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sleet_krkn [62]
3 years ago
12

The ages of dogs at an animal shelter are normally distributed with a mean of 3.9 years and a standard deviation of 1.2 years.

Mathematics
1 answer:
Aleks [24]3 years ago
3 0

Answer:

<u>The correct answer is A.  1.86 years</u>

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Mean of the dogs at an animal shelter = 3.9 years

Standard deviation = 1.2 years

2. What is the age of a dog at the shelter with a z-score of −1.7 ?

Let's recall that z-score in a normal distribution, positive or negative, is the number of times of the standard deviation a certain element is from the mean. If the element is below the mean, then the z-score is negative and if it's above the mean, then the z-score is positive.

Therefore, a z-score of - 1.7 for the ages of dogs is:

-1.7 * 1.2 = -2.04

Now, we calculate the value using the mean, this way:

3.9 + -2.04 = 3.9 - 2.04 = 1.86

<u>The correct answer is A.  1.86 years</u>

Note: Same answer to question 14270011, answered by me today.

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The first step in any problem is to look at what you are given. When solving systems of linear equations, it is often helpful to eliminate one or more of the variables by adding or subtracting a multiple of one equation with a multiple of another. It is convenient when at least one of the multipliers is 1.

Here, we can cancel the y-terms in the 2nd and 3rd equations simply by adding them together. This gives

... (5x +y -4z) +(-3x -y +5z) = (41) +(-45)

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Likewise, we can add 3 times the second equation to the first to cancel y in that sum.

... 3(5x +y -4z) +(2x -3y +z) = 3(41) + (-1)

...15x +3y -12z +2x -3y +z = 123 -1

...17x -11z = 122 . . . . simplified

Now that we have 2 equations in x and z, we can go through the same process. We observe that the coefficient of z is +1 in the first equation and -11 in the second. The means we can cancel the z terms by adding 11 times the first equation to the second:

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...22x +17x = 78 . . . . . . simplify a little bit

... x = 78/39 = 2 . . . . . . divide by 39

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... y = 41 -5x +4z = 41-5(2) +4(-8) = 41 -42 = -1

The solution is (x, y, z) = (2, -1, -8).

_____

The method of elimination used here will vary with the system of equations. If you want to employ a consistent method, you can use Cramer's Rule, Gaussian elimination, or matrix methods. Since you apparently don't mind help from technology, learning to do this on your graphing calculator can also be a good idea.

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