(a) The null and alternative hypothesis using proper notation is
H(0) :p ≤ 0.5
H(1) : p > 0.5
(b) The estimate of the true proportion of all orders that are delivered early is 0.6.
A delivery company samples 500 orders.
Out of 500 records, 300 of them were delivered early.
(a) To determine if the true proportion of orders that were delivered early occurs most of the time or not, i.e., whether the true proportion of orders that were delivered early is more than 0.5, we will perform a one proportion z-test.
Let p stand for the actual ratio. Our theory is stated as follows:
H(0) :p ≤ 0.5
H(1) : p > 0.5
We specifically want to determine whether the true proportion is greater than 0.5, hence this is a right-tailed test.
(b) The sample proportion's estimated value is provided as
P = Number of people who wake up early/Total Number of people
P = 300/500
P = 0.6
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What are the original points for the parent function
of f(x) = -2|1/4(x-1)| +3?
The original points for the parent function of f(x) = -2|1/4(x-1)| +3 is (0, 0)
How to determine the original pointFrom the question, we have the following parameters that can be used in our computation:
f(x) = -2|1/4(x-1)| + 3
The above function is an absoluute value function
The parent function of an absolute value function is represented as
y = |x|
When x = 0. we haeve
y = 0
This means that (0, 0) is the point on the parent function
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Give three examples of a power of 10. Explain why one of your examples is a power of 10
Answer:
100
1,000
10,000
Step-by-step explanation:
10 times 10 is 100.
10 times 10 times 10 is 1,000
10 times 10 times 10 times 10 is 10,000.
x^2-sin(x)-0.5 Use Bisection or Fixed Point Iteration to solve for the root of the equation (Tolerance should be < 0.001, you can choose your desired starting value) Please show detailed solution
change the function f(x) and interval a=1/3 , b=1 in above code (remaining same code) in the iteration
clear all;
s=1200;
h=20;
f(x)= x-2^(-x) ;
a=1/3;
b=1;
format long
eps_ abs = 0.000005;
eps_ step = 0.000005;
n=0;
while ((b - a)/2 >= eps_ step || ( abs( f(a) ) >= eps_ abs && abs( f(b) ) >= eps_ abs )&& n~=100 )
n=n+1;
c = (a + b)/2;
if ( f(c) == 0 )
break;
else if ( f(a)*f(c) < 0 )
b = c;
else
a = c;
end
err=abs( (b-a)/2);
end
n
c
err
out put
n = iteration
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Note:
When solving for k, round to four
decimal places.
A country's population in 1995 was 23 million.
In 2001 it was 25 million. Estimate
the population in 2013 using the exponential
growth formula. Round your answer to the
nearest million.
P=Aekt
Enter the correct answer
A country's population in 1995 was 23 million. In 2001 it was 25 million, the population in 2013 using the exponential growth formula in 2013 will be around 30 million.
For this problem, we have the final population P, the starting population A, and the time passed t.
We still need to determine the value of the growth factor k.
This can be done using the information for the years 1995 and 2001.
In this case, A will be 23 million (the population in 1995), P will be 25 million (the population in 2001), and t will be 6 years (the number of years between 1995 and2001):
[tex]P=Ae^{kt}[/tex]
[tex]25=23e^{k 6}[/tex]
[tex]e^{6k} =\frac{25}{23}[/tex]
[tex]k = \frac{ln(25) - ln(23)}{6}[/tex]
k = 0.013897
Now, let's use this information to determine P in 2013.
A will still be 23 million, but t will be 18 years.
[tex]P= 23e^{0.013897*18} \\P= 23e^{0.250146} \\P=23 * 1.28421\\P=29.5368\\[/tex]
Therefore, the population in 2013 using the exponential growth formula in 2013 will be around 30 million.
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Triangle XYZ with vertices X(5, 4), Y(3, -1) and Z(0, 2) is translated so that X' is at (3, 1). Choose the coordinates of Y'
and Z'.
a. Y'(5, 2) and Z'(2, 5)
b. Y'(0, -3) and Z'(-3,0)
c.
d.
