You score a 65% on your AP Statistics Exam and a 78% on your Economics Exam. The AP Statistics scores were normally distributed with an average of 60% and a standard deviation of 6%. The Economics scores were also normally distributed with an average of 75% and standard deviation of 2.5%. In which class did you perform better relative to the class average? Be sure to justify your answer.

Answers

Answer 1

Answer:

His economics grade had a higher z-score, so you performed better relative to the class average in economics.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In which class did you perform better relative to the class average?

In whichever class you had the higher z-score.

Statistics:

Scored 65, mean 60, standard deviation 6. So [tex]X = 65, \mu = 60, \sigma = 6[/tex]

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{65 - 60}{6}[/tex]

[tex]Z = 0.83[/tex]

Economics:

Scored 78, Mean 75, Standard deviation 2.5. So [tex]X = 78, \mu = 75, \sigma = 2.5[/tex]

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{78 - 75}{2.5}[/tex]

[tex]Z = 1.2[/tex]

His economics grade had a higher z-score, so you performed better relative to the class average in economics.


Related Questions

Jessica bought the ingredients to make chicken soup, and wanted to make a double batch, which would be 18 cups of soup. A quick Google search told her that this was 259.9 cubic inches. She hoped the soup pot below would be big enough. The soup pot is 9 inches tall with a radius of 3.5 inches. What is the volume of the soup pot? Answer choices are rounded to the nearest tenth cubic inch. 169.6 cubic inches 890.6 cubic inches 197.9 cubic inches 346.4 cubic inches

Answers

Answer: 346.4 in^3

Step-by-step explanation:

The pot can be thinked as a cylinder:

The volume of a cylinder is equal to:

V = (pi*r^2)*h

where h is the height, r is the radius and pi = 3.1416

Here we have that: r = 3.5in, h = 9in.

Then the volume is:

V = 3.1416*(3.5in)^2*9in = 346.4in^3

Is OCD and perfectionism the same thing. I need an explanation thanks

Answers

Answer: ocd can be characterized as an extreme form of perfectionism, where anything can lead to anxiety fear, and distress. perfectionism is a personality trait where one drives for flawless ness, it becomes ocd when those strives cause literal disorder in ones life

Step-by-step explanation:

I have the brainy app on my phone, and I have plus on my phone, but when I try to log in on my computer< it says I still need to upgrade, how do I use brainy plus on my computer?

Answers

to use brainy plus on your computer you need to log in with the same account you used on the phone

Answer:

try to restart and delete then re download the app:)

Step-by-step explanation:

22. Find the perimeter of the square:
28

Answers

Answer:

  56√2 ≈ 79.20

Step-by-step explanation:

The hypotenuse of an isosceles right triangle is √2 times the side length, so the side length here is ...

  s·√2 = 28

  s = 28/√2

The perimeter is 4 times the side length, so is ...

  P = 4s = 4·28/√2

  = 4·28·(√2)/2 . . . . . multiply by (√2)/(√2) to rationalize the denominator

  = 56√2 ≈ 79.195959

The perimeter of the square is 56√2, about 79.20 units.

Direct mail advertisers send solicitations​ ("junk mail") to thousands of potential customers in the hope that some will buy the​ company's product. The response rate is usually quite low. Suppose a company wants to test the response to a new flyer and sends it to 1030 people randomly selected from their mailing list of over​ 200,000 people. They get orders from 103 of the recipients.

Required:
Create a 95% confidence interval for the percentage of people the company contacts who may buy something. (Show your work. Step by step)

Answers

Answer:

The interval is (.0817, .118).

Step-by-step explanation:

Let's make this interval! The easy way is to go to STAT->TEST->A, 1-prop z-int, but I will show the long way.

1. Conditions

First we must check the conditions.

Randomization condition: The sample is given to be random, so we can assume independence.

Success/failure condition: Both np>10 and nq>10 must be met.

np = 1030(103/1030) = 103 ✓ nq = 1030(927/1030) = 927 ✓

10% condition: The sample cannot be greater than 10% of the population.

10n < N, 10(1030) < 200000 ✓

All conditions are met, so we can use a 1-proportion z-interval to represent the data.

2. Mechanics

Find [tex]\hat{p}[/tex], the sample proportion.

103/1030 = .1

[tex]\hat{q}[/tex], then, the probability of not p, is 1 - .1 = .9

Find z* (z star), the critical z-value.

