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polet [3.4K]
3 years ago
11

Find the Z scores that separate the middle 27% of the distribution from the area in the tails of the standard normal distributio

n
Mathematics
1 answer:
vekshin13 years ago
5 0
Z- score is a statistical tool that is used to determine the probability of finding a number or a value under a normal distribution plot. A normal distribution assumes that the mean is equal to zero and that the standard deviation is equal to 1. Using the z-score table, we can find the probability either on the right side or the left side. Using the table hence, we find the probability to the left of the value. The probability that is equivalent to the unknown z should be equal to 0.5 + (0.27/2) = 0.635. 0.5 comes from the assumption that the area under the curve on each side is 50% of the total. The equivalent z score is equal to z = 0.345. 
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A line passes through the points (-7, 2) and (1, 6).A second line passes through the points (-3, -5) and (2, 5).Will these two l
BlackZzzverrR [31]

Answer:

Yes, the lines intersect at (3,7). The solution is (3,7).

Explanation:

Step 1. The first line passes through the points:

(-7,2) and (1,6)

and the second line passes through the points:

(-3,-5) and (2,5)

Required: State if the lines intersect, and if so, find the solution.

Step 2. We need to find the slope of the lines.

Let m1 be the slope of the first line and m2 be the slope of the second line.

The formula to find a slope when given two points (x1,y1) and (x2,y2) is:

m=\frac{y_2-y_1}{x_2-x_1}

Using our two points for each line, their slopes are:

\begin{gathered} m_1=\frac{6-2}{1-(-7)} \\  \\ m_2=\frac{5-(-5)}{2-(-3)} \end{gathered}

The results are:

\begin{gathered} m_1=\frac{6-2}{1-(-7)}=\frac{4}{1+7}=\frac{4}{8}=\frac{1}{2} \\  \\  \end{gathered}m_2=\frac{5+5}{2+3}=\frac{10}{5}=2

The slopes are not equal, this means that the lines are NOT parallel, and they will intersect at some point.

Step 3. To find the intersection point (the solution), we need to find the equation for the two lines.

Using the slope-point equation:

y=m(x-x_1)+y_1

Where m is the slope, and (x1,y1) is a point on the line.

For the first line m=1/2, and (x1,y1) is (-7,2). The equation is:

y=\frac{1}{2}(x-(-7))+2

Solving the operations:

\begin{gathered} y=\frac{1}{2}(x+7)+2 \\ \downarrow\downarrow \\ y=\frac{1}{2}x+7/2+2 \\ \downarrow\downarrow \\ y=\frac{1}{2}x+5.5 \end{gathered}

Step 4. We do the same for the second line. The slope is 2. and the point (x1,y1) is (-3, -5). The equation is:

\begin{gathered} y=2(x-(-3))-5 \\ \downarrow\downarrow \\ y=2x+6-5 \\ \downarrow\downarrow \\ y=2x+1 \end{gathered}

Step 5. The two equations are:

\begin{gathered} y=\frac{1}{2}x+5.5 \\ y=2x+1 \end{gathered}

Now we need to solve for x and y.

Step 6. Equal the two equations to each other:

\frac{1}{2}x+5.5=2x+1

And solve for x:

\begin{gathered} \frac{1}{2}x+5.5=2x+1 \\ \downarrow\downarrow \\ 5.5-1=2x-\frac{1}{2}x \\ \downarrow\downarrow \\ 4.5=1.5x \\ \downarrow\downarrow \\ \frac{4.5}{1.5}=x \\ \downarrow\downarrow \\ \boxed{3=x} \end{gathered}

Step 7. Use the second equation:

y=2x+1

and substitute the value of x to find the value of y:

\begin{gathered} y=2(3)+1 \\ \downarrow\downarrow \\ y=6+1 \\ \downarrow\downarrow \\ \boxed{y=7} \end{gathered}

The solution is x=3 and y=7, in the form (x,y) the solution is (3,7).

Answer:

Yes, the lines intersect at (3,7). The solution is (3,7).

6 0
1 year ago
Brainliest will be given to the best answer !!
inna [77]

X difference between a and b is 7

y difference between a and b is 5

1:2 = 1/2 multiplying by 2 will be the whole thing or point c

2x7=14

2x5=10

(6+14,3+10)

Ans: (20,13)

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3 years ago
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