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erma4kov [3.2K]
3 years ago
9

Which of the following graphs shows a negative linear relationship with a correlation coefficient

Mathematics
1 answer:
Aloiza [94]3 years ago
8 0

Answer : Graph D

Question says negative linear relationship. It means the slope is negative.

Option A and C have positive slope because the dots on graph goes up.

So we ignore A and C graph

B and D graphs have negative slope.

Given Correlation coefficient r is close to -0.5

In Graph B the dots are close to one another . It means the correlation coefficient r is close to - 1

Graph D shows a negative linear relationship with a correlation coefficient r close to =-0.5

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From the central limit theorem, since the number of samples is large enough (up to 30), the mean of the the mean of the average number of moths in 30 traps is 0.6.



Part B:

The standard deviation is given by the population deviation divided by the square root of the sample size.

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The probability that an approximately normally distributed data with a mean, μ, and the standard deviation, σ, with a sample size of n is greater than a number, x, given by

P(X\ \textgreater \ x)=1-P(X\ \textless \ x) \\  \\ =1-P\left(z\ \textless \  \frac{x-\mu}{\sigma/\sqrt{n}} \right)

Thus, given that the mean is 0.6 and the standard deviation is 0.4, the probability that <span>the average number of moths in 30 traps is greater than 0.7</span> given by:

P(X\ \textgreater \ 0.7)=1-P(X\ \textless \ 0.7) \\ \\ =1-P\left(z\ \textless \ \frac{0.7-0.6}{0.073} \right)=1-P(z\ \textless \ 1.369) \\  \\ =1-0.91455=\bold{0.0855}
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Keywords: Equation of line, slope

Learn more about equation of line at:

  • brainly.com/question/6569012
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