In a sample of 1000 cases, the mean of a certain test is 14 and the standard deviation is 2.5. Assume the distribution to be normal. The top 20% of the students will score how many points above the mean

Answers

Answer 1

Answer:

The top 20% of the students will score at least 2.1 points above the mean.

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.

The mean of a certain test is 14 and the standard deviation is 2.5.

This means that [tex]\mu = 14, \sigma = 2.5[/tex]

The top 20% of the students will score how many points above the mean

Their score is the 100 - 20 = 80th percentile, which is X when Z has a pvalue of 0.8. So X when Z = 0.84.

Their score is:

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

[tex]0.84 = \frac{X - 14}{2.5}[/tex]

[tex]X - 14 = 0.84*2.5[/tex]

[tex]X = 16.1[/tex]

16.1 - 14 = 2.1

The top 20% of the students will score at least 2.1 points above the mean.


Related Questions

What is the m<3?
m<3 =

Answers

Answer:

105°

Step-by-step explanation:

< 3 = 50° + 55° { exterior angle of a triangle is equal to the sum of two opposite interior angles }

<3 = 105°

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Answers

Answer:

I thinks .... x ... to ...........

Step-by-step explanation:

Can I get brainlest

Answer: ...

Step-by-step explanation:

HELP ME PLEASE PLEASE PLEASEEEEE

Answers

Answer:

B) 14/3 > sq rt 8

Step-by-step explanation:

proof:

14/3=4.67

sq rt 8=2.83

4.67>2.83

The answer is A ........

STAAR
2. Sharon is buying a circular rug for her living room. The diameter of the rug is 8 feet.
Which measurement is closest to the area of the rug in square feet?
A 200.96 square feet
B. 50.24 square feet
C. 25.12 square feet
D. 12.56 square feet

Answers

Answer:

B.50.24

8ft is equivalent to 64ft²

Answer:

50.24

Step-by-step explanation:

Enter your answer in simplest form.

4 ×
3
5
=

Answers

4 · 35 = 140

Hope this helps! Good luck. :)

Answer: since they're stacked, i cant tell if that's a fraction or decimal, or just whole numbers so...

4 times 35 = 140

4 times 3/5 = 2 2/5

4 times 3.5 = 14

Step-by-step explanation:

find the value of x

a. 4
b. 9
c. 18
d. 14

Answers

A. 4
The degree has to equal 180 so 180-140=40 40=(10)(4)

Answer:

4

Step-by-step explanation:

We know that this is a supplementary angle, which means the sum of two angles is 180 degrees.

The Equation would then be:

140+10x=180

All you need to do is solve for x.

140+10x=180

-140         -140 (Subtract 140 from both sides)

        10x=40   (Divide by 10)

           x=4

Two students have a bitter disagreement about the answer to a homework question and decide to settle their differences in a duel at the golf cours. The rules of the duel are simple:

Each student takes a single shot from the 18th tee. If only one student's shot lands on the green, that student is declared the victor and the duel is over. If both students' shots land on the green, the result is a draw and the duel is over. If they both miss the green, then they repeat another round (and so on) until the duel ends in a draw or with a victor. The result of each tee shot is independent. Student A has not spent much time at the golf course, resulting in a 0.55 probability that her tee shot will hit the green. Student B golfs regularly, resulting in a 0.76 probability that his tee shot will hit the green.

Required:
a. Whatâs the probability that the duel ends in round 1?
b.Whatâs the probability that the duel ends in the 3rd round?
c. Whatâs the probability that the duel ends in a draw (i.e., that neither student wins)?

Answers

Answer:

a.) P(duel end in round 1 ) = 0.892

b.) P(duel ends in the 3rd round) = 0.010

c.) P(duel ends in a draw) = 0.418

Step-by-step explanation:

Let

P(A) - Probability that Student A will hit the green.

P(¬A) - Probability that Student A will miss the green.

