According to U.S. News & World Report's publication America's Best Colleges, the average cost to attend the University of Southern California (USC) after deducting grants based on need is . Assume the population standard deviation is $8,200. Suppose that a random sample of USC students will be taken from this population.A. What is the value of the standard error of the mean? (to nearest whole number)
B. What is the probability that the sample mean will be more than $25,050 ?C. What is the probability that the sample mean will be within $1,250 of the population mean? D. How would the probability in part (c) change if the sample size were increased to 200 ?
Answers
Answer:
a) Standard Error of the mean = $980
b) Probability that the sample mean will be more than $25,050 = 0.50
c) Probability that the sample mean will be within $1,250 of the population mean = 0.7995
d) Probability that the sample mean will be within $1,250 of the population mean if the sample size is increased to 200 = 0.9692
Step-by-step explanation:
Complete Question
According to U.S. News & World Report's publication America's Best Colleges, the average cost to attend the University of Southern California (USC) after deducting grants based on need is $25,050. Assume the population standard deviation is $8,200 . Suppose that a random sample of 70 USC students will be taken from this population. Use z-table.
a. What is the value of the standard error of the mean? (to nearest whole number)
b. What is the probability that the sample mean will be more than $25,050 ? (to 2 decimals)
c. What is the probability that the sample mean will be within $1,250 of the population mean? (to 4 decimals)
d. How would the probability in part (c) change if the sample size were increased to 200 ? (to 4 decimals)
Solution
According to the Central limit theorem, for a normally distributed distribution where a random sample of large enough sample size with each variable independent of one another, the mean of the sampling distribution is approximately equal to the population mean and the standard deviation of the sampling distribution or the standard error of the mean (σₓ) is given as
σₓ = (σ/√n)
where σ = population standard deviation = $8,200
n = sample size = 70
Mean of sampling distribution (μₓ) = Population mean (μ) = $25,050
a) Standard Error of the mean = σₓ
= (8200/√70) = 980.09 = $980 to nearest whole number
b) Probability that the sample mean will be more than $25,050 = P(x > 25050)
We first normalize or standardize $25;050
The standardized score for any value is the value minus the mean then divided by the standard deviation.
z = (x - μₓ)/σₓ = (25050 - 25050)/980 = 0
To determine the required probability 45mg/L, P(x > 25050) = P(z > 0)
We'll use data from the normal probability table for these probabilities
P(x > 25050) = P(z > 0) = 1 - P(z ≤ 0) = 1 - 0.50 = 0.50
c) The probability that the sample mean will be within $1,250 of the population mean
(mean of sampling distribution) + 1250 = 25050 + 1250 = $26,300
(mean of sampling distribution) - 1250 = 25050 - 1250 = $23,800
Probability that the sample mean will be within $1,250 of the population mean
= P(23800 ≤ x ≤ 26300)
We first normalize $23,800 and $26,300
For $23,800
z = (x - μₓ)/σₓ = (23800 - 25050)/980 = -1.28
For $26,300
z = (x - μₓ)/σₓ = (26300 - 25050)/980 = 1.28
The required probability
P(23800 ≤ x ≤ 26300) = P(-1.28 ≤ x ≤ 1.28)
We'll use data from the normal distribution table for these probabilities
P(23800 ≤ x ≤ 26300) = P(-1.28 ≤ x ≤ 1.28)
= P(z ≤ 1.28) - P(z ≤ -1.28)
= 0.89973 - 0.10027
= 0.79946 = 0.7995 to 4 d.p
d) How would the probability in part (c) change if the sample size were increased to 200?
If the sample size increase to 200, the standard deviation of the sampling distribution or standard error of the mean changes to
σₓ = (σ/√n)
where σ = population standard deviation = $8,200
n = sample size = 200
Standard Error of the mean = σₓ
= (8200/√200) = 579.83 = $580 to nearest whole number
Probability that the sample mean will be within $1,250 of the population mean
= P(23800 ≤ x ≤ 26300)
We first normalize $23,800 and $26,300
For $23,800
z = (x - μₓ)/σₓ = (23800 - 25050)/580 = -2.16
For $26,300
z = (x - μₓ)/σₓ = (26300 - 25050)/980 = 2.16
The required probability
P(23800 ≤ x ≤ 26300) = P(-2.16 ≤ x ≤ 2.16)
We'll use data from the normal distribution table for these probabilities
P(23800 ≤ x ≤ 26300) = P(-2.16 ≤ x ≤ 2.16)
= P(z ≤ 2.16) - P(z ≤ -2.16)
= 0.98461 - 0.01539
= 0.96922 = 0.9692 to 4 d.p
Hope this Helps!!!