OA
OB
OC
OD
Y'(1,-4) and Z'(-2, -1)
Y'(11, 4) and Z'(8, 6)
Please select the best answer from the choices provided
The right solution is option C, which is Y'(1, -4) and Z'(-2, -1).
What is triangle?A triangle is a three-sided polygon that is sometimes (but not always) referred to as the trigon. Every triangle has three sides and three angles, which may or may not be the same. A triangle is a three-sided polygon with three edges and three vertices in geometry. The total of a triangle's interior angles equals 180 degrees, which is its most essential feature. This is known as the angle sum property of a triangle.
Here,
To translate a triangle, you need to add the same value to each x-coordinate and each y-coordinate. In this case, the translation moves each point 2 units to the left and 3 units down, so the new coordinates of Y and Z would be:
Y'(3 - 2, -1 - 3) = Y'(1, -4)
Z'(0 - 2, 2 - 3) = Z'(-2, -1)
The correct answer is Y'(1, -4) and Z'(-2, -1) that is option C.
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A radius of a circle has endpoints (-4,3) and (1,-2). What is the equation that
defines the circle if its center is at the second quadrant?
By applying standard equation of a circle concept, it can be concluded that the equation that defines the circle is (x + 4)² + (y - 3)² = 50.
Circle is a collection of points on a plane line that are all the same distance (the radius) from a given point (the center).
Standard equation of a circle can be written as:
(x - h)² + (y - k)² = r² , where:
(h,k) = center of the circle
r = radius
We know that the radius of the circle has endpoints (-4,3) and (1,-2), which means that one of these points is the center of the circle.
Since we know that its center is in the second quadrant, we can conclude that (-4,3) is the center.
Now we can substitute these values into the equation:
(x - h)² + (y - k)² = r²
(1 - (-4))² + (-2 - 3)² = r²
5² + (-5)² = r²
25 + 25 = r²
50 = r²
As we know the r, now we can have the standard equation of the circle:
(x - h)² + (y - k)² = r²
(x - (-4))² + (y - 3)² = 50
(x + 4)² + (y - 3)² = 50
Thus the equation that defines the circle is (x + 4)² + (y - 3)² = 50.
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In ΔFGH, f= 67 inches, m∠G=66° and m∠H=30°. Find the length of g to the nearest inch
Answer:
62
Step-by-step explanation:
Use the Law of Sines: sinA/a = sinB/b = sinC/c, where A, B, and C are the angles and a, b, and c are the sidelengths opposite of their corresponding angles.
If angle G = 66 and angle H = 30, then angle F = 180-66-30 = 84 degrees.
Therefore sin84/67 = sin66/g.
Multiple both sides by g and divde by sin84/7 to get
g = sin66/(sin84/67) = 61.5... which is about 62 inches.
Christy went jogging on a saturday. The table shows how far she had jogged after various times. distance (miles) 4.5, 7.5, 10.5. Time (hours) 0.75, 1.25, 1.75. Did christy run the same pace from when she began until she reached 7.5 miles?
Yes, Because the paces are 6 miles/hour.
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
We have to given that;
Christy went jogging on a saturday. The table shows how far she had jogged after various times.
Now, Based on the given table;
⇒ 4.5 ÷ 0.75
⇒ 6
⇒ 7.5 ÷ 1.25
⇒ 6
Thus, She ran the same pace at 6 miles/hour.
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Albert combined some grated cheese. He mixed together ⅔ cup cheddar, ⅚ cup mozzarella, and ¾ cup parmesan. How many cups of cheese does Albert have in his mixture altogether?
Albert have 9/4 cups of cheese in the mixture.
What is fraction?Fractions in Math, represent a numerical value that expresses a part of a whole. The whole can be any number, a specific value, or a thing.
