A standardized​ exam's scores are normally distributed. In a recent​ year, the mean test score was 1521 and the standard deviation was 314. The test scores of four students selected at random are 1920​, 1290​, 2220​, and 1420. Find the​ z-scores that correspond to each value and determine whether any of the values are unusual

Answers

Answer 1

Answer:

A score of 1920 has a z-score of 1.27.

A score of 1290 has a z-score of -0.74.

A score of 2220 has a z-score of 2.23.

A score of 1420 has a z-score of -0.32.

The score of 2220 is more than two standard deviations from the mean, so it is unusual.

Step-by-step explanation:

When the distribution is normal, we use 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.

If X is 2 or more standard deviations from the mean, it is considered unusual.

In this question, we have that:

[tex]\mu = 1521, \sigma = 314[/tex]

Score of 1920:

X = 1920. Then

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

[tex]Z = \frac{1920 - 1521}{314}[/tex]

[tex]Z = 1.27[/tex]

A score of 1920 has a z-score of 1.27.

Score of 1290:

X = 1290. Then

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

[tex]Z = \frac{1290 - 1521}{314}[/tex]

[tex]Z = -0.74[/tex]

A score of 1290 has a z-score of -0.74.

Score of 2220:

X = 1290. Then

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

[tex]Z = \frac{2220 - 1521}{314}[/tex]

[tex]Z = 2.23[/tex]

A score of 2220 has a z-score of 2.23.

Since it is more than 2 standard deviations of the mean, the score of 2220 is unusual.

Score of 1420:

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

[tex]Z = \frac{1420 - 1521}{314}[/tex]

[tex]Z = -0.32[/tex]

A score of 1420 has a z-score of -0.32.


Related Questions

The probability that an event will happen is P(E)=34. Find the probability that the event will not happen.

Answers

Answer:

.66

Step-by-step explanation:

1minus .34

Correct me if I am wrong

Please answer this correctly

Answers

Answer:

538

Step-by-step explanation:

l x w

7x39

12x20

5x5

538

Solve Systems of Algebraic Equations in Two Variables
Hello I need some help on setting up 2 equations of this problem. The answers are cheeseburger costs $1.55 and the milkshake $0.85

Four cheeseburgers and two chocolate milkshakes cost a total of $ 7.90. Two
Shakes cost 15 cents more than a hamburger with
cheese so What is the price of a cheeseburger?
And the price of a shake?

Answers

Answer:

4c+ 2m = 7.90

2m -.15 = c

Step-by-step explanation:

Let c = cheese burger

m = milkshake

4c+ 2m = 7.90

2m -.15 = c

Substitute into the first equation

4( 2m -.15) +2m = 7.90

Distribute

8m -.6 +2m = 7.90

Combine like terms

10m - .6 = 7.90

Add .6 to each side

10m = 7.90+.6

10m = 8.50

Divide by m

10m = 8.50/10

m = .85

Now find c

2m -.15 = c

2(.85) - .15=c

1.70-.15 = c

1.55 =c

On hot, sunny, summer days, Jane rents inner tubes by the river that runs through her town. Based on her past experience, she has assigned the following probability distribution to the number of tubes she will rent on a randomly selected day.

x 25 50 75 100 Total
P(x) 0.16 0.36 0.38 0.10 1.00

Find the probability expressions: (Round your answers to 2 decimal places.)

a. P(X=50)P(X=50).
b. P(X≤75)P(X≤75).
c. P(X>50)P(X>50).
d. P(X<100)P(X<100).

Answers

Answer:

a. P(X=50)= 0.36

b. P(X≤75) =  0.9

c. P(X>50)=  0.48

d. P(X<100) = 0.9

Step-by-step explanation:

The given data is

x                      25        50       75        100          Total

P(x)                0.16       0.36    0.38    0.10          1.00

Where X is the variable and P(X) = probabililty of that variable.

