On a commercial fishing boat, the two fish being caught are Mackerel and Snapper. Typically, there is around 180 ± 30 kg of Mackerel per net brought up and 460± 140 kg of Snapper. If the amount of each fish caught per net is positively correlated, with a correlation of Corr(S,M) = 0.4 [S representing Snapper and M representing Mackerel]. (a) Calculate the total amount of fish caught per net, in terms of mean and standard deviation
On a commercial fishing boat, the two fish being caught are Mackerel and Snapper. Typically, there is around 180 ± 30 kg of Mackerel per net brought up and 460± 140 kg of Snapper. If the amount of each fish caught per net is positively correlated, with a correlation of Corr(S,M) = 0.4 [S representing Snapper and M representing Mackerel]. (a) Calculate the total amount of fish caught per net, in terms of mean and standard deviation
On a commercial fishing boat, the two fish being caught are Mackerel and Snapper. Typically, there is around 180 ± 30 kg of Mackerel per net brought up and 460± 140 kg of Snapper. If the amount of each fish caught per net is positively correlated, with a correlation of Corr(S,M) = 0.4 [S representing Snapper and M representing Mackerel]. (a) Calculate the total amount of fish caught per net, in terms of mean and standard deviation
(a) Calculate the total amount of fish caught per net, in terms of mean and standard deviation
Transcribed Image Text:Example Problem 4
On a commercial fishing boat, the two fish being caught are Mackerel and Snapper. Typically, there is
around 180 ± 30 kg of Mackerel per net brought up and 460 ± 140 kg of Snapper. If the amount of
each fish caught per net is positively correlated, with a correlation of Corr(S,M) = 0.4 [S representing
Snapper and M representing Mackerel].
(a) Calculate the total amount of fish caught per net, in terms of mean and standard deviation
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
Expert Solution
Step 1: Overview
Given that:
Mean of Mackerel, E(M) = 180 kg and its standard deviation, s(M) = 30 kg
Mean of Snapper, E(S) = 460 kg and its standard deviation, s(S) = 140 kg
![Example Problem 4
On a commercial fishing boat, the two fish being caught are Mackerel and Snapper. Typically, there is
around 180 ± 30 kg of Mackerel per net brought up and 460 ± 140 kg of Snapper. If the amount of
each fish caught per net is positively correlated, with a correlation of Corr(S,M) = 0.4 [S representing
Snapper and M representing Mackerel].
(a) Calculate the total amount of fish caught per net, in terms of mean and standard deviation](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7b298802-1d5a-44de-8cc9-46b18708a6bd%2F77d4264c-5e4e-44fd-b9b1-3f81b080d509%2Fd2vsku_processed.png&w=3840&q=75)