Given,
Amount of cheddar = 2/3 cup
Amount of mozzarella = 5/6 cup
Amount of parmesan = 3/4 cup
Total cups of cheese
= cheddar + mozzarella + parmesan
= 2/3 + 5/6 + 3/4
= 8 + 10 + 9 /12
= 27/12
= 9/4
There is 9/4 cups of cheese in the mixture.
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What is the measure of∠ b ?
The measure of angle B from the given hexagon ABCDEF is 108°.
What is hexagon?In geometry, a hexagon or sexagon is a six-sided polygon or 6-gon creating the outline of a cube. The total of the internal angles of any simple hexagon is 720°.
In the given hexagon ABCDEF, ∠A=170°, ∠C=133°, ∠D=102°, ∠E=117° and ∠F=90°.
Here, ∠A+∠B+∠C+∠D+∠E+∠F=720°
170°+∠B+133°+102°+117°+90°=720°
612°+∠B=720°
∠B=720°-612°
∠B=108°
Therefore, the measure of angle B from the given hexagon ABCDEF is 108°.
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In two or more complete sentences, identify the parent function, and describe the transformations that were applied to obtain the graph, f(x) - 2x + 6-2
The transformations that were applied to obtain the graph will be Multiply by 4 and Shift the function 3 units downwards and 6 units left.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The function is given below.
f(x) = √(2x + 6) - 3
The parent function is given as,
f(x) = √x
Multiply by 4, then we have
f(x) = 4√x
f(x) = √2x
Shift the function 3 units downwards and 6 units left.
f(x) = √(2x + 6) - 3
The transformations that were applied to obtain the graph will be Multiply by 4 and Shift the function 3 units downwards and 6 units left.
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The complete question is given below.
What is the value of x in this system of equations? Express the answer as a decimal rounded to the nearest tenth.
Negative 5 x minus 12 y = negative 8. 5 x + 2 y = 48
The value of x in the system of equations is: x = 11.2.
How to Solve a System of Equations?The value of x can be found by solving the system of equations.
One method is to substitute the value of x from one equation into the other equation, solve for y, then use the value of y to find x.
Starting with the second equation: 5x + 2y = 48
Solve for y: y = (48 - 5x) / 2
Now substitute this expression for y into the first equation:
-5x - 12((48 - 5x) / 2) = -8
-5x - 6(48 - 5x) = -8
-5x - 288 + 30x = -8
25x - 288 = - 8
25x = -8 + 288
25x = 280
x = 280/25
x = 11.2
Finally, solving for x:
x = 11.2
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Answer:
-11.8
Step-by-step explanation:
To find the value of x in this system of equations, we can use substitution or elimination method.
Using substitution:
Solve for one of the variables in one of the equations and substitute it into the other equation. We can start by solving for y in the second equation:
[tex]\sf:\implies{5x + 2y = 48}[/tex]
[tex]\sf:\implies{2y = -5x + 48}[/tex]
[tex]\sf:\implies{y = (-5/2)x + 24}[/tex]
Now, substitute this expression for y into the first equation:
[tex]\sf:\implies{-5x - 12y = -8}[/tex]
[tex]\sf:\implies{-5x - 12((-5/2)x + 24) = -8}[/tex]
[tex]\sf:\implies{-5x + 30x + 288 = -8}[/tex]
[tex]\sf:\implies{25x = -296}[/tex]
[tex]\sf:\implies{x = -11.84}[/tex]
The value of x rounded to the nearest tenth is -11.8.
pls hellp 30 points 3(2a+5)(4+1) select all true statements in 2a, 2 is a coefficient
The correct statements regarding the algebraic expression are given as follows:
In 2a, 2 is a coefficient.4 and 1 are like terms.How to interpret the algebraic expressions?In 2a, 2 is a coefficient, as it multiplies the letter that composes the expression.
(2a + 5) is a sum of two terms.
In (2a + 5), 5 is the constant.
4 and 1 are like terms, as they have the same variable part of x^0 = 1.
2a + 5 is a factor, not just 2a.
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Find the value of x.
A: 80 degrees
B: 40 degrees
C: 60 degrees
D: 140 degrees
Show work.
