50 points
A finance magazine did a survey and found that the average American family spends $1,600 on a summer vacation. If the distribution is normal with standard deviation $411, find the amount a family would have spent to be the 80th percentile.
Answers
Answer:
$1,945.91
Step-by-step explanation:
To find the amount a family would have spent to be at the 80th percentile, we can use the normal distribution.
If a continuous random variable X is normally distributed with mean μ and variance σ², it is written as:
[tex]\boxed{X \sim\text{N}(\mu,\sigma^2)}[/tex]
Given that the average spending on a summer vacation is $1,600 and the standard deviation is $411:
Mean μ = $1,600Standard deviation σ = $411We need to convert the problem to the standard normal distribution by calculating the z-score.
The z-score represents the number of standard deviations a data point is away from the mean. To find the z-score corresponding to the 80th percentile, we need to find the critical value or z-score that corresponds to an area of 0.80 under the standard normal curve.
Using a standard normal distribution table or a calculator, the z-score corresponding to an area of 0.80 is 0.84162084...
Next, we use the formula for the z-score:
[tex]\boxed{z = \dfrac{x - \mu}{\sigma}}[/tex]
where z is the z-score, x is the data point, μ is the mean, and σ is the standard deviation.
Substitute z = 0.84162084..., μ = 1600, σ = 411 into the z-score formula:
[tex]0.84162084... = \dfrac{x - 1600}{411}[/tex]
Solving for x:
[tex]x=1945.90616...[/tex]
Therefore, a family would have spent approximately $1,945.91 to be at the 80th percentile of spending on a summer vacation.
Answer:
$1,945.03
Step-by-step explanation:
To find the amount a family would have spent to be at the 80th percentile, we need to find the z-score that corresponds to the 80th percentile and then use that z-score to calculate the corresponding amount.
First, we find the z-score using the standard normal distribution table or a calculator:
z = InvNorm(0.8) ≈ 0.8416
Next, we use the formula for transforming a z-score to a raw score:
z = (x - μ) / σ
where x is the raw score, μ is the mean, and σ is the standard deviation.
Substituting the given values and solving for x, we get:
0.8416 = (x - 1600) / 411
x - 1600 = 0.8416 * 411
x - 1600 = 345.0256
x = 1945.0256
Therefore, a family would have spent about $1,945.03 to be at the 80th percentile.
Related Questions
For some linear relationships, doubling the independent variable results in doubling the function value. For example, doubling the number of steps in a staircase doubles the height of the staircase. Does this doubling property hold for every linear relationship?
Answers
Using linear function concepts, it is found that this doubling property does not hold for every linear relationship.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.One example of function is:
y = 4x + 3.
When x = 1:
y = 4 + 3 = 7.
When x = 2:
y = 8 + 3 = 11.
The input did not double, meaning that this doubling property does not hold for every linear relationship, it doubles only for a linear function with a slope of 2 and intercept of 0.
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A28% income tax on a 80,000 income
Answers
Total amount you take home is 57,600
Kary took 4 courses last semester: History, Biology, Calculus, and Physics. The means and standard deviations for the final exams, and Kary's scores are given in the table below. Convert Kary's score into z scores.
Subject Mean Stand. dev. Kary's score Kary's z score
History 53 16 69
Biology 77 10 74.5
Calculus 70 12 88
Physics 60 14 67
Answers
The highest z-score is corresponding to Calculus, hence in Calculus Kary have the highest relative score using standard deviation and mean concept i.e. 2.5.