From the above

a. P(X=50)= 0.36

We add the probabilities of the variable below and equal to 75

b. P(X≤75) = 0.16+ 0.36+ 0.38= 0.9

We find the probability of the variable greater than 50 and add it.

c. P(X>50)= 0.38+0.10=  0.48

It can be calculated in two ways. One is to subtract the probability of 100 from total probability of 1. And the other is to add the probabilities of all the variables less than 100 . Both would give the same answer.

d. P(X<100)= 1- P(X=100)= 1-0.1= 0.9

ASK YOUR TEACHER Two streets meet at an 84° angle. At the corner, a park is being built in the shape of a triangle. Find the area of the park if, along one road, the park measures 190 feet, and along the other road, the park measures 235 feet. (Round your answer to the nearest whole number.)

Answers

Answer:

22,203 ft^2

Step-by-step explanation:

The area of a triangle with angle ∅ and two sides a and b is;

Area A = 1/2 × absin∅ ......1

The park is in the shape of a triangle, with two sides and an angle given;

Given;

a = 190 ft

b = 235 ft

∅ = 84°

Substituting the values into equation 1;

Area of the park;

A = 1/2 × 190 × 235 × sin84°

A = 22,202.70131409 ft^2

A = 22,203 ft^2 (to the nearest whole number)

Area of the park is 22,203 ft^2

I need help with solving this

Answers

Answer:

49

Step-by-step explanation:

Positive 49 not -49

Describe the solutions of the following system in parametric vector form,and provide a geometric comparison with the solution set .

x1 + 3x2- 5x3 = 4
x1+ 4x2 - 8x3 = 7
-3x1- 7x2 +9x3 =6

Answers

Answer:

The equations are linearly independent so there is no parametric vector form

Step-by-step explanation:

I attached the solution.

maths
Ella mixes cordial and water in the ratio of 1:4 how much water should be mixed with 50ml or cordial

Answers

200ml of water should be mixed

Dan earns £8.10 per hour how much will he earn for 7 hours work

Answers

56.7 because you multiply 8.10 by 7

i have a daily allowance of 70grm but have only used 48 what percentage do i have left

Answers

Answer:

You have 31.43% of your allowance left.

Step-by-step explanation:

This question can be solved using a rule of three.

Your initial amount, of 70, is 100%.

The remaining amount, of 70 - 48 = 22, is x%. So

70 - 100%

22 - x%

[tex]70x = 100*22[/tex]

[tex]x = \frac{100*22}{70}[/tex]

[tex]x = 31.43[/tex]

You have 31.43% of your allowance left.

linear function for f(-11)=5, slope of f= -2/3

Answers

Answer:

  f(x) = -2/3(x +11) +5

Step-by-step explanation:

The point-slope form of the equation of a line will give you the desired linear function:

  y = m(x -h) +k . . . . . for slope m through point (h, k)

You are give point (x, f(x)) = (-11, 5) = (h, k), and you are given slope m = -2/3. Putting these values into the function form gives ...

  f(x) = -2/3(x +11) +5

Give your answers in pi

Answers

Answer:

36π

Step-by-step explanation:

area=πr²

=πx6x6

6x6=36

area = 36π

write this small number in standard form. 0.00078

Answers

Answer:

78/100000

Hope it helps you

7.8^ -4 is scientific notation

The mean of the data set(9,5,y,2,x)is twice the data set (8,x, 4,1,3).What is (y-x)

Answers

Answer:

y - x = 16

Step-by-step explanation:

Explanation:-

Step(i):-

Given data set A  is  9,5,y,2,x

Mean of the Data set A

                         =   [tex]\frac{9 + 5 + y + 2 +x}{5}[/tex]

                         = [tex]\frac{16 +x+y}{5}[/tex]

Given data set B is 8, x, 4, 1, 3

Mean of the Data set B

                         =   [tex]\frac{8+ x+4+1+3}{5}[/tex]

Step(ii):-                          

Mean of the Data set A  = 2 X Mean of the Data set B

              [tex]\frac{16 +x+y}{5} = 2 X \frac{16+x}{5}[/tex]

On simplification , we get

           16 +x + y = 2( 16 +x)

           16 + x + y = 32 + 2 x

            16 + x + y - 32 - 2 x = 0

            y - x -16 =0

           y - x = 16

PLEASE HELP ?


