After deducting grants based on need, the average cost to attend the University of Southern California (USC) is $27,175 (U.S. News & World Report, America’s Best Colleges, 2009 ed.). Assume the population standard deviation is $7,400. Suppose that a random sample of 60 USC students will be taken from this population.

a. Refer to Exhibit 2. What is the value of the standard deviation of the mean? (Note: keep two decimal places.)

b.What is the probability that the sample mean will be more than $27,175

c.What is the probability that the sample mean will be within $1,000 of population mean? (Note: keep two decimal places for the z value and four decimal places for the final probability value.)

d.What would be the probability in Part c if the sample size were increased to 100? (Note: keep two decimal places for the z value and four decimal places for the final probability value.)

Answers

Answer 1

The solutions are:

(a) Standard error is 957.04. (b) The probability is 50%. (c)The probability is 0.8491. (d) The probability is 0.8617.

To calculate the values, use the standard error formula for the sample mean:

(a)

The standard error is given by:

[tex]Standard\ error =\dfrac{ Population \ standard \ deviation}{\sqrt{sample\ size}}\\Standard\ error=\dfrac {\$ 7,400 }{ \sqrt60}\\Standard\ error =\ $957.04[/tex]

(b)

To find the probability that the sample mean will be more than $27,175, convert it into a z-score and then find the area under the normal distribution curve:

z = (sample mean - population mean) / standard error

z = ($27,175 - $27,175) / $957.04

z = 0

Since the z-score is 0, the area under the curve to the right of this point is 0.5 or 50%.

c. To find the probability that the sample mean will be within $1,000 of the population mean, we need to find the area between the range of $(27,175 - $1,000) and $(27,175 + $1,000).

Lower limit: $27,175 - $1,000 = $26,175

Upper limit: $27,175 + $1,000 = $28,175

Now, we calculate the z-scores for both limits:

lower = ($26,175 - $27,175) / $957.04 ≈ -1.045

upper = ($28,175 - $27,175) / $957.04 ≈ 1.045

Using a standard normal distribution table or calculator, the probability of a z-score being between -1.045 and 1.045 is approximately 0.8491.

(d)

If the sample size were increased to 100.

[tex]Standard error = \dfrac{ \$7,400}{ \sqrt{100}} \\Standard error = \$740[/tex]

Find the probability that the sample mean will be within $1,000 of the population mean, did in part c:

Lower limit: $27,175 - $1,000 = $26,175

Upper limit: $27,175 + $1,000 = $28,175

lower = ($26,175 - $27,175) / $740

lower ≈ -1.351

upper = ($28,175 - $27,175) / $740

upper ≈ 1.351

Using a standard normal distribution table or calculator, the probability of a z-score being between -1.351 and 1.351 is approximately 0.8617.

Hence,

Standard error is 957.04.The probability is 50%.The probability is 0.8491.The probability is 0.8617.

Learn more about Probability here:

https://brainly.com/question/32117953

#SPJ12


Related Questions

PLEASE PLEASE PLEASE SOMEONE HELP ME PLEASE I BEG U PLEASE PLEASE !!!!!!!

Answers

Answer:

Right ear     a.d. = auris dextra

Step-by-step explanation:

mathematics may not have been the best place to ask this question.

Answer:

ad meaning right ear so C

Step-by-step explanation:

Hey mathematicians ! Can anyone help me with these problems please ! Will give brainly !

Answers

27) 115=5(5a-2)

115= 25a-10

125=25a

a=5

28) -72=-x-6(x+5)

-72=-7x-30

-42=-7x

x=6

i did two of them. now i gtg so won't do the rest

Given that f(x) = ax – 5 and f(4) = 15, determine the value of a.