As per the question statement, It is given that Kary took 4 courses last semester i.e., History, Biology, Calculus, and Physics. The means and standard deviations for the final exams, and Kary's scores are given as follows:
History 53 16
Blology 77 10
Calculus 70 12
Physlcs 60 14
Kary's score In the above four subjects are: 69,74.5,88,67
We are supposed to convert Kary's score in z-score which is as follows:
History : [tex]\frac{69-53}{16} =1[/tex]
Biology: [tex]\frac{74.5-77}{10}=-0.25[/tex]
Calculus: [tex]\frac{88-70}{12} =1.5[/tex]
Physics: [tex]\frac{67-60}{14} = 0.5[/tex]
From the above calculations, it is clear that The highest z-score is corresponding to Calculus, hence in Calculus Kary have the highest relative score using standard deviation and mean concept i.e., [tex]1.5[/tex]
Mean: The most typical or average value among a group of numbers is called the mean. It is a statistical measure of a probability distribution's central tendency along the median and mode.Standard Deviation: A measure of how far a group's members deviate from the average value for the group.To learn more about Standard Deviation and Mean, click on the link given below:
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WILL GIVE BRAINLIEST
Answers
Answer:
a. = 1
b. = 0
c. = 2
d. = 7
Hopefully this helps
Find two - 3 - digits which are divisible by 8 and 11?
Answers
Answer:
88,86416
Step-by-step explanation:
PLEASEEEE HELPPP!!!! THIS IS DUE ON WEDNESDAY
Jeri bought 32 cookies and 56 slices of pizza for his sisters birthday. Each guest will receive the same number of cookies and pizza, with nothing left over. If Jeri wants to invite the greatest number of guests, how many cookies will each guest receive?
Answers
Reason:
32 = 8*4
56 = 8*7
We see that 8 is the largest common factor, aka GCF, of 32 and 56
So this is the greatest number of guests possible.
Each guest will get 32/8 = 4 cookies and 56/8 = 7 slices of pizza.
Need help with This assignment asap will mark brainless
Answers
Answer:
Hello,
Answer: B : y=(m-3)*(x+1)²3
Step-by-step explanation:
The parabola with vertex (-1,3)
is y=k(x+1)²+3
(0,m) is a point of the parabola:
m=k*(0+1)²+3 ==> k=m-3
So, y=(m-3)*(x+1)²+3 is the correct equation.
AB=[1+4.5]=5.5 describe and correct
Answers
The required solution is correct. AB = 5.5.
Given that,
AB=[1+4.5]=5.5
To describe the expression and to determine whether the expression is correct or not.
What is arithmetic?
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
here,
Simplifying the given expression, AB = 1 + 4.5
AB = 1 + 4.5
Addition property of alike terms
AB = 1.00 + 4.50
AB = 5.50
AB = 5.5
Thus, the required solution is correct. AB = 5.5
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xy + 8
Click on the correct answer.
monomial
binomial
trinomial
Answers
Answer:
Binomial
Step-by-step explanation:
There are only 2 terms
Apple weights in an orchard are normally distributed. From a sample farmer Fred determines the mean weight of a box of apples to be 270 oz. with a standard deviation of 10 oz. He wonders what percent of the apple boxes he has grouped for sale will have a weight less than 255 oz.
Answers
Carl calculates the z-score corresponding to the weight 255oz= -1.5.
Now, Carl decides to find the percent associated with boxes less then 255 oz, so he rounds to hundred and substract 50% - 7% = 43%.
Given that,
In an orchard, apple weights are typically distributed. Fred the farmer concludes from a sample that the average weight of a box of apples is 270 ounces, with a standard deviation of 10 ounces.
He is interested in knowing what proportion of the apple boxes he has gathered for sale will weigh less than 255 oz.
Mean is 270
Standard deviation is 10
x = 255
Formula for z-score,
z = (x - mean)/SD
z = (255 - 270) / 10
=> z = -15 / 10
=> z = -1.5
Hence, by using z-table,
-1.5 equates to 0.0668, which suggests that 0.07
Therefore, 7% of Apple boxes weigh less than 255 oz.
The ratio of boxes is between 255 oz and 270 oz,
Calculating the proportion
Now,
50% - 7% = 43%.
Therefore, Carl calculates the z-score corresponding to the weight 255oz= -1.5.
Carl decides to find the percent associated with boxes less then 255 oz, so he rounds to hundred and substract 50% - 7% = 43%.