The range is the set of

A: first coordinates

B: ordered pairs

C:second coordinates

Answers

Answer:

C:second coordinates

Step-by-step explanation:

A range is the set of output coordinates

The domain is the input coordinates

Domain is the x, range is the y

Answer: its definitly c

Step-by-step explanation:

A college student is interested in investigating the TV-watching habits of her classmates and surveys 20 people on the number of hours they watch per week. The results are provided below. Calculate the 80% confidence interval of the true average number of hours of TV watched per week.
P.S: excel formola needed only. For lower and Upper Bound
CBB K-6 4 3 6 6 0 9 4 5 5 8 8 7 4 8 89265 123456789 0123456789 20 2

Answers

Answer:

80% confidence interval of the true average number of hours of TV watched per week is [8.28 hours, 11.02 hours].

Step-by-step explanation:

We are given that a college student is interested in investigating the TV-watching habits of her classmates and surveys 20 people on the number of hours they watch per week. The results are provided below;

Hours of TV per week (X): 6, 14, 13, 6, 16, 10, 19, 4, 5, 5, 18, 8, 7, 14, 8, 8, 9, 12, 6, 5.

Firstly, the Pivotal quantity for 80% confidence interval for the true average is given by;

                                P.Q. =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean number of hours of TV watched per week = [tex]\frac{\sum X}{n}[/tex] = 9.65

            s = sample standard deviation = [tex]\sqrt{\frac{\sum (X -\bar X)^{2} }{n-1} }[/tex]  = 4.61

            n = sample of people = 20

           [tex]\mu[/tex] = true average number of hours of TV watched per week

Here for constructing 80% confidence interval we have used One-sample t-test statistics as we don't know about population standard deviation.

So, 80% confidence interval for the true average, [tex]\mu[/tex] is ;

P(-1.33 < [tex]t_1_9[/tex] < 1.33) = 0.80  {As the critical value of t at 19 degrees of

                                               freedom are -1.33 & 1.33 with P = 10%}  

P(-1.33 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 1.33) = 0.80

P( [tex]-1.33 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]1.33 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.80

P( [tex]\bar X-1.33 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+1.33 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.80

80% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-1.33 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+1.33 \times {\frac{s}{\sqrt{n} } }[/tex] ]

                                         = [ [tex]9.65-1.33 \times {\frac{4.61}{\sqrt{20} } }[/tex] , [tex]9.65+1.33 \times {\frac{4.61}{\sqrt{20} } }[/tex] ]

                                         = [8.28 hours, 11.02 hours]

Therefore, 80% confidence interval of the true average number of hours of TV watched per week is [8.28 hours, 11.02 hours].

y=2x−4y=−12x+1 Question 1 options: a) (3, 2) b) (0, 2) c) (2, 0) d) (2, 3)

Answers

The correct answer is d

Let $A_1 A_2 A_3 A_4$ be a regular tetrahedron. Let $P_1$ be the center of face $A_2 A_3 A_4,$ and define vertices $P_2,$ $P_3,$ and $P_4$ the same way. Find the ratio of the volume of tetrahedron $A_1 A_2 A_3 A_4$ to the volume of tetrahedron $P_1 P_2 P_3 P_4.$

Answers

Answer:

  27 : 1

Step-by-step explanation:

The faces of a regular tetrahedron are equilateral triangles. The incenter, circumcenter, and centroid are all the same point, located 1/3 of the distance from the edge to the opposite vertex of the face. The vertical height of the point that is 1/3 the slant height from the base is 1/3 of the height of the tetrahedron.

Then the "inscribed" tetrahedron has 1/3 the height of the original. The ratio of volumes is the cube of the ratio of linear dimensions, so the ratio of the larger volume to the smaller is ...