Answers

Given that f(x) = ax – 5 and f(4) = 15, then the value of a is 5

The given function is:

f(x)  =  ax  -  5

If f(4)  =  15, then x = 4

Substitute x = 4 into f(x) = ax - 5

f(4)  =  a(4)  -  5

15   =  4a   -  5

Solve for a by adding 5 to both sides

15  +  5  =  4a  -  5  +  5

20    =  4a

Divide both sides by 4

4a/4   =  20/4

a    =  5

Given that f(x) = ax – 5 and f(4) = 15, then the value of a is 5

Learn more on linear functions here: https://brainly.com/question/15602982

Solve and check answer 3(4-5x)=3(4x+3)

Answers

Hey there!

3(4 - 5x) = 3(4x + 3)

3(4) + 3(-5x) = 3(4x) + 3(3)

12 - 15x = 12x + 9

-15x + 12 = 12x + 9

SUBTRACT 12x to BOTH SIDES

-15x + 12 - 12x = 12x + 9 - 12

SIMPLIFY IT!

-27x + 12 = 9

SUBTRACT 12 to BOTH SIDES

-27x + 12 - 12 = 9 - 12

CANCEL out: 12 - 12 because it gives you 0

KEEP: 9 - 12 because it helps solve for the x-value

NEW EQUATION: -27x = 9 - 12

SIMPLIFY IT!

-27x = -3

DIVIDE -27 to BOTH SIDES

-27x/-27 = -3/-27

CANCEL -27/-27 because that gives you 1

KEEP: -3/-27 because it helps solve for the x -value

NEW EQUATION: x = -3/-27

SIMPLIFY IT/REDUCE the FRACTION!

x = 1/9

Therefore, your answer is: x = 1/9

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Using Converting The Percentages First Into Fractions, Determine The Following

a) 10% of 120
b) 25% of 16
c) 30% of 20
d) 40% of 25
e) 75% of 48
f) 60% of 140
g) 90% of 50
h) 12.5 of 32​

Answers

Answer:

a)12

b)4

c)6

d)10

e)36

f)84

g)45

h)4

HELP ASAP
The temperature was -1°F at noon and dropped to -14°F by the evening.

What was the change in temperature?

13°F
-13°F
-15°F
15°F

Answers

ΔT = T(final)-T(initial)

ΔT= -14 - (-1)
= -14 + 1
= -13F

Answer:

The change in temperature is -13°F.

Step-by-step explanation:

The change in temperature is,

→ -1 + x = -14

→ x = -14 + 1

→ [ x = -13 ]

Therefore, -13°F is the change.

If I have 5 classes and they each take 40 minutes how many hours will it take me to do all my classes?

Answers

Answer:200 minutes or 3 hours and 20 minutes

Step-by-step explanation:

multiple 5 and 40 and you’ll get the answer 200

Answer:

200 minutes which is 3 hours and 20 minutes.

Step-by-step explanation:

FIrst you multiply 5 x 40 which equals 200

To find out how many hours there are in 200 minutes, you divide it by 60.

200 divided by 60 = 3.3...

3 hours. The remander is 20 minuites and there you have it.

​​​​​​Jocelyn gave the cashier $50 to pay for 3 shirts. The cashier gave her $5.03 in change. Each shirt cost the same amount. What is the cost in dollars and cents for each pair of shirts?

Answers

Answer:

14.9

Step-by-step explanation:

50-5.03 = 44.97

44.97 ÷ 3 = 14.99

A line with a slope of 2 passes through the point (3,9).
Write an equation for this line in point-slope form.

Answers

Answer:

y-9=2(x-3)

Step-by-step explanation:

y-y1=m(x-x1)

y-9=2(x-3)

A boat is traveling at a constant speed. In 2 hours, the boat travels 180 miles. How many hours will it
take the boat to travel 225 miles?

Answers

Answer:

2 1/2 hours

Step-by-step explanation:

For 1 hour, it would travel 90 miles.

For half of 90 which is 45 it would travel 1/2 hr.

225-180 is 45 miles, which is another half hr.

2 hrs plus 1/2 hr is 2 1/2 hours.

can anyone pls help?

