A sample has a mean of 500 and standard deviation of 100. Compute the z score for particular observations of 500 and 400 and interpret what these two z values tell us about the variability of the observations. Compute z score for the observation of 500. Interpret the results Compute z score for the observation 400 and explain the result.
Answers
In terms of variability, the z-scores help us understand how each observation deviates from the mean in terms of standard deviations. A z-score of 0 means the observation has no deviation, while a negative z-score suggests the observation is below the mean and indicates a lower value relative to the average.
We use the following formula to get the z-score:
z = (x - μ) / σ
where:
x is the observation,
μ is the mean, and
σ is the standard deviation.
Let's compute the z-scores for the observations of 500 and 400.
For the observation of 500:
z score = (500 - 500) / 100 = 0
The z-score of 0 indicates that the observation of 500 is exactly at the mean of the sample. It tells us that this observation has no deviation from the mean and falls directly on the average value.
For the observation of 400:
z score= (400 - 500) / 100 = -1
The z-score of -1 indicates that the observation of 400 is 1 standard deviation below the mean. It tells us that this observation is relatively low compared to the mean and is one standard deviation away from the average value.
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Related Questions
The temperatures (in degrees Fahrenheit) in Long Island recorded by the weather bureau over a week were 42, 49, 53, 55, 50, 47, and 52. Which measure should the weather bureau use to calculate how far apart the upper and lower quartiles of the week's daily temperatures were?
A
mode
B.
mean absolute deviation
C.
interquartile range
D.
mean
Answers
A plant is already 15.00 meters tall, and it will grow 9 centimeters every month. The plant's height, H (In meters), after x months is given by the following
function.
H(x) = 15.00 +0.09x
What is the plant's height after 30 months
Answers
Answer:
17.7 meters
Step-by-step explanation:
x = 30
15 + 0.09*30
0.09*30 = 2.7
2.7 + 15 = 17.7 meters
It costs $2.37 to paint one square foot of wall. You need to paint a wall that measures 864.5 square feet. It will cost to paint that wall. (Round your answer to the nearest hundredth)
a $204.88
b $2,048.87
c $2,048.86
d. $2,848.87
Answers
Answer:
B- hope this helps:)
Step-by-step explanation:
The total cost to paint 864.5 square feet of wall is $2,048.87.
It is given that the cost to paint one square foot of wall is $2.37.
We are asked to find the total cost to paint 864.5 square feet of wall.
What are the different place values in a given number with a decimal point?If we have a number that has a decimal point then we have two parts.
The whole number part and the fractional part.
After the decimal point, we will count the place value as tenths, hundredths, thousandths, and so on.
You can also see the given figure below.
We know that,
One square foot = $2.37.
Remember that Feet is the plural form of the foot.
We can write,
864.5 square feet = 864.5 x one square foot
Because in 864.5 square feet we have 864.5 one square foot.
And since one square foot cost $2.37.
864.5 square feet will cost 864.5 x 2.37 dollars.
Now,
864.5 x 2.37 = $2048.865.
Rounding to the nearest hundredth.
6 is in the hundredth place so we will round 86 to 87 since the number in the thousandth place is greater than 4.
Thus the total cost to paint a wall of 864.5 square feet is $2,048.87.
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The mean is ? = 137.0 and the standard deviation is ? = 5.3.
Find the probability that X is between 134.4 and 140.1.
0.4069
0.6242
0.8138
1.0311
Answers
The probability that X is between 134.4 and 140.1 is approximately 0.4076, which is closest to the option 0.4069.
To calculate this probability, we need to standardize the values using the standard normal distribution. First, we find the z-scores for the lower and upper bounds:
z1 = (134.4 - 137.0) / 5.3 ≈ -0.4906
z2 = (140.1 - 137.0) / 5.3 ≈ 0.5849
Next, we use a standard normal distribution table or a calculator to find the probabilities associated with these z-scores. The probability corresponding to z1 is P(Z < -0.4906) ≈ 0.3131, and the probability corresponding to z2 is P(Z < 0.5849) ≈ 0.7207.
To find the probability that X is between 134.4 and 140.1, we subtract the probability associated with the lower bound from the probability associated with the upper bound:
P(134.4 < X < 140.1) = P(Z < 0.5849) - P(Z < -0.4906) ≈ 0.7207 - 0.3131 = 0.4076.
As a result, the chance that X lies between 134.4 and 140.1 is roughly 0.4076, which is closest to the value of 0.4069 for the option.
