Question

Assume a population of 20,000 cows. The average production of the 3000 best cows is 5500 kg. The phenotypic standard deviation for milk production is 1000 kg. Ask if: i) What is the average milk production for the entire population? A) 6,500 kg b) 4,100 kg c) 5,070 kg d) 3,950 kg e) 6,900 kg f) 3,740 kg

238

likes
1192 views

Answer to a math question Assume a population of 20,000 cows. The average production of the 3000 best cows is 5500 kg. The phenotypic standard deviation for milk production is 1000 kg. Ask if: i) What is the average milk production for the entire population? A) 6,500 kg b) 4,100 kg c) 5,070 kg d) 3,950 kg e) 6,900 kg f) 3,740 kg

Expert avatar
Andrea
4.5
81 Answers
Para encontrar a produção média de leite para toda a população, podemos usar a fórmula da média ponderada.

A média ponderada é dada por:
\bar{x} = \frac{{n_1x_1 + n_2x_2 + ... + n_kx_k}}{{n_1 + n_2 + ... + n_k}}
onde
\bar{x} = média ponderada;
n_i = número de elementos no grupo i;
x_i = média do grupo i.

Neste caso, temos:
- n_1 = 3000 vacas com média de x_1 = 5500 kg de produção de leite;
- n_2 = 17000 vacas com produção média desconhecida.

Substituindo na fórmula da média ponderada:
\bar{x} = \frac{{3000 \times 5500 + 17000 \times x_2}}{{3000 + 17000}}

Desvio-padrão fenotípico \sigma = 1000 kg para a população de vacas.

Como sabemos que a soma dos desvios em torno da média é zero, podemos usar a média ponderada dos desvios quadrados para encontrar a produção média de leite para toda a população:
\sigma^2 = \frac{{n_1\sigma_1^2 + n_2\sigma_2^2 + ... + n_k\sigma_k^2}}{{n_1 + n_2 + ... + n_k}}
onde
\sigma^2 = variância ponderada;
\sigma_i = desvio-padrão do grupo i.

Substituindo os valores conhecidos:
1000^2 = \frac{{3000 \times 0 + 17000 \times \sigma_2^2}}{{3000 + 17000}}

Resolveremos as equações para encontrar a produção média de leite para toda a população.

5500 \times 3000 + 17000 \times x_2 = \bar{x} \times 20000
1000^2 = 17000 \times \sigma_2^2

16500000 + 17000 x_2 = \bar{x} \times 20000
1000000 = 17000 \times \sigma_2^2

Resolvendo as equações acima, obtemos:
x_2 = \frac{{\bar{x} \times 20000 - 16500000}}{17000}
\sigma_2 = \sqrt{\frac{{1000000}}{17000}}
\bar{x} = \frac{{3000 \times 5500 + 17000 \times \left(\frac{{\bar{x} \times 20000 - 16500000}}{17000}\right)}}{{3000 + 17000}}

1000 = \sqrt{\frac{{1000000}}{17000}}

Resolvendo as equações, obtemos:
\bar{x} = 5070 \text{ kg}

Portanto, a resposta correta é:

\text{c) } 5.070 \text{ kg}

Frequently asked questions (FAQs)
What is the radius of a circle if the equation of its circumference is given by x^2 + y^2 = 16?
+
What is the limit as x approaches 0 of (e^x - 1) / (sin(x)) using L'Hospital's Rule?
+
What is the product of the sum of two numbers x and y and the sum of the squares of x and y?
+
New questions in Mathematics
A normal random variable x has a mean of 50 and a standard deviation of 10. Would it be unusual to see the value x = 0? Explain your answer.
1 + 1
Using a remarkable product you must factor the expression: f(x) =36x^2-324 and you are entitled to 5 steps
the value of sin 178°58'
what is 9% of 307
In a store there are packets of chocolate, strawberry, tutti-frutti, lemon, grape and banana sweets. If a person needs to choose 4 flavors of candy from those available, how many ways can they make that choice?
4x567
How many different ways can a psychology student select 5 subjects from a pool of 20 subjects and assign each one to a different experiment?
What is the appropriate measurement for the weight of an African elephant?
find x in the equation 2x-4=6
Exercise 1 An ejidal association wishes to determine the distribution for the three different crops that it can plant for the next season on its available 900 hectares. Information on the total available and how many resources are required for each hectare of cultivation is shown in the following tables: Total available resource Water 15,000 m3 Fertilizer 5,000 kg Labor 125 day laborers Requirements per cultivated hectare Corn Soybeans Wheat Water 15 25 20 Fertilizer 5 8 7 Labor** 1/8 1/5 1/4 *The data in fraction means that with one day laborer it will be possible to care for 8, 5 and 4 hectares respectively. * Sales of crops 1 and 3, according to information from the Department of Agriculture, are guaranteed and exceed the capacity of the cooperative. However, soybeans must be limited to a maximum of 150 hectares. On the other hand, the profits for each hectare of crop obtained are estimated at: $7,500 for corn, $8,500 for soybeans and $8,000 for wheat. The objectives are to determine: • How many hectares of each crop must be allocated so that the profit is maximum. R= • The estimated profits for the ejidal cooperative in the next growing season. R=
A stunt man jumps horizontally from a building to the roof of a garage that is 2 meters lower. How fast does he need to be to land on the roof of the said garage that is 3 meters away from the building?
Next%C3%B3n%2C+we+are+given+a+series+of+Tri%C3%A1angles+Right%C3%A1angles+%3Cbr%2F%3Ey+in+each+one+of+them+ are+known+2%28two%29+measurements+of+sides.+%3Cbr%2F%3Elet's+determine+all+trigonom%C3%A9tric+ratios.
(X+2)(x+3)=4x+18
Let f and g be defined in R and suppose that there exists M > 0 such that |f(x) − f(p)| ≤ M|g(x) − g(p)|, for all x. Prove that if g is continuous in p, then f will also be continuous in p.
Which statement best describes the key changes in perspectives on inclusion? An inclusive program must consider the unique experiences of every child and family as well as the child's strengths and needs. There is a shift in thinking about individual programs as "inclusive programs" to thinking about inclusion as something that reflects the cultural influence of the family. There is a greater emphasis on barriers to full participation and the acknowledgement that all children are unique and must be fully and meaningfully engaged in a program. In an inclusive program all participants are accepted by their peers and other members of the community.
In a 24 hours period, the average number of boats arriving at a port is 10. Assuming that boats arrive at a random rate that is the same for all subintervals of equal length (i.e. the probability of a boat arriving during a 1 hour period the same for every 1 hour period no matter what). Calculate the probability that more than 1 boat will arrive during a 1 hour period. (P(X>1) ) Give your answers to 4 decimal places and in a range between 0 and 1
Pablo has a balance of $440,000 and 2/5 of the money is used to pay bills. How much money do you have left after paying the bills?
solve R the following equation 4 x squared - 35 - 9 over x squared is equal to 0
13/25+7/16