Answers

Answer:

5x+12+x'

_______

2x'-2x-4

'=2

Find the sum. 2/5(d-10)-2/3(d+6)

Answers

Answer:

-4d

Step-by-step explanation:

L.c.m=15

15×2/5(d-10)-2/3×15(d+6)

3×2(d-10)-2×5(d+6)

6(d-10)-10(d+6)

6d-60-10d-60

6d-10d-60-60

-4d-0

-4d

Pleaseeeee heeeeelp!!!

Answers

The answer is
A=35
B=14
C=5

Answer:

a=35 b=14 c=5

Step-by-step explanation:

a

180-55-90=35

b

b+6=20

b=14

c

4c-6=14

14+6=20

20/4=5

which system of equation does the graph represent

Answers

we cant answer these type of questions if theres no picture of the graph sorry

Students from CAMPA participated in a school fundraiser. The six graders raised $600. The seventh graders raised 35% more than the six graders. The eighth graders raised. 10% less than the seventh graders. What is the total amount the school raised?

Answers

Answer:

$2,139 was the total amount the school raised.

Step-by-step explanation:

35% of 600= 210

210+600 = $810

10% of 810= 81

810-81= $729

6th Graders= $600

7th Graders= $810

8th Graders= $729

Find a polynomial with the following zeros.

HELPPPP ASAPPP

Answers

Answer:

x³ - 4x² + 2x + 4 = 0

Here's how I solved this:

You start off by rewriting the zeros into factors:

1 - √3    →    x = 1 - √3    →    (x - 1 - √3)

  2        →    x = 2           →    (x - 2)

1 + √3   →    x = 1 + √3   →    (x - 1 + √3)

Now you want to multiply the factors together:

     (x - 1 - √3) · (x - 2) · (x - 1 + √3)

- Multiply the first two factors together -

                (x - 1 - √3) · (x - 2)

                              ↓

    (x · x - x · 2 - √3 · x + √3 · 2 - x + 2)

 

   - Combine like terms and simplify -

    (x · x - x · 2 - √3 · x + √3 · 2 - x + 2)

                              ↓

          (x² - 3x - √3 · x + 2√3 + 2)

      - Now multiply the third factor -

   (x² - 3x - √3 · x + 2√3 + 2)(x - 1 + √3)

                              ↓

(x² · x + x² · √3 - x² - 3x · x - 3x · √3 + 3x - √3 · xx - √3 · x · √3 +√3 · x + 2 · √3 · x + 2 · √3 · √3 - 2 · √3 + 2x + 2 · √3 - 2)

                              ↓

(x³ + x² · √3 - x² - 3x² - 3x · √3 + 3x - √3 + 3x - √3 * x² - x · 3 + √3 · x + 2 · √3 · x + 2 · 3 - 2 × √3 + 2x + 2 √3 - 2)

   - Combine like terms and simplify -

(x³ + x² · √3 - x² - 3x² - 3x · √3 + 3x - √3 + 3x - √3 * x² - x · 3 + √3 · x + 2 · √3 · x + 2 · 3 - 2 × √3 + 2x + 2 √3 - 2)

                              ↓

                 x³ - 4x² + 2x + 4

--------------------------------------------------------------------------------------------------------------

And there we get our solution: x³ - 4x² + 2x + 4  

can someone please help me with this and the first to answer will get marked as brainiest also i need the work to be shown cause i know the answer but just not the work cause i’m confused pls help

Answers

Answer:

x = 3

Step-by-step explanation:

a triangle has 180 degrees in all

a square for an angle is 90 degrees

we can add them all together and get 180

90 + 45 + 8x + 21 = 180

combine like terms

156 + 8x = 180

subtract 156 to each side

8x = 24

then find x

x = 3

Answer:

x=3

Step-by-step explanation:

So the sum of angles of triangle is always 180 degrees.

We already have 45 and 90 but 8x+21 is unknown.