You can do this on your calculator using 2nd->VARS->3 (or you can memorize it - it's 1.96. Winky face.) This is called the invNorm function, that takes the left side area under the normal curve. But what do we plug in to the invNorm function?

invNorm(.975) = 1.96

Plug values into the equation.

[tex]\hat{p}[/tex] ± z*[tex]\sqrt{\frac{\hat{p}\hat{q}}{n} }[/tex]

.1 ± 1.96[tex]\sqrt{\frac{.1*.9}{1030} }[/tex]

.1 ± 1.96(.00935)

.1 - .0183 = .0817

.1 + .0183 = .118

(.0817, .118)

3. Conclusion

Based on this sample, we are 95% confident that the proportion of people the company contacts who may buy something is between .0817 and .118. That isn't very likely, but maybe they'll make a little profit!

anyone knows the answer

Answers

Answer:C

Step-by-step explanation:

3.1 x 10^(-4) x 8.5 x 10^(-2)

3.1 x 8.5 x 10^(-4) x 10^(-2)

26.35 x 10^(-4-2)

26.35 x 10^(-6)

2.635 x 10^1 x 10^(-6)

2.635 x 10^(1-6)

2.635 x 10^(-5)

The answer plz hurryyy

Answers

Answer:

The answer is that the y-coordinate should be -3 1/2.

Step-by-step explanation:

First, look at the graph. On the x-axis, the dot is at -5, since it is 5 units to the left of the origin. On the y-axis, the dot is at -3 1/2. It is between -3 and -4, not -4 and -5. Therefore, the answer is that the y-coordinate should be -3 1/2, not -4 1/2. You can also check by seeing if -4 1/2 is reasonable. -4 1/2 would mean the dot would be more than 4 units below the origin. On the graph, the dot is clearly above the -4 mark, so the -4 1/2 must not be correct.

find the missing measurement lesson 13.1, 13.2 A=62.5 length is 14 and width is 11 what is the highth.​

Answers

Answer:

11.36

Step-by-step explanation:

A=1/2*b*h

62.5=1/2*11*x(height)

62.5= 1/2*11*x

62.5=5.5*x

X=62.5/5.5

=11.36

Round 38 to the nearest ten. Enter your answer in the box below.

Answers

Answer:

40

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

Here are the rules;

• If the number undergoing the rounding is followed by 5, 6, 7, 8, or 9, round the number up

• If the number undergoing the rounding is followed by 0, 1, 2, 3, or 4, round the number down.

Example: 32 and 38 rounded to the nearest ten is 30 and 40 respectively.

what is the area of the triangle shown below?

Answers

Answer: Please provide the triangle

James rented a car for 4 days plus $0.25 per mile. He took the collision waiver for $19.95 per day. He drove the car 352 miles. Gasoline cost $41.38. What was the total cost of renting the car?
1 point
$61.58
$149.33
$413.33
$209.18

Answers

Answer:

$209.18

Step-by-step explanation:

352 miles*$0.25 per mile = $88 for mileage.

$19.95 per day * 4 days = $79.80

88+ 79.80 + 41.38 for gass = $209.18 Total Cost

on a piece of paper, graph f(x)= {x if x<2 2 if x>2}

Answers

Answer:

  see below

Step-by-step explanation:

The graph has two parts. There is one line for x < 2. It has a slope of 1 and a y-intercept of 0.

The line for x > 2 is the horizontal line x=2.

The point at x=2 is not defined by the function you have posted here, so there is a "hole" in the graph at that point.

Answer:

the person above is correct

Step-by-step explanation:

:p

You have 9 pets:
4 fish,
1 cat,
2 dogs
and 2 birds. What is the probability a pet chosen at random is a dog or a four legged pet?

Answers

Answer:

1/3

Step-by-step explanation:

4 fish, 1 cat,2 dogs,and 2 birds = 9

dogs or 4 legged = cats and dogs = 1+2 = 3

P(dog or 4 legged) = number of dogs or 4 legged / total

                                 =3/9

                                =1/3

Answer:

Step-by-step explanation:

Total pets:

4+1+2+2 = 9

Dog or four legged pets: 2 + 1 = 3

Probability: 3/9 = 1/3

The Senate in a certain state is comprised of 58 ​Republicans, 39 ​Democrats, and 3 Independents. How many committees can be formed if each committee must have 3 Republicans and 2 ​Democrats?