Related Questions
A rectangle is h units high. It's length 3 units more than it's height. What is the perimeter?
Answers
The perimeter of the rectangle is 4h + 6
What is an algebraic expression?An algebraic expression can be defined as an expression that is composed of terms, variables, coefficients, constants and factors.
These expressions are also made up of arithmetic operations, such as;
SubtractionAdditionMultiplicationDivisionBracketParenthesesThe formula for calculating the perimeter of a rectangle is expressed as;
Perimeter = 2( l + h)
Where;
l is the lengthh is the height of the rectanglel = 3 + h
Substitute the values
Perimeter = 2( 3 + h+ h)
expand the bracket
Perimeter = 2(3 + 2h)
Perimeter = 4h + 6
Hence, the expression is 4h + 6
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a⃗ =⟨4, −3⟩ and b⃗ =⟨−1,−2⟩.
Represent a⃗ +b⃗ by using the head to tail method.
Use the Vector tool to draw the vectors, complete the head to tail method, and draw a⃗ +b⃗ . Do not draw any unnecessary vectors.
To use the Vector tool, select the initial point and then the terminal point.
Answers
The vector addition of vector a = < 4, - 3 > and b = < - 1, - 2 > is given by,
a + b = < 3, -5 >
The graph of the vector sum is given below.
The addition of vectors suggests the addition of the corresponding components of the involving vectors.
Given the vectors are:
a = < 4, - 3 >
b = < - 1, - 2 >
So doing vector addition we get,
a + b = < 4, - 3 > + < - 1, - 2 > = < (4 + (-1)), (-3+(-2)) > = < (4 - 1), (-3 -2) > = < 3, -5>
Head to tail method is a method to draw vector addition, where the initial point of a vector involved in vector addition is started from tail point of another vector involved in vector addition.
Using vector tool we draw the vector addition of given vectors 'a' and 'b' we get,
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Answer: Look at the image below
Step-by-step explanation: I took the test.
Step 1: Select Vector
Step 2: Click on (0, 0), then click on (4, -3); (for every point your going to have to click on where you start then where you want to go.)
Step 3: Click on (4, -3), then (3, -5). Why?: ((4 - 1), (-3 - 2)) = (3, -5)
Step 4: To complete the problem and thus completing the "head to tail" method, you need to click on the origin (0,0) and finally click on (3, -5)
Your answer should now look like mine, now go get that A.
Solve for q: 2q- 12 = -40
Answers
Answer:
q = -14
Step-by-step explanation:
2q - 12 = -40
Add 12 to both sides
2q - 12 + 12 = - 40 + 12
2q = - 28
Divide both sides by 2
2q/2 = -28/2
q = - 14
Given the inscribed polygon, find the value of both x .and y.
X =
y =
please help!!!
Answers
y= 107
This is because opposite angles in a cycling quadrilateral ( the inscribed polygon) are equal to 180
A parallelogram has a base of 45 meters and a height of 11 meters what is the area of the parallelogram?
Answers
Answer:495
Step-by-step explanation: 45x11 I believe, and thats 495
Explanation: A=BH
A= 45•11
A=495
what is the absolute value of -6.8
Answers
Answer: 6.8
Step-by-step explanation:
absolute value turns the number into the positive value.
PLEASE HELP
3. The function E(v)= 15v^2 / 2 models the
kinetic energy E in joules of an object
with a mass of 15 kilograms, where v is
the velocity of the object in meters per
second. Write the inverse function v(E) to
find the velocity of a 15-kilogram object
with kinetic energy E.
Answers
Answer:
i think it is 15v (E) = √(2E/m)
Step-by-step explanation:
From the question given:
E = ½mv²
E is the kinetic energy
m is the mass of object
v is the velocity.
To find a model v(E) for the velocity of the object, we simply make V the subject of the above equation.
This can be obtained as follow:
E = ½mv²
Cross multiply
mv² = 2E
Divide both side by m
v² = 2E/m
Take the square root of both side
v = √(2E/m)
Therefore, the model v(E) for the velocity of the object is given by:
v (E) = √(2E/m)
The inverse function v(E) to find the velocity of a 15-kilogram object
with kinetic energy E should be \(15v (E) = \sqrt (2E/m)\)
Calculation of the inverse relation:Since we know that
\(E = 1\div 2mv^2\)
Here,
E is the kinetic energy
m is the mass of object
v is the velocity.
Now we can write like
\(mv^2 = 2E\)
So,
\(v^2 = 2E/m\)
Now Take the square root of both side
So,
\(v = \sqrt (2E/m)\\\\v (E) = \sqrt (2E/m)\)
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[!]Urgent[!] What is another way to summarize the outcome of this proof?