P(B) - Probability that Student B will hit the green.

P(¬B) - Probability that Student B will miss the green.

Given,

P(A) = 0.55 , P(B) = 0.76

As we know that,

P(A) + P(¬A) = 1

⇒P(¬A) = 1 - P(A)

            = 1 - 0.55

            = 0.45

⇒P(¬A) = 0.45

And

P(B) + P(¬B) = 1

⇒P(¬B) = 1 - P(B)

            = 1 - 0.76

            = 0.24

⇒P(¬B) = 0.24

So, we get

P(A) = 0.55 , P(B) = 0.76

P(¬A) = 0.45, P(¬B) = 0.24

a.)

P(duel end in round 1 ) = P( both hit on green or only one hit on green )

                                     = P(A).P(B) + [ P(A).P(¬B) + P(¬A).P(B) ]

                                     = 0.55(0.76 ) + [ 0.55(0.24) + 0.45(0.76) ]

                                     = 0.418 + [ 0.132 + 0.342 ]

                                     = 0.418 + [ 0.474 ]

                                     = 0.892

⇒P(duel end in round 1 ) = 0.892

b.)

P(duel ends in the 3rd round) = P( duel miss green in 1st round × duel miss green in 2nd round × both hit on green or only one hit on green in 3rd round )

                                                = [ P(¬A).P(¬B) ] × [ P(¬A).P(¬B) ] × { P(A).P(B) + [     P(A).P(¬B) + P(¬A).P(B) ] }

                                               = [ 0.45(0.24) ] ×  [ 0.45(0.24) ] × { 0.55(0.76 ) + [ 0.55(0.24) + 0.45(0.76) ] }

                                               = [ 0.108 ] ×  [0.108] × { 0.418 + [ 0.132 + 0.342 ] }

                                               = 0.011664 × 0.892

                                               = 0.010404 ≈ 0.010

⇒P(duel ends in the 3rd round) = 0.010

c.)

P(duel ends in a draw) = P(both students' shots land on the green)

                                     = P(A).P(B)

                                     = 0.55(0.76)

                                     = 0.418

⇒P(duel ends in a draw) = 0.418

When graphed, will the line x - 2y = 6 be
parallel, perpendicular or neither to a line that
passes through the points (5,2) and (3,6)?

Answers

Answer:

Step-by-step explanation:

Slope of x-2y=6 is ½.

Slope of line through (5,2) and (3,6) = (6-2)/(3-5) = -2

The two slopes are negative reciprocals of each other (i.e., their product is -1), so the two lines are perpendicular.

Lamar went to a baseball game. The game started at
11;50AM, and it was 3 hours 39minutes long. When did the game end?

Answers

3:29

11:50 + 3 hours = 2:50
2:50+ 39 mins = 3:29

Answer:

The game ends at 2:39

Step-by-step explanation:

11:50 + 3 hours (3:00) = 2:00

2:00+ 0:39 = 2:39

Why I'm so happy today?​

Answers

it’s raining tacosssssss

Answer:

ldk and I'm jealous

Step-by-step explanation:

Thanks for the free points, and have a nice day! :)

What is the equation of the given line? (-4,3) (2,-3)

Answers

Answer:

y=-x-1

Step-by-step explanation:

Y = -4x + 3
Y = 2x -3

What is the purpose of the air in air hockey?

Answers

Answer:

A fan within the center of the table blows air through these holes in order to allow the puck to quickly glide across the table surface. This movement of air is the reason why we call the sport "air" hockey vs. just table hockey. There are two holes at opposite ends of the table that make up a goal.

Step-by-step explanation:

Solve 7k÷3=21 Math Problem

Answers

Do you mean 7000? Or k as a variable?

Answer:

k = 9

Step-by-step explanation:

do you need an explantion?

If the simple interest on $4,000 for 7 years is $1,400

Answers

Answer: $5400

im assuming you want the total cost?