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To compare the effectiveness of two treatments, researchers conducted a well-designed experiment using a randomized block design in which the subjects were blocked by age-group (under 40 40 years and 40 40 years or older). What must be true about the randomized block design of the experiment?
Answers
In the context of your experiment comparing the effectiveness of two treatments using a randomized block design, the following must be true:
1. The subjects are divided into two blocks based on their age: under 40 years and 40 years or older.
2. Randomization is used within each block to assign subjects to one of the two treatments. This ensures that each treatment group within a block has a random mix of subjects, reducing potential biases.
3. The purpose of blocking by age is to control for any confounding variables or potential effects that age might have on the treatment outcomes. By blocking, researchers can more accurately measure the differences between the two treatments.
4. The experiment is well-designed, which means it should minimize potential sources of error, include sufficient sample size, and ensure proper randomization and data collection.
5. To analyze the results, researchers will compare the treatment outcomes within each age block and then combine the results to get an overall measure of the effectiveness of the two treatments.
By using a randomized block design in this experiment, researchers can control for age-related factors and obtain a more accurate comparison of the treatment effectiveness.
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If y varies directly as x, and y=13 when x=12, find y when x=6
Answers
\(\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill\)
\(\stackrel{\textit{"y" varies directly with "x"}}{y = k(x)}\hspace{5em}\textit{we also know that} \begin{cases} y=13\\ x=12 \end{cases} \\\\\\ 13=k(12)\implies \cfrac{13}{12}=k\hspace{5em}\boxed{y=\cfrac{13}{12}x} \\\\\\ \textit{when x = 6, what's "y"?}\qquad y=\cfrac{13}{12}(6)\implies y=\cfrac{13}{2}\)
derive the complete response x(t) for the system below with the following initial conditions: x(0) = 1, x_ (0) = 1, input u(t) = 5t for t 0. sketch the response x(t). x 3x_ 2x = u(t)
Answers
The complete response x(t), with initial conditions and input, can derived using Laplace transform and inverse Laplace transform techniques.
How to find the complete response?To derive the complete response x(t), we first take the Laplace transform of the given differential equation, applying the initial conditions to obtain the transformed equation in the Laplace domain.
Next, we solve the transformed equation for the Laplace transform X(s) of x(t) using algebraic manipulations and inverse Laplace transforms
We consider the input u(t) = 5t, and take its Laplace transform U(s) to express it in the Laplace domain.
By substituting X(s) and U(s) into the transformed equation, we solve for X(s) to obtain the Laplace transform of the complete response.
Finally, we use inverse Laplace transform techniques to find the time-domain expression for x(t), the complete response of the system.
Sketching the response x(t) involves plotting the function x(t) with respect to time, considering the given initial conditions and input.
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The sum of two numbers is 15 The second number is 3 less than the first number.
Answers
Answer:
first number: 9
second number: 6
Step-by-step explanation:
15 = x + (x - 3)
2x = 15 - 3
2x = 12
x = 6
what is the square root of 16 to the nearest tenth
Answers
Answer:
4
Step-by-step explanation:
4 x 4 = 16
hope dis helps :)
Answer:
the square root of 16 is 4 the nearest tenth is 4
when estimating a population​ mean, are you more likely to be correct when you use a point estimate or an interval​ estimate? explain your reasoning.
Answers
When estimating a population mean, you are more likely to be correct when using an interval estimate rather than a point estimate. An interval estimate provides a range of values within which the true population mean is likely to fall, accounting for uncertainty. This range provides a higher level of confidence compared to a single point estimate.
When estimating a population mean, you are more likely to be correct when using an interval estimate rather than a point estimate. The reason is that an interval estimate provides a range of values within which the population mean is likely to fall, taking into account the inherent uncertainty in the estimation process.
A point estimate, on the other hand, provides a single value as an estimate of the population mean, without accounting for the variability or margin of error. While a point estimate may be close to the true population mean, there is no measure of confidence or precision associated with it.
An interval estimate, such as a confidence interval, incorporates both a point estimate and a margin of error, which quantifies the uncertainty in the estimate. By providing a range of values, the interval estimate acknowledges that the true population mean may fall within that range with a certain level of confidence.
Using an interval estimate allows for a more comprehensive understanding of the population mean and provides a measure of the reliability of the estimate. It acknowledges the inherent variability in sampling and estimation processes, ultimately increasing the likelihood of being correct in estimating the population mean.
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Scenario #2
Mary Beth's checking account balance on her bank statement shows $184.32. However,
she wrote checks for $41.78 and $12,10 that have not cleared the bank yet. How much is
Mary Beth's outstanding check total?