A. Angles forming a linear pair are supplementary
B. Vertical angles are congruent
C. Vertical angles are supplementary
D. Angles forming a linear pair are congruent
![[!]Urgent[!] What is another way to summarize the outcome of this proof?A. Angles forming a linear pair](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/IdYaHnrKQBjJhKi0bk5hvCNy5SEhXEDF.jpeg)
Answers
Answer:
B. Vertical angles are congruent
Step-by-step explanation:
The instructions are to prove that ∠ANR and ∠VNE are congruent, and ∠ANR and ∠VNE are vertical angles.
I hope this helps :)
The ratio of 1.5 to 33 is the same as the ratio of 4.5 to
Answers
Answer:
132
Step-by-step explanation:
a) is y=3/2x proportional and what is the constant of proportionality ?
b) is -x=y proportional and what is the constant of proportionality
Answers
Answer:
In y = 3/2x, x and y are inversely propotional
In -x = y, x and y are directly propotional
Step-by-step explanation:
In y = 3/2x, the constant of propotionality is 3/2.
In -x = y, the constant of propotionality is -1.
What is the next time: 8:30 A.M., 10:00 A.M., 11:30 A.M., _______? A) 1:00 P.M. B) 1:00 A.M. C) 1:30 P.M. D) 1:30 A.M.
Answers
Answer:
A 1 PM
Step-by-step explanation:
Becasue it grows by an hour and a half each time
Answer: Easy. A. 1 pm.
.
|2x+1| < 5
help please
Answers
Answer:
3
Step-by-step explanation:
Answer: x=2 and x=-3
Step-by-step explanation:
|2x+1|=5>|2x+1|=-5
2x+1=5 > 2x+1=-5
2x+1-1=5-1 > 2x+1-1=-5-1
2x=4 > 2x=-6
2x÷2=4÷2 > 2x÷2=-6÷2
x=2 > x=-3
help me, please I am in need for
Answers
Answer:
I think it must be between 75 and 76
PLEASE HELP!!! IT WOULD MEAN A LOT!
Answers
Answer:
The answer is 207 ft^2
Step-by-step explanation:
Answer:
207
Step-by-step explanation:
Hey There!
So the first step is to solve for the figure with a length of 9 and a width of 15
15x9=135
The other figure has a length of 12 and a width of 6
6x12=72
No we just add them
135+72=207
therefore 207 is your answer
If they take 5 days to drive 679 miles to Seattle, how many miles will they drive each day?
Answers
Determine whether the statements in (a) and (b) are logically equivalent.
a. Bob is a double math and computer science major and Ann is a math major, but Ann is not a double math and computer science major.
b. It is not the case that both Bob and Ann are double math and computer science majors, but it is the case that Ann is a math major and Bob is a double math and computer science major.
Answers
Answer:
The two statements are logically equivalent.
Step-by-step explanation:
Let X be the statement that Bob is a double math and computer science major.
Y be the statement that Ann is a maths major.
Z be the statement that Ann is a double maths and computer science major.
The two statements written in terms of X, Y and Z now
a. Bob is a double math and computer science major and Ann is a math major, but Ann is not a double math and computer science major.
(x and y) and not z
b. It is not the case that both Bob and Ann are double math and computer science majors, but it is the case that Ann is a math major and Bob is a double math and computer science major.
not (x and z) and (x and y)
Noting that for logical statements,
Negation is represented by ~
And is represented by conjunction sign Λ
Or is represented by disjunction sign V
(x and y) and not z
(x Λ y) Λ (~z)
not (x and z) and (x and y)
~(x Λ z) Λ (x Λ y)
We can then simplify the second statement to obtain the first statement and prove the equivalence of both sides
~(x Λ z) Λ (x Λ y)
Using DE MORGAN'S theory, ~(x Λ z) = (~x) V (~z)
~(x Λ z) Λ (x Λ y) = ((~x) V (~z)) Λ (x Λ y)
Then applying the distributive law to the expression, we can open the bracket up
((~x) V (~z)) Λ (x Λ y)
= ((~x) Λ (x Λ y)) V ((~z) Λ (x Λ y))
Opening the first bracket up further
((~x) Λ (x Λ y)) V ((~z) Λ (x Λ y))
= ((~x) Λ x) Λ y) V ((~z) Λ (x Λ y))
The NEGATION law shows that (~x Λ x) = c (where c is a negation law parameter for when two opposite statements are combined in this manner, it works like a 0 in operation)
((~x) Λ x) Λ y) V ((~z) Λ (x Λ y))
= (c Λ y) V ((~z) Λ (x Λ y))
But (c Λ y) = (y Λ c) = c (according to the UNIVERSALLY BOUND law, see how c works like a 0 now?)