Answers

YuAnswer:

Step-by-step explanation:

I really don't know the answer sorry

Kali has a 666 meter ladder that she wants to use to get her cat out of a tree. She puts the base of the ladder 222 meters away from the base of the tree.

How high into the tree will the ladder reach?
Round your answer to the nearest tenth of a meter.

Answers

I think it is 123 meters Answer:

Step-by-step explanation:

The value of 8 in the hundreds place is how many times the value of the 8 in the tens place

Answers

Answer:8 in the hundreds place is 10 times the value of the 8 in the tens place.

Step-by-step explanation:its easy

The hundreds place is 10 times of the tens place.

What is Algebra?

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Division means the separation of something into different parts, sharing of something among different people, places, etc.

The value of 8 in the hundreds place. If the value of the 8 is in the tens place. Then the number will be 880.

Then the number of times of the hundreds place and tens place will be given by the division of the numbers 800 and 80.

⇒ 800 / 80

⇒ 10

The hundreds place is 10 times of the tens place.

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ2

What equations have many solutions
76x+76=76x+76
76x+76=-76x+76
-76x+76=-76x+76
-76x+76=76x+76

Answers

Answer:

[tex]76x+76=76x+76\\-76x+76=-76x+76[/tex]

Step-by-step explanation:

They have the same values and the same signs, therefore, they cancel each other giving a result of 0=0

Answer:

0

Step-by-step explanation:

This equation actually has more than one equal sign

A local eat-in pizza restaurant wants to investigate the possibility of starting to deliver pizzas. The owner of the store has determined that home delivery will be successful if the average time spent on the deliveries does not exceed 34 minutes. The owner has randomly selected 23 customers and has delivered pizzas to their homes in order to test if the mean delivery time actually exceeds 34 minutes. Suppose the P-value for the test was found to be 0.0290. State the correct conclusion

Answers

Answer:

We conclude that the mean delivery time actually exceeds 34 minutes.

Step-by-step explanation:

We are given that the owner of the store has determined that home delivery will be successful if the average time spent on the deliveries does not exceed 34 minutes.

The owner has randomly selected 23 customers and has delivered pizzas to their homes in order to test if the mean delivery time actually exceeds 34 minutes. Suppose the P-value for the test was found to be 0.0290.

Let [tex]\mu[/tex] = average time spent on the deliveries.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\leq[/tex] 34 minutes    {means that the mean delivery time is less than or equal to 34 minutes}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 34 minutes     {means that the mean delivery time actually exceeds 34 minutes}

Now, the decision rule based on the P-value to whether null hypothesis should be accepted or rejected is given by;

If the P-value of test statistics is less than the level of significance, then we will reject our null hypothesis.If the P-value of test statistics is more than the level of significance, then we will not reject our null hypothesis.

Here, we assume that the level of significance is 5%.

Since, the P-value of test statistics is less than the level of significance as 0.029 < 0.05, so we have sufficient evidence to reject our null hypothesis.

Therefore, we conclude that the mean delivery time actually exceeds 34 minutes.

if a punnet of strawberrier weighs 100g
how many punnets would weigh 1 kg

Answers

Answer:

10

Step-by-step explanation:

1 kg = 1000 g

1000/100=10

Identify Y, inscribed angels

Answers

Answer:

  y = 2

Step-by-step explanation:

PQ is a diameter, so arc PQ has a central angle of 180°. Inscribed angle PRQ has a measure half that, or 90°. (An inscribed triangle with one side a diameter is a right triangle.)

Then you can write ...

  53y -16 = 90

  53y = 106 . . . . . add 16

  y = 106/53 = 2 . . . . divide by the coefficient of y

y = 2

Please help ASAP! I will mark Brainliest! Please answer CORRECTLY! No guessing! CHECK ALL THAT APPLY

Answers

Answer:

A) 26

E) 12

Step-by-step explanation:

11x ≥ 132

x ≥ 12

The solution set would include numbers greater than or equal to 12

Find the limit of the function by using direct substitution lim (x^2+8x-2) x-> 2

Answers

Answer:

[tex] lim_{x \to 2} x^2 +8x -2 [/tex]

And using the properties of limit we got:

[tex] lim_{x \to 2} x^2 +8 \lim_{x \to 2} x - lim_{x \to 2} 2 [/tex]

And replacing we got:

[tex] 2^2 + 8 (2) -2 = 4 +16-2 =18[/tex]

Step-by-step explanation:

For this case we want to find this limit:

[tex] lim_{x \to 2} x^2 +8x -2 [/tex]

And using the properties of limit we got:

[tex] lim_{x \to 2} x^2 +8 \lim_{x \to 2} x - lim_{x \to 2} 2 [/tex]

And replacing we got:

[tex] 2^2 + 8 (2) -2 = 4 +16-2 =18[/tex]

Do you remember the difference between a row and a column
in Math?