  3³ : 1³ = 27 : 1

Which expression is equivalent to 3(x-6)+5(x-4)

Answers

Answer:

[tex]8x-38[/tex]

Step-by-step explanation:

[tex]3(x-6)+5(x-4)\\3x-18+5x-20\\3x+5x-18-20\\8x-38[/tex]

What are the next two numbers in the pattern of numbers;
45, 15, 44, 17, 40, 20, 31, 25, …

Answers

Answer:

Next two numbers are 15 and 32 respectively.

Step-by-step explanation:

The given pattern is  

45, 15, 44, 17, 40, 20, 31, 25, …

Here, we have two patterns.

Odd places : 45, 44, 40, 31,...

Even places : 15, 17, 20, 25,...

In series of odd places, we need to subtract square of integers.

[tex]45-(1)^2=45-1=44[/tex]

[tex]44-(2)^2=44-4=40[/tex]

[tex]40-(3)^2=40-9=31[/tex]

So, 9th term of given pattern is  

[tex]31-(4)^2=31-16=15[/tex]

In series of even places, we need to add prime numbers.

[tex]15-2=17[/tex]

[tex]17+3=20[/tex]

[tex]20+5=25[/tex]

So, 10th term of given pattern is  

[tex]25+7=32[/tex]

Therefore, the next two numbers in the pattern of numbers are 15 and 32 respectively.

Carefully review the research matrix presented below. If this is a within subjects design, how many total participants will be used in the experiment?
Immaculate Appearance Neat Appearance Sloppy Appearance
15 participants 15 participants 15
participants
a. 15
b. 30
c. 45
d. 60

Answers

Answer:

c. 45

Step-by-step explanation:

there are 15 participant in each category, and there are 3 categories, so total participants = 15 * 3

= 45

Hope this helps, and please mark me brainliest if it does!

Suppose parts are of two varieties: good (with probability 90/92) and slightly defective (with probability 2/92). Parts are produced one after the other. What is the probability that at least 3 parts must be produced until there is a slightly defective part produced

Answers

Answer:

95.69%

Step-by-step explanation:

We have X is the number of parts produced up to (and including) the first slightly defective part. So, X is Geometric (2/92), which would be the following:

P (X => 3) = Summation i = 3, up to infinity of {[(90/92)^(i-1)] * (2/92)}

We replace and solve and we are left with:

P (X => 3) = (2/92) * (90/92)^(3-1) * 1/(1 - 90/92)

P (X => 3) = 0.9569

Which means that the probability that at least 3 parts must be produced until there is a slightly defective part produced is 95.69%

The manager of the motor pool wants to know if it costs more to maintain cars that are driven more often. Data are gathered on each car in the motor pool regarding number of miles driven (X) in a given year and maintenance costs for that year (Y) in thousands of dollars. The regression equation is computed as: Y-60+0.08X, and the p-value for the slope estimate is 0.7. What conclusion can we draw from this study? a. Cars that are driven more tend to cost more to maintain. b. There's no statistically significant linear relationship between the number of miles driven and the maintenance cost c. The correlation between the response variable and independent variable is significant. d. The slope estimate is significantly different from zero.

Answers

Answer:

b. There's no statistically significant linear relationship between the number of miles driven and the maintenance cost

Step-by-step explanation:

The p-value for the slope estimate show us how strong is the certainty that there are a linear relationship between both variables. In this case, the p-value for the slopes shows if there is a significant relationship between the number of miles driven and the maintenance cost.

If we have a high p-value like 0.7 we can said that there is no certainty in the linear relationship. it means that there's no statistically significant linear relationship between the number of miles driven and the maintenance cost.

1.82 /6 pls answer with rounding to the nearest cent plzzzz I'll mark the 1st answer brainlist​

Answers

Answer:

.30

Step-by-step explanation:

the answer is .30333 (with the 3 repeating) and since 3 is less than 5 you leave the second number as is.

While filing your income tax, you report annual contributions of $100 to a public radio station, $300 to PBS (television station), $150 to a woman’s shelter, and $450 to other charitable organizations.

Find your monthly expense.