The community health clinic you volunteer for aims to develop a strategy allowing the most vulnerable members of the community to have first access to the Flu vaccine. The clinic has collected data finding that the total number of people in their service area is 50,000, 27% of the community is over the age of 65 and immunocompromised, and 11% of the community under 65 is immunocompromised. While the clinic wishes to market to all members of the community, immunocompromised people over 65 are their current priority. 1. Express the total number of people to which the health clinic must do outreach
There are 71515 total number of people to which the health clinic must do outreach.
The term percentage refers to a denominator of 100. Here are some actions we can take to find the people the company needs to get in touch with:
About 27% of elderly persons have weakened immune systems.
So here we do that the total number of people multiplied by the 27 percentage of people,
27/100 x 50,000 people is 13500 people.
And 50,000 - 13500 = 36,500
Now;
11% of persons in this category are under 65 and have immune system impairments;
Eleventh part of 100 which is 36,500 results in 4015 people.
The firm should be able to contact a total of 17515 people that is,
(13500 + 4015).
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Please help!
Question:
The space Needle is 605 feet tall. A model of the building is 15 inches tall. What is the ratio of the height of the model to the height of the actual Space Needle?
Answer Choices:
A- 12:484
B- 1:484
C- 484:12
D- 484:1
Answer:
The ratio they are asking for is Model height to actual height. Rewritten that is:
Model Height: Actual Height
So the ratio after plugging in numbers is;
15:605
Ratios can be simplified by dividing both sides.
Both numbers are divisible by 5.
Therefore the ratio is;
3:121
(this is the simplest form of the ratio because 121
is not evenly divisible by 3)
Now, that is not an answer you can select,
however you can also multiply both sides by theKalius Call be simple by uviuiny po siues. Both numbers are divisible by 5.
Therefore the ratio is;
3:121
(this is the simplest form of the ratio because 121 is not evenly divisible by 3)
Now, that is not an answer you can select, however you can also multiply both sides by the same number. Take 4 for example (I'm choosing 4 because 3*4=12)
12:484
The time to complete a constructions project is normally distributed with a mean of 60 weeks and a standard deviation of 4 weeks. a. What is the probability the project will be
If time to complete a constructions project is normally distributed , then the probability the project will be finished in 62 weeks or less is 0.6915 or 69.15% .
The required probability can be calculated using the Z-score.
The Z-score is defined as a measure of how many standard deviations a value is from mean.
The mean = 60 and standard deviation = 4 of the normal distribution, the Z-score can be calculated as follows:
⇒ Z = (x - mean) / standard deviation = (62 - 60) / 4 = 0.5
Using a standard normal table, the p value for z = 0.5 is approximately 0.6915.
Therefore, the probability that the project will be finished in 62 weeks or less is approximately 0.6915.
The given question is incomplete , the complete question is
The time to complete a constructions project is normally distributed with a mean of 60 weeks and a standard deviation of 4 weeks. What is the probability the project will be finished in 62 weeks or less ?
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(bonus) prove ∃x(a(x) ∧ ¬b(x)) ∀x(a(x) −→ c(x)) ∴ ∃x(c(x) ∧ ¬b(x))
(bonus) prove the equation ∃x(a(x) ∧ ¬b(x)) ∀x(a(x) −→ c(x)) ∴ ∃x(c(x) ∧ ¬b(x))
Proof by Contradiction:Assume that ∃x(c(x) ∧ ¬b(x)) is false.
Therefore, we can conclude that ∀x(c(x) ∧ ¬b(x)) is true.
This implies that for all x, either c(x) is false or b(x) is true.
But, from our assumption, we know that ∃x(a(x) ∧ ¬b(x)) is true.
Therefore, there must exist an x such that a(x) is true and b(x) is false.
Since a(x) is true, we can conclude from ∀x(a(x) −→ c(x)) that c(x) must also be true.
But this is a contradiction since we previously assumed that the equation ∀x(c(x) ∧ ¬b(x)) is true, which implies that c(x) must be false.