Answers
Answer:
Step-by-step explanation:
Mar Beth will have
41.78+12.10=53.88 outstanding check
184.32-53.88=130.44 balance in the account
Colton's gross pay is $1421.50 and his net pay is $973.48.
What percent of his gross pay is take-home pay?
31.5%
44.8%
46%
68.5%
Answers
68.5% of Colton's gross pay is take-home pay. To find the percentage of Colton's gross pay that is take-home pay, we need to divide his net pay by his gross pay and then multiply by 100 to convert the resulting decimal to a percentage.
To find the percentage of Colton's gross pay that is take-home pay, we need to divide his net pay by his gross pay and multiply the resulting decimal by 100 to express it as a percentage. Colton's gross pay is $1421.50 and his net pay is $973.48. Dividing the net pay by the gross pay gives a result of 0.685, or 68.5% when converted to a percentage. This means that 68.5% of Colton's gross pay is take-home pay, or the amount of money that he receives after deductions are made. Therefore, Colton's take-home pay is $973.48, which is 68.5% of his gross pay.
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Find the value of TN.
A. 32
B. 30
C. 10
D. 38
Answers
The value of TN for this problem is given as follows:
B. 30.
How to obtain the value of TN?A chord of a circle is a straight line segment that connects two points on the circle, that is, it is a line segment whose endpoints are on the circumference of a circle.
When two chords intersect each other, then the products of the measures of the segments of the chords are equal.
Then the value of x is obtained as follows:
8(x + 20) = 12 x 20
x + 20 = 12 x 20/8
x + 20 = 30.
x = 10.
Then the length TN is given as follows:
TN = x + 20
TN = 10 + 20
TN = 30.
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What do you mean by 3 more than 7?
Answers
The statement 3 more than 7 means, a number is 3 more than a given number. Since here the number is 7 so the required number will be 7+3= 10
In numerical more than simply refers to adding and less than refers to subtracting. If it is given that a number let's say Z is Y more than X then the value will be Z= X+Y
If a given number let's say Z is Y less than X then the value of Z will be
Z=X-Y
More than means add which gives us a bigger value. Less than means subtract which gives us a smaller value
So, 3 more than 7 means 7+3 = 10
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Sombody pls help me:(
Answers
1: 8:1
2: 2/4:3/4
3: 1:2
4: 32/4:3/4
charles owns a catering business. the amount his 10 most recent clients spent is shown in the histogram below. a bar graph is entitled cost per event. the event cost is on the x-axis and the number of events is on the y-axis. there are 2 events with a cost of 1,000-1,499; 4 with a cost of 1,500 to 1,999; 3 with a cost of 2,000 to 2,499; 1 with a cost of 3,000 to 3,499. why is the graph misleading?
Answers
The graph is misleading because the x-axis scale shows that the given data is more clustered than it actually is.
What is a misleading graph?
A misleading graph, sometimes referred to as a distorted graph, misrepresents data, amounts to statistical abuse, and may lead to the drawing of an inaccurate conclusion.
What is a data set?
A data set is a grouping of connected, discrete pieces of connected data that can be viewed separately, together, or handled as a single unit. A data structure of some kind is used to arrange a data set.
Here, we have
2 events with a cost of 1,000-1,499;
4 events with a cost of 1,500 to 1,999;
3 events with a cost of 2,000 to 2,499;
1 event with a cost of 3,000 to 3,499
We concluded from the given dataset that the cost of the event is plotted on the x-axis.
In a given dataset, the entry from 2500 to 2599 is missing.
The graph generates a point cluster that isn't actually displayed on the data components because of the missing item.
Hence, the graph is misleading because the x-axis scale shows that the given data is more clustered than it actually is.
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WILL GIVE BRAINLIEST!
A shopping mall has a moving sidewalk that takes shoppers from the shopping area to the parking garage, a distance of 220 ft. If your normal walking rate is 5 ft/s and the moving sidewalk is traveling at 3 ft/s, how many seconds would it take for you to walk from one end of the moving sidewalk to the other end?
Answers
You then divide 220/8
So it should be 27.5 seconds.
Sorry about that other guy. Hope this helps!
what is the correlation
Answers
Answer: moderate, C, B
Step-by-step explanation:
A) A shows a moderate negative correlation. It is moderate because the scattered points are sort of close to the line so it has moderate/medium correlation. It is also negative because it has a negative slope
B) C shows the strongest correlation because the points around the line are tight and close.
C) B should not have been drawn. The correlation is very weak. You do know where the line should be because the points are all over the place.