We can solve this by making an equation which is

45 + 90 + (8x+21) = 180.

If we solve this it will be

8x+21+135=180

8x+156 (-156) =180 (-156)

8x (/8) = 24 (/8)

x=3

A father is 33 years old. Which is 3 less than 12 times his son's age. How old is the son?

Answers

Answer:

His son is 3 years old.

Step-by-step explanation:

33 years old ... 3 less than ....  =  36

36/12  =  3

Giải phương trình vi phân sau
Y"=2y'+y=e^x

Answers

You likely mean to write the differential equation,

y'' - 2y' + y = exp(x)

The homogeneous part

y'' - 2y' + y = 0

has characteristic equation

r² - 2r + 1 = (r - 1)² = 0

with a root at r = 1 with multiplicity 2, so the characteristic solution is

y = C₁ exp(x) + C₂ x exp(x)

For the particular solution, we assume an ansatz

y = ax² exp(x)

where a is an unknown constant. Differentiating the ansatz twice:

y' = ax² exp(x) + 2ax exp(x) = (ax² + 2ax) exp(x)

y'' = (ax² + 2ax) exp(x) + (2ax + 2a) exp(x) = (ax² + 4ax + 2a) exp(x)

Substitute y and its derivatives into the DE:

(ax² + 4ax + 2a) exp(x) - 2 (ax² + 2ax) exp(x) + ax² exp(x) = exp(x)

Solve for a :

(ax² + 4ax + 2a) - 2 (ax² + 2ax) + ax² = 1

2a = 1

a = 1/2

Then the particular solution is

y = 1/2 x² exp(x)

The general solution is then

y = C₁ exp(x) + C₂ x exp(x) + 1/2 x² exp(x)

subtract the polynomials (4x^2-9x-7)-(3x^2-5x-6)

Answers

Answer:

x^2 - 4x - 1

Step-by-step explanation:

Can someone help me out? Will mark brainiest

Answers

Ok done. Thank to me :>

Miguel buys eggs and apples at the store.
• He pays a total of $56.97.
• He pays a total of $6.17 for the eggs.
• He buys 8 bags of apples that each cost the same amount.
.
Write and solve an equation which can be used to determine x, how much each bag
of apples costs.

Answers

The cost of each bag of apple is $6.35

Let the cost of a bag of apple be x

If Miguel buys eggs and apples at the store.

• He pays a total of $56.97.

• He pays a total of $6.17 for the eggs.

• He buys 8 bags of apples that each cost the same amount

The correct equation that represents the statement will be given as:

6.17 + 8x = 56.97

Make x the subject of the formula

8x = 56.97 - 6.17

8x = 50.8

x = 50.8/8

x = 6.35

Hence the cost of each bag of apple is $6.35

Learn more on equations here: https://brainly.com/question/2972832

You have been assigned to determine whether more people prefer Coke or Pepsi. Assume that roughly half the population prefers Coke and half prefers Pepsi. How large a sample do you need to take to ensure that you can estimate, with 95% confidence, the proportion of people preferring Coke within 3% of the actual value?

Answers

You have to add.

Step-by-step explanation:

I'm trash at math.

Carla waters the flowers every other day and
pulls weeds every 5th day. If she did both
chores today, how many days until she has to
do both chores again on the same day?

Answers

Answer:

Using the number 4 as a place holder I think it would be 20 days before she has both chores on the same day

x=y^2+4y+4 solve for y

Answers

Answer:

y=

x

−2

y=−

x

−2, x≥0

y=−

x−2, x≥0

Step-by-step explanation:

LAST ATTEMPT MARKING AS BRAINLIEST!! (Graph the image of the figure using the dilation given)

Answers

Answer:

There ya go

Step-by-step explanation:

9. The 10,000 seat stadium is 89% full. How many people are watching the game inside the stadium? with solution pls. ​

Answers

What they said mannn^^^^^^

A basketball player made 80 out of 100 attempted free throws what percent of free throws was made ?