Therefore, our initial assumption must be false, and we can conclude that ∃x(c(x) ∧ ¬
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A roast turkey is taken from an oven when its temperature has reached 185°F and is placed on a table in a room where the temperature is 75°F. (Round your answers to the nearest whole number.)(a) If the temperature of the turkey is 150°F after half an hour, what is the temperature after 55 minutes?T(55) = 1 °F(b) When will the turkey have cooled to 105°?t = 2 min
Using unitary method, turkey's temperature after 55 minutes is 120.815° Also, it will take approximately 68 minutes for the turkey to cool down to 105°.
Now, According to the question:
What is unitary method?
The formula of the unitary method is to find the value of a single unit and then multiply the value of a single unit to the number of units to get the necessary value.
Reduction in temperature after 30 minutes = 185° - 150° = 35°
Reduction in temperature after 1 minute = 35/30 = 1.167°
Reduction in temperature after 55 minutes = 55 × 1.167 = 64.185°
Temperature after 50 minutes = 185° - 64.185° = 120.815°
Decrease in temperature when the turkey has cooled down to 105° = 185° - 105° = 80°
Time taken by the turkey to cool down 80° = 80/1.167 = 68.55 minutes.
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Mrs mills buys 4 packs of treats for her cats, fluff and tigger. She gives fluff 1 6 of a pack each day. She gives tigger 1 5 of a pack each day. For how many complete days will the 4 packs of treats last?.
The number of complete days that 4 packs of treats will last, we need to determine the total number of packs each day and divide it into the total number of packs Mrs. Mills has bought.
Let's call the number of days the treats will last "d".
Then, the number of packs Fluff eats in "d" days is d * (1/6 of a pack per day) = (1/6)d.
Similarly, the number of packs Tigger eats in "d" days is d * (1/5 of a pack per day) = (1/5)d.
The total number of packs they eat in "d" days is (1/6)d + (1/5)d = (11/30)d.
Since Mrs. Mills has bought 4 packs, we have 4 = (11/30)d.
Finally, solving for "d", we have d = (30/11) * 4 = 120/11 days.
Since "d" must be a whole number, we round down to get 10 complete days that the 4 packs of treats will last.
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The total number of packs they eat in "d" days is (1/6)d + (1/5)d = (11/30)d.
Since Mrs. Mills has bought 4 packs, we have 4 = (11/30)d.
Finally, solving for "d", we have d = (30/11) * 4 = 120/11 days.
Use the linear correlation coefficient given to determine the coefficient of determination, R2.
r = -0.28
the linear correlation coefficient given to determine the coefficient of determination, R² = 0.0784.
What is linear correlation coefficient?The strength of the linear link between two variables, x and y, is measured by the linear correlation coefficient, which is a number derived from the supplied data. The linear link between variables x and y is indicated by the sign of the linear correlation coefficient.
In order to examine the relationship between two quantitative variables, correlation and linear regression are the two methods that are most frequently utilised. As opposed to regression, which expresses the connection as an equation, correlation measures the strength of the linear relationship between two variables.
The linear correlation coefficient is given as:
r = -0.28
Calculation of coefficient of determination:
R² = r²
R² = (-0.28)²
or, R² = 0.0784
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Liam earned $30 for mowing his neighbor's lawn 6 times. If Liam charged the same rate and earned $35, how many times did he mow his neighbor's lawn? Use a unit
Answer:
7
Step-by-step explanation:
30÷6=5
$5 per mow
35÷5=7
7
Write 5.2288888… repeating as a fraction
5.228 written as fraction is 1307/250
What does rounded to the nearest degree mean?
Answer: Rounding degrees is similar as to answering decimals. How ever, there is 60 minutes in a degree. If the numbers is less than 30, you round down to the nearest degree, and if its 30 or up, you round up to the nearest degrees.
What is the total amount of deposits shown?
The total amount of deposits shown is, $713.29.
What is Addition?The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
We have to given that;
The graph of a passbook is shown in figure.