Charlotte wants to know which website has more user engagement per a single dollar expense.
Answers
Answer:
Part 1:
Total number of comments divided by the expenses
Total number of likes divided by the expenses.
Part 2:
Yes. According to both definitions, website A has more user engagement per a single dollar expense.
Step-by-step explanation:
User Engagment: Likes and comments
Website A:
500 comments/$20,000= .025
3500 likes/$20,000= .175
Website B:
450 comments/$47,000= .0095
3500 likes/$47,000= .07
Website A has more user engagement per a single dollar expense.
Answer:
Top Answer Worked for me
Step-by-step explanation:
Need help please anyone
Answers
Answer:
The answer is C
Step-by-step explanation:
I may be wrong but you need to line the decimal
Please help!!! thank you!
Answers
Answer:
30 again if I’m wrong then it’s 40
Step-by-step explanation:
most of the pizzas that are sold are in the 30’s or below
What is the value of the expression 12 x (-1.6)
Answers
Answer: -19.2
Step-by-step explanation:
Lisa smiled at her reflection, then made a funny face. She wore a cap, and her long hair blew in the wind. Her cheeks were pinkish from the cold and the wind, and her nose was moist. Lisa stepped away from nature’s mirror and was debating what after-school snack she would fix when she spied a lake of rainwater that extended from their squat trailer to the rusting tractors parked in the back.
“Oh, wow,” she remarked. The afternoon glare off the lake made her squint. How strange, she mused. It had rained just after lunch at school, but the downpour hadn’t seemed that heavy. Had a cloud stalled above their trailer and poured out its little heart?
She strolled around the new lake, occasionally gazing back at her footprints in the soggy earth. The chickens in the yard were soggy, too, their feathers parted and showing the yellow skin underneath. Still, they scratched and pecked at the ground and left their own shallow prints in the wet earth.
I’ll draw the lake, Lisa decided. She liked drawing birds, but had grown tired of sparrows, blue jays, and blackbirds wrapped in glossiness. These days she liked doing portraits, though she could draw objects, too. The previous week she had drawn the pile of tires behind the tractors; the drawing now adorned the front of the refrigerator.
Lisa produced a pencil and her sketch pad from her backpack. She had to capture this lake before it disappeared into the earth, taking with it the fluffy clouds mirrored on its surface. Birds the color of asphalt flittered about the edges of the puddle, and she recognized them as common finches. She knelt on the wet ground, putting down on paper what her eye beheld, what her fingers were able to portray.
Her gift was a mystery, as neither of her parents could draw. Their talent was to bring their faces together, like lovebirds, and warble Mexican songs, although most of the time they were working. Her father was employed by a dairy and her mother, from windy March to scorching July, worked in the fields—she thinned beets and cotton and was sometimes on a women’s crew that harvested cantaloupes. There were also two seasons when she packed peaches.
Lisa’s dog, Pecas, roamed in the background. He paused, head raised and fur parting from the wind. Lisa had to smile. He seemed to be posing as the subject of her artwork. His breath hung in the air when he barked at movement in the grass—a rabbit, she wondered, or a quail in search of a mate? The gopher that had tunneled under their garden patch last summer and nibbled at everything her father had planted: cucumbers, tomatoes, chilies, and eggplant?
I’ll surprise my parents with this new drawing, Lisa thought. “Cállate!” 1 she ordered Pecas, who turned, head lifted and tail wagging, and happily trotted toward her. But when two large white birds dropped from the sky, Pecas lurched in fear, kicking up water. “Oh my gosh,” Lisa uttered, dropping her pencil. She searched the sky for other birds. But the sky was vacant, except for blackbirds wheeling over the fields across the street.
As she took a cautious step toward the birds, she remembered that the night before she had been looking in her Audubon book at a picture of a bird that she would like to draw: the egret. Now before her stood a pair of egrets, which, against the backdrop of the grayish lake, were white as snow.
Lisa’s heart thumped with excitement and Pecas’s tail wagged briskly. Lisa again turned her attention skyward: Where had they come from? What wind had brought them here at this moment? She reached for the pencil on the ground and rolled it between her palms to spark the fires of creation. She had to draw these rare and silent birds, who, if she remembered right, seldom whistled or twittered with song.
Lisa turned and gasped. Over the lake arched a rainbow that began somewhere behind the tractors. The centerpiece was the pair of egrets, still as statues. Even Pecas stopped his whining. Lisa wondered, Can he really see the rainbow? She had read that dogs were mostly color-blind, but that birds, even common ones like the sparrow and finch, could slice the color red into a dozen shades. Their world was richer in color than some of the greatest paintings.