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What are the values of a and r of the geometric series?
2-2+2-2+2
Answers
The given geometric series, the first term is a₁ = 2 and the common ratio is r = -1
What are some examples of geometric series?
In mathematics, a geometric series is an infinite series with the formula a + ar + ar2 + ar3 +, where r is referred to as the common ratio. The geometric series for a = 1 and r = 1/2, or 1 + 1/2 + 1/4 + 1/8 +, is a straightforward illustration and converges to a sum of 2. (or 1 if the first term is excluded).We are given to find the values of a₁ and r of the following geometric series
2 - 2 + 2 - 2 + 2 - ........
We know that
a₁ is the first term and r is the common ratio of the given geometric series.
We can see that the first term of the given geometric series is 2.
So. we must have
a₁ = 2
Also, common ratio is found by dividing a term by its preceding term.
Therefore, the common ratio r of the given geometric series is
r = -2/2 = 2 / -2 = ...... = -1
Thus, for the given geometric series, the first term is a₁ = 2 and the common ratio is r = -1.
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please help
please hurry
Answers
To mail a letter to Vienna, Austria the post office charges a flat rate of $8.00 and an additional $0.75 for every ounce the letter weighs. The cost of mailing a letter is
determined by the equation y = 0.75x+8.00, where y is the cost of the postage and x is the weight of the letter in ounces.
Step 2 of 2: Use the graph to estimate to the nearest quarter of a dollar ($0.25) the cost to send a letter that weighs 5 ounces.
Enable Zoom/Pan
Price for Postage
15
10
S
5
10
Weight (oz)
15
Answers
The cost to send a letter that weighs 5 ounces is $11.75.
Flat rate = $8.00
Charges on every ounce = $0.75
Given equation :
y = 0.75x + 8.00
'y' = Cost of the postage
'x' = Weight of the letter in ounces
According to the question we can determine the cost of mailing a letter with the help of given equation (y = 0.75x + 8.00).
We have given that the weight of letter that need to send is 5 ounces.
So, x = 5
Lets find the cost of postage,
y = 0.75x + 8.00
y = (0.75 × 5) + 8.00
y = 3.75 + 8.00
y = $11.75
Hence, it will take $11.75 to mail a letter or we can say cost of postage.
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4. Communicate Precisely What does it mean for a figure to have 60° rotational symmetry?
Answers
It means that if you rotated the figure 60 degrees (clockwise or counterclockwise) about its center, then the figure does not change.
The "before" and "after" are identical. In other words, the preimage and image are the same.
what Robert decided to buy half a dozen mangoes priced at $0.15 each.he gives $20 to the cashier.how much change should he receive
Answers
The profit or loses change should he receive is $19.5
Given,
The price of Dozen of mangoes is $.15
Robert gives $20
The change should be is $20-$.15 =$19.5
When a person buys an item at one price and later sells it at a different one, he either earns a profit or loses money. There are several phrases that are involved with the complete transaction procedure. For instance, cost price (C.P. ), selling price (S.P. ), discount, marked price, profit, and loss. Let us go through the definitions of these terminologies one by one.
Price Cost
For example, if Neil purchased an umbrella for $8, the cost price of the umbrella is $8. The abbreviation is C.P.
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Convert 3/7 to percent
Answers
Answer:
42.857143%
Step-by-step explanation:
As a decimal, this would equal, 0.428!
When you convert that into a percentage, you'll get 42.857143%, which btw, you can round to 43%!
I hope this helps!
Find the measure of each angle specified below.
Answers
Answer:
Step-by-step explanation:
angle 5 = 52, therefore angle 6 = 180 - 52 = 128
angle 7 = 52
Please hurry i need an answer
Answers
Answer:
sum = addition. p+157=171
Step-by-step explanation:
Answer: P + 157 = 171
Step-by-step explanation:
Given 1 mile ≈ 1.6 kilometers, what is the standard deviation in kilometers? (Enter your answer to two decimal places.)
s =
Answers
The required value of the standard deviation is 0.04.