(c Λ y) V ((~z) Λ (x Λ y))
= c V ((~z) Λ (x Λ y))
= ((~z) Λ (x Λ y)) V c (commutative)
And one of the foremost IDENTITY laws is that (any statement) V c = c
((~z) Λ (x Λ y)) V c
= ((~z) Λ (x Λ y))
= (x Λ y) Λ (~z)
Which is the same as the first statement!
PROVED!!!
Hope this Helps!!!
Answer:
Not 100% but I think they are equal logically.
COULD YALL HELP ME ?!???!
Answers
Answer:
28 degrees
Step-by-step explanation:
We know that (4x + 7) + (2x + 5) add up to a straight angle = 180 degrees, so we have the equation 4x + 7 + 2x + 5 = 180.
By combining like terms, we get 6x + 12 = 180.
Subtract 12 from both sides of the equation to get 6x = 168. Divide both sides by 6 and you get x = 28.
During a sale, a store offered a 25% discount on a bed that originally sold for $800. After the sale, the discounted price of the bed was marked up by 25%. What was the price of the bed after the markup? Round to the nearest cent.
Answers
The price of the bed after mark up is $475.00
What is discount?Discount results in the reduction of the selling price of the product, which makes it more attractive for the customer.
The first discount given is 25% , therefore the price of the bed before mark up is
25/100 × 800
= 25×8
= 200
the price before mark up = 800-200 = $600
Another 25% is given after the first sale, there the price of the bed after mark up is
25/100 × 600
=$ 125
price after markup = 600-125
= $475.00
therefore the price of the bed after markup is $475.00
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PLease help i dont know how to do this please explain too!!
Answers
Answer:
6.25
Step-by-step explanation:
The perimeter is the sum of the lengths of the sides.
For a rectangle, it's the two widths plus the two heights.
P = 2W + 2H
Plugging in values:
52 = 2(3x − 1) + 2(x + 2)
52 = 6x − 2 + 2x + 4
52 = 8x + 2
50 = 8x
x = 6.25
Find the value of x.
Formula used:-Perimeter of rectangle = 2 ( l + b )
Solution:-We know that,
Perimeter of rectangle = 52 [ Given ]
⇒ 2 ( l + b ) = 52
⇒ 2 ( 3x - 1 + x + 2 ) = 52
⇒ 2 ( 4x + 1 ) = 52
⇒ 8x + 2 = 52
⇒8x = 52 - 2
⇒ 8x = 50
⇒ x = 50/8
⇒ x = 6.25 inches
Given the lines are parallel, find the value of x.
Answers
Answer:
x = 7Step-by-step explanation:
52 = 5x + 17
52 - 17 = 5x
x = 35 / 5
x = 7
Evaluate this expression: Write only the answer.
*
12 X (3 + 22) - 2 - 10
Your answer
Answers
Simplify
300x+-2+-10
Combine Like Terms
300x-12
ANSWER
300x-12
I WILL GIVE YOU BRAINLIEST!!
a pet store has 8 empty fish tanks that each hold 5544 cubic inches of water one goldfish requires a minimum of 1386 cubic inches of water.
What is the greatest number of goldfish that the pet store can have given the volume of water needed for one goldfish?
Answers
Answer:
32 goldfish
Step-by-step explanation:
Given:
Number of fish tanks = 8Volume of water per fish tank = 5,544 in³Water required by 1 goldfish = min 1,386 in³Number of fish per tank = water per tank ÷ water per goldfish
= 5544 ÷ 1386
= 4
Therefore, each tank can hold a maximum of 4 goldfish.
Greatest number of goldfish = number of tanks × fish per tank
= 8 × 4
= 32
Which of the following tables represents a linear function?
Answers
The required relationship shown between x and y in table 1 is a function.
What are functions?Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variables.
Here,
The relationship shown between x and y in table 1 is a function.
To determine if the relationship between x and y is a function, we need to check if each x-value corresponds to exactly one y-value.
We can see that for each x-value, there is only one corresponding y-value:
When x = -6, y = 2
When x = -4, y = 4/3
When x = -2, y = 2/3
When x = 0, y = 0
When x = 2, y = 2/3
Each value of x corresponds to only one value of y, so the relationship is a function.
Therefore, the relationship shown between x and y in table 1 is a function.
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Evaluate
2^-4/4^0
Write your answer as a fraction in simplest form
Answers
Answer:
1/16 or 0.0625
Step-by-step explanation:
Im not sure but this may be the answer
The given fraction in simplest form is 1/16.