Lisa tried to sketch the scene quickly before it disappeared: First the egrets would fly away, then the rainbow fade, and finally the deposit of rain sink into the earth.
“It’s so beautiful,” she remarked.
A black-and-white calf ambled out from between the rusty tractors. Splattered with mud, it moved with a heavy sway toward the water. The calf stopped, then raised its heavy head to Lisa, as if saying, “Go ahead—draw me.” It lowered its gaze to turn and present a mournful profile, spittle hanging from its mouth.
“Oh,” Lisa let out, and added the cow to the scene. She made a face when she heard the telephone ring.
Answers
Answer:
1. A
2. Part A: B
3. Part B: C
4. Part C: B
5. B
6. Part A: B
7. Part B: C
8. A
Hope this helps!! :)
Answer:tyer5aghfdtr
Step-by-step explanation:
Answer:tyer5aghfdtr
rgtedrgdgdgdgd
Step-by-step explanation:
Answer:tyer5aghfdtr
gdgdhjkygkyuity7uindr6n6usre6rsnu6nrsu
Step-by-step explanation:
6nrus6nru5unrys6sr5n6urn56ur5n6usr6un
Please answer I'm not good at algebra
Answers
Answer:
8
Step-by-step explanation:
In algebra, an exponent represents the number of times you're multiplying the coefficient by itself. In this case, since we have 2³, we know that we are multiplying the number 2 together 3 times, or 2*2*2.
2*2 is 4, and 4*2 is 8.
Hope this helps!
Ms. Franco bought her daughter a new scooter. The scooter cost $40.00. Sales tax was
7.5%. What was the total price Ms. Franco paid for the scooter? ASAP please
Answers
Answer: $43.00
Step-by-step explanation:
40.00 + 40.00 ÷ 100 × 7.5 = 43.00
The area is 93.6 and the width is 13 cm what is the height
Answers
The width of the rectangle is 7.2 cm because if you divide 93.6 cm by 13 cm you will get 7.2 cm.
Brainliest please that would be nice of you(:
(a+b)²= ?
please tell the correct answer
Answers
This is all it’s saying.
Step-by-step explanation:
\((a + {b)}^{2} = {a}^{2} + 2ab + {b}^{2} \)
A student simplified the rational expression
using the steps shown.
2/3
25
X
48-
=
X
Is the answer correct? Explain.
X
2/5
DONE
12
45
63
112
225
= (x³) ³ = x ²
Answers
No, the answer is not correct
What is a Rational Expression?Simply put, a rational expression is the product of two polynomials. Or to put it another way, it is a fraction using polynomials as the numerator and denominator.
In the second step, the student didn’t use the quotient of powers property correctly.
They should have subtracted inside the parentheses instead of dividing. This would have left them with x^(4/5).
They should have then multiplied this power by ^(1/2) resulting in x^(4/10) which simplified is x^(2/5) which is the correct answer.
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Katherine wants to classify the quadrilateral below. Select all of the names that apply.
A.
parallelogram
B.
quadrilateral
C.
rectangle
D.
rhombus
PLSSSSS HELP
Answers
In the figure, all sides are equal then the geometry is known as Rhombus. Then the correct option is D.
What is a quadrilateral?It is a polygon with four sides. The total interior angle is 360 degrees.
Types of a quadrilateral are as follows
Rectangle - A rectangle's opposite sides are parallel and equal, and each angle is 90 degrees. Its diagonals are all the same length and intersect in the center.
Parallelogram - In a Parallelogram, opposite sides are parallel and the angle is not the right angle.
Rhombus- In a Rhombus, opposite sides are parallel and the angle is not the right angle. All sides are equal.
The diagram is given below.
Then the given figure is a rhombus.
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Which expression is equivalent to (2.1)5 (0.9)?
Answers
The equivalent expression is 9.45
How to find the equivalent expression?
Calculating the product,
(21.)5 (0.9) = 10.5 *0.9
= 9.45
Other equivalent expressions are:
\(\frac{189}{20} \text{ and } 9 \frac{9}{20}\)
What is a product?
In mathematics, a product is the outcome of multiplication or an expression that specifies the elements, or objects that can be numbers or variables, that are to be multiplied. The commutative law of multiplication states that the result is unaffected by the order of multiplying real or complex numbers. A number that is obtained by multiplying two or more other numbers together is known as the product .Multiplication in other algebras in general, as well as matrix multiplication as an example, is non-commutative.To learn more about products, refer:
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