Given that,
1 mile ≈ 1.6 kilometers, what is the standard deviation in kilometers is to be determined. Where s = 5
What is Statistic?Statistics is the study of mathematics that deals with relations between comprehensive data.
Here,
1 miles = 1.60934 Km
Given
1 mile = 1.6
Standard deviation = 1.60934 - 1.6000
= 0.00934
S = 5
Standard deviation = 5 * 0.00934
= 0.04670
Thus, the required value of the standard deviation is 0.04.
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Which set of points represents a nonlinear function?
A (-3,-6) (0,1) (3,8)
B (-2,2) (0,0) (2,2)
C (0,4) (3,3) (6,2)
D (8,0) (9,1) (10, 2)
Answers
Answer:
The answer would be B.
Step-by-step explanation:
(-2,2)(0,0)(2,2) represents a nonlinear function.
b. Write the set of natural numbers greater than 22 using the most concise method.
(Use a comma to separate answers as needed.)
A. The set of numbers is {}
B. The set of numbers is {x|XEN and x> }}
C. The set of numbers is {x|XEN and x< }
D. The set of number is {xXEN and x =}
Answers
The set of numbers is S = { x ∈ N ; x > 22 }.
We have the statement:
Set of natural numbers greater than 22.
We need to make the set from it.
A set is a collection of different things objects or elements that are used to represent a situation or a function in a concise form.
For example a set of real numbers can be denoted by x ∈ R.
There can be finite or infinite sets. In finite sets, the number of elements are limited whereas in infinite sets it is not limited.
Here, the set that will be formed can be written as:
S = { x ∈ N ; x > 22 }
Therefore, the set of numbers is S = { x ∈ N ; x > 22 }.
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Please help me is this problem <, >, or =
Answers
[tex] \sqrt{15} \approx3.873\\ \\ \sqrt{15} < 3.9[/tex]
since 15 square root equals 3.87 it is less than 3.9
My thermometer has a percent error of 3%. The actual temperature is 75°F.
Will the thermometer show the temperature at 72.00 °F or 78.00 °F?
Answers
The thermometer show the temperature at 73°F when there is a percentage error.
How to calculate the value?From the information, the thermometer has a percent error of 3% and the actual temperature is 75°F.
Therefore, the temperature down on the thermometer will be:
= 75 - (3% ×75)
= 75 - 2.25
= 72.75
= 73 approximately.
Therefore, the thermometer show the temperature at 73°F when there is a percentage error.
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If two out of every fifteen trick-or-treaters that came to your house last Halloween were dressed as Spiderman, what proportion of trick-or-treaters were not dressed as
Spiderman?
Answers
The proportion of trick-or-treaters that were not dressed as Spiderman will be 131/15.
How to calculate the value?From the information, two out of every fifteen trick-or-treaters that came to the house last Halloween were dressed as Spiderman.
Therefore the fraction is represented as 2/15.
Therefore, the proportion of trick-or-treaters that were not dressed as Spiderman will be:
= 1 - 2/15
= 13/15.
Therefore, the proportion of trick-or-treaters that were not dressed as Spiderman will be 131/15.
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The circumference of a circle is 30. What is its area?
Answers
2 pi r is circumference.
a =c^2 / 4pi = 30^2 / 4 * pi = 71.619
Answer:
71.62
Step-by-step explanation:
[tex]A = \frac{C^2}{4 \times \pi }\\A = \frac{30^2}{4 \times 3.14 }\\A = 71.62[/tex]
Drag the tiles to the boxes to form correct pairs.
Match the pairs of equivalent expressions.
Answers
The pairs of equivalent expressions are:
(-14 + 3/2b) - (1 + 8/2b) --> -15 - 5/2b
(5 + 2b) + (2b + 3/2) --> 4b + 13/2
(7/2b - 3) - (8 + 6b) --> -5/2b - 11
(-10 + b) + (7b - 5) --> 8b - 15
How to Determine Equivalent Expressions?Evaluate each of the given expressions in order to find out which expression is equivalent to each.