Answers

Answer:

8/10

Step-by-step explanation:

id hope your have a great day

Answer:

80%

Step-by-step explanation:

80÷100=.8 which is 80%

A large community college has professors and lecturers. The total number of faculty members is 136. The school reported that they have 6 professors for every 11 lecturers. How many professors does the community college employ?

Answers

Your answer is 88 I believe.

What are the coordinates of B

Answers

Answer:

(-4,-5)

Step-by-step explanation:

The coordinates of the midpoint for x = sum of x/2=2

The coordinates of the midpoint for y = sum of y/2=-2

firstly to work out x coordinate:

[tex] \frac{x + 8}{2} = 2[/tex]

rearrange to find x which is -4

work out y coordinate:

[tex]\frac{y + 1}{2} = - 2[/tex]

rearrange to find y which is -5

so coordinates are (-4,-5)

Other Questions
Simplify. Dividing radicals Although all organelles of the eukaryotic cell interact with each other within the cell to maintain homeostasis, the mitochondrion has a unique evolutionary history. It is proposed that this organelle originated as an engulfed aerobic bacterial cell that lived in a symbiotic relationship with its host cell. This explanation for the origin of the mitochondria can be supported by multiple lines of evidence. Select ALL statements that could provide accurate support for the theory of endosymbiosis as it relates to the mitochondrion. A) Mitochondria have multiple membrane layers. B) Mitochondria are the largest and most numerous organelle in the cell. C) Mitochondria have their own ribosomes separate from the ribosomes in the cell. D) Mitochondria have their own DNA that resembles the circular chromosome of bacteria. Eliminate E) Mitochondria have the ability to control when the cell undergoes mitosis or exits the cell cycle. Which inequality represents all the solutions of 8(6x 7) < 5(9x 4)? The coastal plains are fertile. True or False. Cotton grows well in the Northeast. True or False. Select the three nations that explored most of the United States. Italy, Spain, England, France, Germany. What was the period of time when Congress tried to punish the South for the Civil War? Reconstruction Period, Retribution Period, Renaissance Period, Revolution Period. Settlers used rivers for travel and exploration. True or False. Brainliest for best answers! Does the graph represent a function? Shivani had 3/10 of a pound of blueberries. Shivani let her friend Rosa eat 1/4 of theblueberries. How many pounds of blueberries did Rosa eat?Write your answer as a fraction or as a whole or mixed number.apounds 135% as a fraction or a mixed number fully simplified please PLEASE HELP ME, I NEED HELP ASAP!!!! :(ty ty Luke tried his best to remember the items from his grocery list he left at home, but he could only remember the first few items. This is an example of __________. A. Primacy B. Recency C. Chunking D. Blocking Please select the best answer from the choices provided A B C D. Not sure where to start grade de malha metlica da janela wiremeshaibeiduo.pt Which graph best represents the solution set of y 3 x 4? Listen and choose the correct option.Based on the audio, what's the time? 2:20 8:43 3:24 9:33I asked the question and here's the answer: B. 8:43 When the sea level rises, an ocean may invade a river valley, producing a nearshore body of water of mixed and variable salinity termed a(n) A person who is not satisfied with an appellate courts decisionA)can take the case to another states court. B)can take the case to a different trial court. C)can take the case to a higher court.D)can take the case to a federal court. What expression is equal to 4/8 How far do you think a plate can move in one day? which two observers would be experiencing the same apparent solar time? please help due any minute 1. You are planning an extended trip to Mexico. You have a new smartphone to keep in touch with your friends but are concerned about the roaming charges since you will be outside the home network service area. Your plan costs $40.00 per month plus $0.35 per minute for roaming charges. Write a linear model relating your monthly cost, C, and the roaming minutes, t.A: C = $40 + $0.35tB: C = $40 $0.35tC: C = $0.35 + $40tD: C = $0.35 $40t