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Captain Richards has two separate lines of lobster traps in Narraguagus Bay. The East Bay trap
yields a mean of 12 pounds of lobsters per day with a standard deviation of 7 pounds. The West
Bay trap yields a mean of 10 pounds of lobsters a day with a standard deviation of 4.5 pounds.
The weight of lobsters caught in each trap is independent of the other. Which of the following
are the mean and approximate standard deviation of the total weight of lobsters Captain Richards
traps in a day?
(A) Mean = 22 pounds; Standard deviation = 5.75 pound
(B) Mean = 22 pounds; Standard deviation = 8.32 pounds
(C) Mean = 22 pounds; Standard deviation = 11.50 pounds
(D) Mean = 11 pounds; Standard deviation = 11.50 pounds
(E) Mean = 11 pounds; Standard deviation = 8.32 pounds

Respuesta :

Using addition of variables, it is found that the mean and approximate standard deviation of the total weight of lobsters Captain Richards traps in a day are given by:

(B) Mean = 22 pounds; Standard deviation = 8.32 pounds.

What is the mean and the standard deviation of the sum of two independent variables?

When two independent variables are added, we have that:

  • The mean is the sum of the means.
  • The standard deviation is the square root of the sum of the variances.

In this problem:

  • The means are of 12 pounds and of 10 pounds.
  • The variances, in pounds squared, are of [tex]7^2[/tex] and [tex]4.5^2[/tex], respectively.

Then:

[tex]M = 12 + 10 = 22[/tex]

[tex]S = \sqrt{7^2 + 4.5^2} = 8.32[/tex]

Hence option B is correct.

You can learn more about addition of variables at https://brainly.com/question/25769446

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