4000+1400=5400

Answer:

Step-by-step explanation:

Simple interest is

I=Prt where P= principle, r=rate, t=time

r=I/(Pt)

r=1400/(4000(7))

r=0.05

r=5%

The Maryland State Department of Education reports that 12% of the high school students in that state attend private high schools. The University of Maryland wonders if the percentage is the same in their applicant pool. Admissions officers plan to check a random sample of the over 10,000 applications on file to estimate the percentage of students applying for admission who attend private schools. They select a random sample of 450 applications, and find that 46 of those students attend private schools.

Answers

The question is incomplete. Here is the complete question.

The Maryland State Department of Education reports that 12% of the high school students in that state attend private high schools. The University of Maryland wonders if the percentage is the same in their applicant pool. Admissions officers plan to check a random sample of the over 10,000 application on file to estimate the percentage of students applying for admission who attend private schools. They select a random sample of 450 applications, and find that 46 of those students attend private schools. Create and interpret a 95% confidence interval.

Answer and Step-by-step explanation: Th proportion of students that attend private schools in the sample is

[tex]p=\frac{46}{450}[/tex]

p = 0.102

At 95% confidence, z-score is 1.96.

Standard deviation for sample proportion is calculated as

[tex]\sigma = \sqrt{\frac{p(1-p)}{n} }[/tex]

For this sample, it will be

[tex]\sigma = \sqrt{\frac{0.10(1-0.1)}{450} }[/tex]

[tex]\sigma=\sqrt{0.0002}[/tex]

[tex]\sigma=0.01414[/tex]

Interval is calculated as

p ± zσ

Then

0.102 ± 1.96(0.01414)

0.102 ± 0.028

Interval is 0.074 < p < 0.13

What confidence interval means is that with a certainty of 95%, we are confident that  the true population proportion of students who attend private schools are between 0.074 and 0.13.

Rafael is building a circular table with a radius of 1.75 feet. The wood costs $32.50 per square foot. How much will it cost Rafael to make the table?​

Answers

Answer:

so um your answer is in step by step

Step-by-step explanation:

I assume you just want to calculate the cost of making a circle with a diameter of 2.5 feet.

The area of a circle can be calculated using the following formula:   A = pi * r2

The radius of a circle is half of the diameter.  For this problem, the radius will be 2.5 / 2 or 1.25 feet and pi is 3.14

Then the area will be :  A= 3.14 * 1.252

A= 3.14 * 1.5625 = 4.90625 ft2

If each square foot cost $32.50, then the wood will cost $32.50 * 4.90625 = $159.45


Order of operations. Need to find the unknown number. Help?

8 + 2 x 5 = m
9 - 7 + 2 = k
7 x 8 - 6 = g
16 + 4 divide 2 = s
12 - 6 divide 2 = y
36 divide 6 + 13 = f

Answers

Answer:

m = 18

k = 4

g = 50

s = 18

y = 9

f = 19

Step-by-step explanation:

M = 18
K = 4
G = 42
S = 18
Y = 9
F = 19

Marie made the box plot below to display a set of data. Which set of data could the box plot
represent?

Answers

Answer:

(5, 6, 10, 12, 13, 15, 17, 25, 30, 35) would be your best answer.

Step-by-step explanation:

(x - 1) (x – 12) = 0
What’s the value of X?

Answers

Answer:

either 1

or 12

(sorrryy if its not correct:( )

Step-by-step explanation:

Craig treated his sister to lunch while visiting her in Campbell. Their lunch cost $40, and the sales tax in Campbell is 5%. If Craig left a 15% tip on the $40, how much in total did he pay?
Pleasee give correct

Answers

Answer:

$48

Step-by-step explanation:

5% of 40 = 2 and 15% of 40 = 6. 6 + 2 = 8. 40 + 8 = $48.

(6th grade)
i would really appreciate if someone could help me, and tell me how you got the answer, along with the steps !!

