Tara is researching the stork population living in a bird reserve. On her first day, she captures and tags 37 birds. Two weeks later, she captures 48 birds and finds that 30 are not tagged. Estimate the actual number of storks in the bird reserve.
27. In a marketing survey involving 910 randomly chosen people, it is found that 550 use brand P, 360 use brand Q, and 90 use both brands. How many people in the survey use brand Q and not brand P?
a.
This is a typical case of a hypergeometric distribution where
Suppose
N=total population, (unknown)
n=sample size (48)
a=total number of tagged birds (37)
x=number (18) of tagged birds out of n (48)
Then approximately,
x/n = a/N
or
N=an/x = 37*48/18 = 99 (approximately).
b.
Q\P=Q-Q∩P=360-90=370
The first question is 98.6666666, but if it is for a test, put "approximately 99".
The second question's answer is 270.
i think the second answer is 315 because not all 90 people use brand Q. so take 90 divide by 2 then subtract.+
To estimate the actual number of storks in the bird reserve, we can use the concept of proportion.
First, we can assume that the ratio of tagged birds to the total number of birds in the reserve is equal to the ratio of tagged birds captured by Tara to the total number of birds captured by Tara.
Let's denote the total number of storks in the bird reserve as "x."
From the given information, we know that Tara tagged 37 birds initially, and two weeks later, she captured 48 birds with 30 not being tagged. This means that in the second capture, only 18 out of 48 birds were tagged.
So, we can set up the proportion:
37/x = 18/48
To solve for x, we cross-multiply and solve the equation:
18 * x = 37 * 48
x = (37 * 48) / 18
x ≈ 98
Therefore, the estimated actual number of storks in the bird reserve is approximately 98.
--------------------------------------------------
To find the number of people in the survey who use brand Q and not brand P, we can use set theory and the principle of inclusion-exclusion.
Let's denote the number of people using brand P as "P," the number of people using brand Q as "Q," and the number of people using both brands as "P∩Q." We are given that P = 550, Q = 360, and P∩Q = 90.
To find the number of people using brand Q and not brand P (Q-P), we can use the formula:
Q - P∩Q
Substituting the given values:
360 - 90 = 270
Therefore, in the survey, 270 people use brand Q and not brand P.