What is the fraction?In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.
The given fraction is 2⁻⁴/4⁰.
Now, 2⁻⁴/4⁰ =2⁻⁴/4⁰
= 2⁻⁴/1
= 1/2⁴
= 1/16
Therefore, the given fraction in simplest form is 1/16.
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If every 2 cm on a scale drawing is equal to 7 feet in real life, which lines on the drawing would be greater than 21 feet in real life? Select all that apply. A) 7 cm B) 5 cm C) 9 cm D) 12 cm
Answers
The correct answers are A) 7cm, C) 9cm and D) 12cm
Define the Conversion of units?The process of changing a given quantity that is expressed in one unit of measurement to another unit of measurement that is equivalent in value is referred to as conversion of units.
If every 2 cm on a scale drawing is equal to 7 feet in real life, then we can use proportions to find out which lines on the drawing would be greater than 21 feet in real life.
Let x be the length of a line on the scale drawing in centimeters. Then, we can set up the following proportion:
⇒ \(\frac{2cm}{7 feet} = \frac{x cm }{yfeet}\)
where y is the length of the line in real life. Solving for y, we get:
⇒ \(y = \frac{7 feet} {2cm} *x\)
⇒ \(y = 3.5 x feet\)
If we put x = 2cm (given) then, y = 7 feet
For y = 21 feet, the value of x = 6cm.
Therefore, any line on the scale drawing that is greater than 6cm in length corresponds to a length greater than 21 feet in real life.
So, the lines on the drawing that are greater than 21 feet in real life are:
A) 7cm, C) 9cm, D) 12cm
Therefore, the correct answers are A) 7cm, C) 9cm and D) 12cm
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(I will give a brainliest)
Please help :)
Answers
1=8
3=12
5=16
total cost for 7 would be 20
The numbers of beads on 500 handcrafted bead necklaces follow a normal distribution whose mean is 24 beads and standard deviation is 4 beads. Which sentence most closely summarizes the data?
Answers
About 80 necklaces have more than 28 beads. Then the correct option is C.
What is a normal distribution?The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.
The numbers of beads on 500 handcrafted bead necklaces follow a normal distribution whose mean is 24 beads and the standard deviation is 4 beads.
P(x > 28) = P(x - 24 / 4 > 28 - 24 / 4)
P(x > 28) = P(x - 24 / 4 > 1)
P(x > 28) = 1 - ∅1
P(x > 28) = 1 - 0.8413
P(x > 28) = 0.1587
Multiply both sides by 500, then we have
500 P(x > 28) = 0.1587 × 500
500 P(x > 28) = 79.35
500 P(x > 28) ≈ 80
About 80 necklaces have more than 28 beads. Then the correct option is C.
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The missing options are given below.
A. About 24 devices have more than 28 beads.
B. About 48 necklaces have more than 28 beads.
C. About 80 necklaces have more than 28 beads.
D. About 96 necklaces have more than 28 beads.
If you know the answer put and explanation for it please thank you
Answers
Answer:
14 students have to retake the test
Step-by-step explanation:
to calculate the mean mark as
sum of ( product of mark and frequency ) ÷ total
mean = \(\frac{14(2)+15(10)+16(2)+17(3)+18(13)}{30}\)
= \(\frac{28+150+32+51+234}{30}\)
= \(\frac{495}{30}\)
= 16.5
students who score less than 16.5 will retake the test , that is
2 scored 16 , 10 scored 15 , 2 scored 14
number who have to retake test = 2 + 10 + 2 = 14
Write an equation of the line that passes through (2,-1) and (-3,3)
Answers
Answer:
Y=-4/5x+3/5y
Step-by-step explanation: first get the gradient
3--1/-3-2
=4/-5
y-3/x+3=4/-5
-5y+15=4x+12
-5y=4x-3
y=4/-5x+3/5
My cookbook's pancake recipe states that it makes 12 standard sized pancakes. The nutritional information says 2 pancakes is a serving containing 150 calories. For breakfast, I prepared half a recipe, but made smaller sized pancakes, so ended up preparing 8 pancakes. I ate 4 of them. How many calories did I consume?
Answers
Answer:
225 calories
Step-by-step explanation:
1 recipe makes
12 standard sized pancakes
2 pancakes are 1/6 of the recipe
1/6 of the recipe has 150 calories
6 × 150 calories = 900 calories
The full recipe of 12 pancakes has 900 calories
1/2 recipe was made
1/2 recipe has 1/2 × 900 calories = 450 calories
1/2 recipe made 8 pancakes
4 pancakes are half of the half recipe or 1/4 recipe
1/4 × 900 calories = 225 calories