Answers

Hey there! I'm happy to help!

Let's add up all of these contributions.

100+300+150+450=1000

However, this is annual. We want monthly. So, we simply divide by 12.

1000/12≈83.33

Therefore, the monthly expense is $83.33

I hope that this helps! Have a wonderful day!

$17,500,000 is what percent of $70,000,000?

Answers

Answer: 1/4 of 70,000,000

Step-by-step explanation: 17,500,000 / 70,000,000 = 0.25

Answer:

[tex]25\%[/tex]

Step-by-step explanation:

[tex]\frac{17,500,000}{70,000,000}[/tex]

[tex]\frac{1}{4}=0.25=25/100=25\%[/tex]

The probability of randomly selecting a white flower from a garden that has green, pink, yellow, and white flowers is 6%.

Which of the following describes the likelihood of selecting a white flower?
A.
likely
B.
unlikely
C.
neither unlikely nor likely

Answers

Answer:

b. unlikely

Step-by-step explanation:

I don't really know a step by step explanation :( sry

Unlikely because 50% would be c and anything above 50% would be a

The currency in Bolivia is the Boliviano. The exchange rate is approximately $1 = 8 Bolivianos. At this rate, how many Bolivianos would you get if you exchanged $3?

Answers

Answer:

24 bolivianos

Step-by-step explanation:

$1=8b

$3=?

Cross multiply: ($3*8)/1 =24

When writing expressions for complex numbers, what does i represent?

Answers

Answer: See below

Step-by-step explanation:

[tex]i[/tex] is an imaginary number.

[tex]i=\sqrt{-1}[/tex]

[tex]i^2=-1[/tex]

calculate the
Simple interest on a
7,500,00 for 4 years
at 4½
per
annum​

Answers

Step-by-step explanation:

