data points.
Using the point (120, 2.4):
b = y - mx = 2.4 - (0.02 * 120) = 2.4 - 2.4 = 0
Therefore, the linear equation relating the weight of the mother ostrich (x) to the weight of the egg (y) is:
y = 0.02x
To estimate the weight of the egg from a mother ostrich weighing 175 lbs, we can substitute this value into the equation:
y = 0.02 * 175 = 3.5 lbs
So, the estimated weight of the egg from a mother ostrich weighing 175 lbs is approximately 3.5 lbs (rounded to one decimal place).
To estimate how much an egg would weigh from a mother ostrich weighing 190 lbs, we can use the same linear equation:
y = 0.02 * 190 = 3.8 lbs
Therefore, the estimated weight of the egg from a mother ostrich weighing 190 lbs is 3.8 lbs.