(-14 + 3/2b) - (1 + 8/2b) = (-14 + 3/2b) - (1 + 4b)
= -14 + 3/2b - 1 - 4b
= -15 - 5/2b
(5 + 2b) + (2b + 3/2) = 5 + 2b + 2b + 3/2
13/2 + 4b
4b + 13/2
(7/2b - 3) - (8 + 6b) = 7/2b - 3 - 8 - 6b
-5/2b - 11
(-10 + b) + (7b - 5) = -10 + b + 7b - 5
= -15 + 8b
= 8b - 15
Thus, the pairs of equivalent expressions are:
(-14 + 3/2b) - (1 + 8/2b) --> -15 - 5/2b
(5 + 2b) + (2b + 3/2) --> 4b + 13/2
(7/2b - 3) - (8 + 6b) --> -5/2b - 11
(-10 + b) + (7b - 5) --> 8b - 15
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patty has just completed her second semester in college. She earned a grade of in her -hour course, a grade of in her -hour course, a grade of in her -hour course, and a grade of in her -hour course. Assuming that A equals 4 points, B equals 3 points, C equals 2 points, D equals 1 point, and F is worth no points, determine 's grade-point average for the semester.
Answers
The second semester grade point average for Patty was 2.21.
Due to that,
She received an upper D mark in the five hours of discrete math.
A higher B in her three-hour sociology class,
In her one-hour engineering course, she received an upper C.
And an upper B mark in her five-hour philosophy course.
A is worth four points, B is worth three, C is worth two, D is worth one, and F is worth none.
We must discover,
The semester's grade point average for Patty.
The answer to the query is
The student's grade point average is:
multiplying each point by its corresponding credit hour, adding them all up, and then dividing the result by the total amount of credit hours.
Then,
A single point is equal to 5(1) + 3(3) + 1(2) + 5(3), which is 5 + 9 + 2 + 15 = 31.
The numbers outside of the parentheses represent the credit hours while those inside represent the points.
Now,
Total credits earned equal 14 (5 + 3 + 1 + 5).
Patty's semester grade point average was 2.21.
Patty's semester grade point average is 2.21 as a result.
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Which of the following is true about parallel lines? Select all that apply.
*
They will never cross.
They have the same slope.
Their slopes are opposite reciprocals.
They will cross at a right angle.
They are in the same plane.
Answers
The statements which are true about parallel lines are;
They will never cross.They have the same slope.They are in the same plane.What are parallel lines?Parallel lines in their simplest description are lines which would never meet or cross each other under any circumstance.
Also, It follows from line geometry that such lines have the same slope and are coplanar, exist in the same plane.
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PLA HELP I WILL GOVE BRAINLIEST
Find the x-intercept and the y-intercept of each line. Express the answers as ordered
pairs.
y = 5x-10
x-intercept is
y - intercept is
Answers
Answer:
the answer is x intercept is 8 and the y intercept is 10
Jonah measured a picnic area near the river and made a scale drawing. The picnic area,
which is 70 yards wide in real life, is 10 inches wide in the drawing. What scale did Jonah
use?
Answers
The scale used by Johan is 1: 252.
Here, we are given that Jonah made a scale drawing of the picnic area in which the 70 yards wide picnic area in real life, was 10 inches wide in the drawing.
As per mathematical measurements-
1 yard = 3 feet
and 1 feet = 12 inches
Thus, 3 feet = 12 x 3 inches
= 36 inches
Therefore, we get that 1 yard = 36 inches
Now, the picnic area is 70 yards
the picnic area in inches is = 70 x 36 inches wide
= 2520 inches
Thus the scale used by Johan will be-
10 : 2520
= 1 : 252
Thus, the scale used by Johan is 1 : 252.
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