Now, By figure,
The total amount of deposits is,
⇒ $310.58 + $402.71
⇒ $713.29.
Thus, The total amount of deposits shown is, $713.29.
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How many ways can 6 people be lined up to get on the bus.
If certain 2 people refuse to follow each other how many ways are possible?
6 people be lined up to get on the bus in 480 ways
What is permutation and combination?A permutation is an act of arranging objects or numbers in order. Combinations are the way of selecting objects or numbers from a group of objects or collections, in such a way that the order of the objects does not matter.
For this, the easiest way is doing the complement. Calculate how many the 2 people are together and subtract from the total, so:
We can consider 2 people a block that will permutation, so, instead of 6 people we have 5 [a block of 2 people and 4 more):
5! = 5.4.3.2.1 = 120
The 2 people from the block will permutation as well:
2! = 2.1 = 2
Total: 5!.2! = 120.2 = 240.
For the case they are not following each other:
720 - 240 = 480
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A cubic function of the form y = ax³ + bx² + cx+dyields the following table:
X Y
0 0
1 -2
2-26
3-54
The coefficient a =
and d=
b=
,C=
Answer:
The coefficient a = -1, b = 4, c = -1 and d = 0. To solve for the coefficients, substitute the values from the table into the equation y = ax³ + bx² + cx+d. When x = 0 and y = 0, we get 0 = -1a + 4b + c + d, so d = 0. When x = 1 and y = -2, we get -2 = -1a + 4b + c, so c = -1. When x = 2 and y = -26, we get -26 = -1a + 4b, so b = 4. Finally, when x = 3 and y = -54, we get -54 = -1a, so a = -1.
Step-by-step explanation:
It’s a given transformations apply to figure with image be congruent to the pre-image?
Place an x in the table to show whether each information result in an image that is congruent or not congruent to the pre-image
The second and third image will be congruent to the pre-image. The solution has been obtained by applying the concept of transformations.
What is transformation?
Any action that moves a polygon or other two-dimensional object on a plane or coordinate system is referred to as a transformation.
Pre-image or "inverse image" refers to the two-dimensional shape that exists before any change. The transformed shape is represented by the image.
1. This is not congruent because both the coordinates are dilated and after dilation the size of the image is not the same as of original figure.
2. This is congruent because there is only translation which means it is same as the original figure but the position is different.
3. This is congruent because only translation has taken place which means it is same as the original figure but the position is different.
4. This is not congruent because one coordinate i.e. x has been dilated and after dilation the size of the image is not the same as of original figure.
Hence, second and third are congruent to the pre-image.
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Abigail i 15 year old and Cynthia i 27 year old. How many year ago wa Cynthia twice wa old a Abigail?
Cynthia was twice as old as Abigail 3 years ago.
Let x be the number of years ago when Cynthia was twice as old as Abigail
If Abigail is 15 years old and Cynthia is 27 years old today, then "x" years ago, the algebraic expression that represents their age was"15 - x" and "27 - x", respectively.
If "x" years ago, Cynthia was twice as old as Abigail, then the equation will be
27 - x = 2(15 - x)
Simplify the equation and solve for the value of x.
27 - x = 30 - 2x
x = 3
Therefore, 3 years ago, Cynthia was twice as old as Abigail.
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for normally distributed scores, what percentage of scores (or cases) would fall: between the mean and z = -1
Approximately 84% of scores fall between the mean and z = -1 for normally distributed scores.
In a normal distribution, approximately 68% of the scores fall within one standard deviation of the mean, both above and below. Z-scores are used to describe the location of a score relative to the mean, in terms of standard deviations.
A z-score of -1 indicates that a score is 1 standard deviation below the mean. So, if we consider all the scores that are 1 standard deviation below the mean or closer to the mean, then we would have a total of 68% of the scores, which includes the mean.
And, if we consider only the scores that are between the mean and 1 standard deviation below the mean, then we would have 84% of the scores. Hence, approximately 84% of scores would fall between the mean and z = -1 for normally distributed scores.
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