Answers

the answer is to this is, 1. :)

Answer:

-4

Step-by-step explanation:

-8×-8/-8+-8

-8•(-8)/-16

-8•8/16

-8/2

-4

A square rug has an area of 121 ft?. Write the side length as a square root. Then decide if the side
length is a rational number.
HELP ASAP

Answers

Square root of 121 which is 11

Brainliest :)
(Score for Question 3: ___ of 5 points)

(a) Order the popularity of the choices from greatest to least.
(b) It was estimated that 280 people were going to vote. If this was true, how many people would have voted for Goron? Show your work.
(c) 40 people voted for “Other.” Was the estimate of total voters from Part (b) accurate? Explain.
this is for k12 so click off if u dont have an answer or ill report

Answers

Goron should get 98 votes

 

The question breaks down to taking 35% of 280.  

Votes = 35/100 * 280 = people who will vote for Goron

Votes = 9800 / 100 = people who will vote for Goron.

Votes = 98

The Smith family had a meal catered for a wedding rehearsal dinner. The cost of the dinner was $325. There is 6% sales tax and they left a 20% tip. What was the total cost of the dinner?

Answers

Answer:

409.5

Step-by-step explanation:

A manager uses the following equation to predict monthly receipts: Y-450-10 Lt time in weeks and y = receipts.) What is the forecast for July 14th ift=4 is the fourth week in January and t = 6 is February 14th of the same year (assume there are 4 weeks in each month)?
a. 690
b. 710
c. 730
d. 750
A major reason that decision making is often not such a rational process is that there are: Suppose we have H0:µ1= µ2 versus HA: µ1 ≠ µ2, with level of significance of α =.05 and critical values of zα/2 = ± 1.96, and the computed Test Statistics value of Z = -1.07. What is our decision?

Answers

Answer:

b. 710

Fail to reject H0

Step-by-step explanation:

Forecast for July 14 :

Assume there are 4 wwwks in each month :

January to June = ( 4 * 6 months) = 24 weeks in 6 months ;

July - July 14 = 2 weeks :

2 + 24 = 26 weeks

The model given :

Y = 450 + 10t

Y = 450 + 10(26)

Y = 450 + 260

Y = 710

2.)

Test is a 2 tail test :

Zstatistic = - 1.07

At 95% confidence = ±1.96

Zcritical = - 1.96

Hence,

Reject H0 if ;

Zstatistic < Zcritical

-1.07 > 1.96

Hence, fail to reject H0.

what is 240 x 343 x 234 x 123 x 23 - 89

Answers

the answer is 54494687431
The answer is 54,494,687,431

Brainliest if you answer the question and 30 points

Answers

Answer:

-2.2, -1 7/10, 1.7, 3 1/4

Answer:

-2.2, -1 7/10, 1.7, 3 1/4

Step-by-step explanation:

What is 9/10-6/10 or can you not do it?

Answers

Answer:

3/10

Step-by-step explanation:

9-6=3

both fractions have the same denominator so they keep it

9/10 - 6/10 = 3/10

3/10 is also 0.33

A survey is taken to figure out the average temperature across all cities in the United States on a particular day. In 10 randomly chosen states, 40 cities are chosen to record the temperature. Which sampling method describes this situation?
a. convenience
b. cluster
c. random
d. stratified

Answers

Answer: Random

Step-by-step explanation:

Answer:

systematic sampling

Step-by-step explanation:

Aka, C random selection

An airplane travels 2,350 miles in 5 hours. Theo did this work to find the unit rate.

Rate = StartFraction 2,350 miles Over 5 hours EndFraction. Unit rate = 470 miles per hour.

What should you do next to find out how far the airplane traveled in 3 hours?
divide 470 by 3
divide 2,350 by 3
multiply 470 by 3
multiply 2,350 by 3

Answers

Answer:

Step-by-step explanation:

Answer:    On Edge this is the answer.

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