Answers

Answer:

Rows are the steps - they go left to right and are numbered 1,2,3,... Columns are the columns - they go up and down and are lettered A,B,C,... Cells are defined by the row and column they are in.

Step-by-step explanation:

Two trains leave stations 390 miles apart at the same time and travel toward each other. One train travels at 70 miles per hour while the other travels at 80 miles per hour. How long will it take for the two trains to meet?
Do not do any rounding.

Answers

Answer:

Let's denote:

x: the time both trains traveled.

Then, we have:

70x + 80x = 390

=> 150x = 390

=> x = 390/150 = 2.6 hour

Answer:

2.6 hours ( or 2 hours 36 minutes).

Step-by-step explanation:

The combined speed is 70+80 = 150 mph.

Speed = distance / time,  so time = distance / speed.

So the time when they will meet

=  390 / 150

= 2.6 hours.

The smallest multiple of 13 is​

Answers

Answer:

0

Step-by-step explanation:

The smallest (greater or equal to zero) multiple of 13 is 0

to get a positive multiple of 13 you have to multiply 13 by a natural number:

0 = 13×0

13 = 13×1

26 = 13×2

.

.

.

then the smallest one is 0.

A submarine is 48 m below sea level, and it descends 28 m.
How far below sea level is it?

Answers

Answer:

The submarine is 76 meters below sea level.

Step-by-step explanation: 48+28=76

If the sub is already 48 meters below sea level, and then it travels another 28 meters further down, you simply add 28 to 48.

Hector invests $20,000 at age 21. He hopes the investment will be worth $200,000 when he turns 40. If the interest compounds continuously, approximately what rate of growth will he need to achieve his goal? Round to the nearest tenth of a percent.

Answers

Answer:

12.12%

Step-by-step explanation:

We have that the formula is given by:

A = p * e ^ (r * t)

From here, we know that A = 200000; p = 20000 and the time we can calculate 40 - 21 = 19

if we replace we have:

200000 = 20000 * e ^ (19 * r)

we must calculate r:

e ^ (19 * r) = 200000/20000

e ^ (19 * r) = 10

19 * r = ln 10

r = ln 10/19

r = 0.1212

In other words, the rate of growth is 12.12%

Answer:

12.1%

Step-by-step explanation:

The ratio of the number of student in mr. Moore’s class compared to the number of student in miss Henry’s class is 5:4. The ratio of the number students in miss Henry’s class compared to the number of students on mr. Wilson’s class is 8:9. What is the ratio of number of students in mr. Moore’s class to mr. Wilson’s class?

Answers

Answer:

10:9

Step-by-step explanation:

First ratio is 5:4. 4 is equal to Henry class

If you múltiply the ratio by 2 you get

10:8, This ratio can be compared because now Henry class has 8

2(5:4)

10:8

8:9

Meaning that the answer is 10:9

The require ratio of number of students in Mr. Moore's class to Mr. Wilson's class is 10:9

What is Ratio?

The ratio can be expression as how many times one number contain another number.

For example, If any bag contain 4 apples and 8 oranges then the ratio of apple to orange is 4:8 while the ratio of the orange to the apple is 8:2

How to find ratio?

Consider M denote the number student present in the Mr. Moore's class

similarly H denote the number of student in miss Henry's class and W denote the number of student present in Mr. Wilson's class

then we have given that

M : H = 5 : 4 or

[tex]\frac{M}{H} = \frac{5}{4}[/tex]

Also we have H : W = 8 : 9

[tex]\frac{H}{W} = \frac{8}{9}[/tex]

Now multiply these two equations we have

[tex]\frac{M}{H}\times \frac{H}{W}=\frac{5}{4}\times\frac{8}{9}[/tex]

[tex]\frac{M}{W}= \frac{10}{9}[/tex]

The ratio of number of student in Mr. Moore's class to Mr. Wilson's class is 10:9

This is the conclusion to the answer.