S.i =principal x rate x time/100

7,50000x4x4.5/100

13500000/100

135000

Other Questions
Specifically, the following critical elements must be addressed: I. Describe the artifact in detail. For instance, how would you describe it to someone who could not see it? II. Choose elements of the artifact that you believe are most important to how you experience it and explain why. For instance, what particularly catches your senses or makes you want to keep experiencing it? Does the choice of medium impact your experience? III. State your opinion on what you believe is the purpose of this artifact and the success of the creator in achieving the purpose. For instance, what message do you believe the creator is trying to express, and is that message successfully expressed? IV. Discuss how the artifact reflects the culture (or context) in which it exists. Be sure to address what aspects of culture have relevance for this artifact: politics, history, religion, social perceptions, technology, media, education, and so on. In other words, how do the artifact and its culture interrelate? For instance, how would a particular form of body modification reflect the urban culture in which you encountered it? V. Use the artifact to discuss how acts of creative expression impact and are impacted by the people and situations that surround it. How might the artifact and the person who created it have impacted each other? For instance, how might the geographic location where the artifact was made, the materials used to create the artifact, the medium of the creative process, or the environment where the artifact is displayed influence the creators life or future creative work? How might the artifact and the culture or context in which it was created have impacted each other? For instance, does the artifact add to the understanding of the culture from which it was created? What contributions does it make to continuing on a dialogue about that culture and the importance of its artifacts? VI. Pose questions you have after thinking deeply about this artifact. What more do you want to know regarding: a. The relationship between human culture and expression? b. Your personal assumptions about artifacts of this sort and why they exist? c. How your values have shaped and are shaped by your expression and that of others? d. The relationship between the possible intent of the creator and your own interpretation of its meaning? VII. Speculate on how you would go about answering these questions. For instance, what sorts of things would you study about these kinds of artifacts and their contexts that might begin addressing these questions? Ms. Jenks bought 1.75 pounds of ham and 0.8 pound of turkey from the deli. How many more pounds of ham than turkey did she buy? Is the term used to deceive the amount of control or influence that consumers have on a market Which statement describes how to determine if a relation given in a table is a function?A. If none of the output values are repeated, the relation is a function.B. If none of the input values are repeated, the relation is a function.C. If any of the input values are equal to the output values, the relation is a function.D. If all the output values are paired with the same input value, the relation is a function. Which is an example of a graphical source?O A. A nonfiction book about the economic consequences of WorldWar IIB. A book of poetry written by a well-known motivational speakerC. A chart that identifies the number of new homes built each yearD. A magazine article that reviews the latest books and movies HELP!!! PLEASE!!!The U.S. Federal Income Tax is a progressive tax, which means that higher incomes are taxed at higher percent rates. The table shows the 2018 Federal Income Tax rates that are applied to the incomes of unmarried individuals.Tuan is an unmarried man who earned a taxable income of $48$48,000000 during 2018.Use the table to complete the statements below. Please help. Ill mark you as brainliest if correct! Select the correct answer.Is this a SENTENCE?Do our leaders always tell the truth?OAYesB.No It has been suggested that night shift-workers show more variability in their output levels than day workers. Below, you are given the results of two independent random samples. Night Shift (N) Day Shift (D) Sample Size 9 8 Sample Mean 520 540 Sample Variance 38 20 Required:a. At 95% confident level, what is the critical value?b. State the null and alternative hypotheses to be tested.c. Compute the test statistic.d. Determine the p-value. Mass is:measured in kilogramsmeasured using a scaleaffected by gravityall of the above Four lines extend from point K. The space between lines K J and K N is 58 degrees. The space between lines K N and K M is 61 degrees. The space between lines K M and K L is 61 degrees. Which statement must be true about the diagram?1. Point K is a midpoint of Line segment J L.2. mAngleJKN = One-halfmAngleJKM3. Ray KM is an angle bisector of AngleNKL.4. JK = One-halfKL Piper is a manager in a corporation that was organized in Canada by one of his former coworkers. The company provides consulting services and training for architects employed by construction companies. The company recently went public, with shares being sold to hundreds of investors. Pipers company would be a __________ corporation. Answer the following question in complete sentences using the RACE method. Romeo pronounces his love for Juliet hours after they have met in the famous balcony scene. What characteristic does Juliet primarily see in Romeo at this point in the play? What evidence is there to support your answer? A Romantic as evidenced by the line "You bring me joy." B Thoughtful as evidenced by the line "Sweet, good night." C Impulsive as evidenced by the line "It is too rash, too unadvised, too sudden." D Sensitive as evidenced by the line "Too like the lightning." Why does Elizabeth Cady Stanton matter today ? Helpp !The nervous system interacts with the endocrine system by _O A. translating messages from endocrine cellsO B. sending neurotransmitters to endocrine target cellsO C. sending neurotransmitters to neuroendocrine cellsD. receiving messages from hormones Three potential employees took an aptitude test. Each person took a different version of the test. The scores are reported below. Norma got a score of 84.2; this version has a mean of 67.4 and a standard deviation of 14. Pierce got a score of 276.8; this version has a mean of 264 and a standard deviation of 16. Reyna got a score of 7.62; this version has a mean of 7.3 and a standard deviation of 0.8. If the company has only one position to fill and prefers to fill it with the applicant who performed best on the aptitude test, which of the applicants should be offered the job? What is the enharmonic of C ? Consider 2.25t + 5 = 13.5t + 14 Write the resulting equation after moving the 2.25t to the right sideIf 13.5t is moved to the left side, what is the resulting equation?--------------------------------------------------------------------------------Andre and Diego were each trying to solve 2x + 6 = 3x -8. Describe the first step they each make to the equation.Andres resulting equation was - x + 6 = -8Diegos resulting equation was 6 = x - 8 Jayne polled 50 students about their preferred after-school sport and then recorded the data in the table below. Which sport is more popular? *A. You can use a relative frequency table to examine how data sets are related by comparing percentages.B. Row and column relative frequency tables tell you the same information as total relative frequency tables.C. A column relative frequency table helps compare data in two different rows.In a column two-way relative frequency table, each column totals 100%. Choose the slope and y-intercept thatcorrespond with the graph.