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Triss [41]
3 years ago
7

A researcher is interested in the lengths of brook trout, which are known to be approximately Normally distributed with mean 80

centimeters and standard deviation 5 centimeters. To help preserve brook trout populations, some regulatory standards need to be set for limiting the size of fish that can be caught. What is the probability of catching a brook trout less than 72 centimeters in length
Mathematics
1 answer:
aliya0001 [1]3 years ago
6 0

Answer:

P(X

And we can find this probability with the normal standard distirbution or excel and we got:

P(z

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the lenghts of a population, and for this case we know the distribution for X is given by:

X \sim N(80,5)  

Where \mu=80 and \sigma=5

We are interested on this probability

P(X

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X

And we can find this probability with the normal standard distirbution or excel and we got:

P(z

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Answer:

x = -2

Step-by-step explanation:

Solve for x:

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5/2×2/5 = (5×2)/(2×5):

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(5×2 (3 x - 4))/(2×5) = (2×5)/(2×5)×(3 x - 4) = 3 x - 4:

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Add 4 to both sides:

3 x + (4 - 4) = 4 - 10

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Divide both sides of 3 x = -6 by 3:

(3 x)/3 = (-6)/3

3/3 = 1:

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The gcd of -6 and 3 is 3, so (-6)/3 = (3 (-2))/(3×1) = 3/3×-2 = -2:

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Step-by-step explanation:

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