Learn more about ratio here-

https://brainly.com/question/2328454

#SPJ2

Two figures are arranged as shown. Which of the following can be used to the area of the figure
shaded light gray?
9
9​

Answers

Answer:

[tex]9^{2} -x^{2}[/tex]

Step-by-step explanation:

The figure is shown in the image attached.

Notice that the shaded light gray area can be calculated by the difference of the bigger square and the smaller square.

The area of the bigger square is: [tex]A_{big}=9^{2}[/tex]

The area of the smaller square is: [tex]A_{small}: x^{2}[/tex]

The difference between these areas is: [tex]A=9^{2} -x^{2}[/tex]

Therefore, the expression that can be used to find the light gray area is: [tex]9^{2} -x^{2}[/tex]

Additionally, the expression [tex]x(9-x)+9(9-x)[/tex] is also a right answer, because it's equivalent to the first answer.

[tex]x(9-x)+9(9-x)=9x-x^{2} +81-9x=81-x^{2} =9^{2} -x^{2}[/tex]

Answer FAST! This is a HARD question! Good luck

Answers

Answer:

Step-by-step explanation:

I only know that number 2 is 56.

Other Questions
30 students apply for a scholarship,10 have college degrees18 have school certificates8 have both qualifications.(a) Draw a Venn diagram to show thiinformation.(b) How many students have noqualification? I need a step by step solution ASAP Which physical structures are present in amphibians, but not in reptiles, when they first hatch? Q1. What is the frequency of rotation of 1000 loop coil of area 20cm2 in a magnetic field of 5T to generate an emf that has a maximum value of 15.7V? Which of the following measures of variability can be used to compare two data sets? Two cars are doing a race around a 20-km track. They start from the same place at the same time. The speed of first car is 60 km/h, speed of second car is 80 km/h. How long will it take second car to lap the first car? Determine the change to diagonal one of a rhombus if the area is multiplied by 1/8 and diagonal two is multiplied by 1/2 . Answer: Diagonal one is multiplied by Critically evaluate how social media reports gender based violence What is the simplest form of this expression?5(-8m - 4) + (-5)(-9m - 5)Enter the correct answer.DOGDONEClear all+ ? avocados cost $3 per pound. write and graph an equation in two variables that represents the cost of buying avocados.pleasee hellpp asappp!!!if possible, whoever answers this can you put a picture of what the graph would look like please and thank you :) Do not do Number 3 or 2!Please help! I need them in complete sentences! I will award Brainliest and answer any questions you have just please help. Which cause and effect demonstrates a negative quality of laissez faire policies Read the following excerpt from the article "Vision, Voice and the Power of Creation: An Author Speaks Out," by T. A. Barron and answer the question that follows:Right now, I am spending a lot of time listening to the voice of a particularly compelling character: the young Merlin. In the end, I finally heard the voice of Merlin thanks to a surprising source: the haunting, mysterious hooting of a great horned owl outside the window of my Colorado home. As I listened to that owl's resonant [echoing] call in the pre-dawn hours one morning, something about it gave me a whole new cadence [rhythm], a whole new sound. And then, a whole new voice.The author states, "I finally heard the voice of Merlin thanks to a surprising source: the haunting, mysterious hooting of a great horned owl outside the window of my Colorado home." What is the author's implicit message in this statement?(10 points)Group of answer choicesThe author realized Merlin's voice should have the same qualities as the owl's voice.The author thought Merlin's voice should seem like it is hooting.The author wished he had thought of Merlin's voice sooner.The author knew the owl would bring Merlin's voice to life. A spinner marked with four sections blue, green, yellow, and red was spun 100 times. The results are below. Find the experimental probability of landing on green? * Can anyone help with this math problem ? Which of the following is stored in the skeletal system?A. potassiumB. calciumphosphorousD. sodium Kelly needs 1/8 cups of sugar to make 1/4 of her cookie recipe. How much sugar does she need to make the entire recipe? Plz help! Will give brainiest!For the girl to lift this rock, she must push her end down _____ to raise the rock _____.A.a lot; a littleB.a little; a lotC.a little; a little What group of hired soldiers helped Rome conquer enemies and expand it's territory Image by HistoricairWhich country is located at number 4 on the map above?A. SingaporeB. the PhilippinesC. IndonesiaD. MalaysiaPlease select the best answer from the choices providedA.SingaporeB. the PhilippinesC. IndonesiaD. Malaysia I know the answer it is B. The philippines on edgeunity or on any other homework it is the philippines