A teacher gives her class a particular examination on mathematics at the end of each year. The results are normally distributed with a mean test score of 60 and a standard deviation of 8. The teacher has told the class that students with a test score in the top 2.5% will win a special prize. Calculate the test score above which 2.5% of all test scores lie. Give your answer to 1 decimal place. Test score

Answers

Answer 1

Answer:

Test score of 75.7.

Step-by-step explanation:

Problems of normal distributions can be 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.

The results are normally distributed with a mean test score of 60 and a standard deviation of 8.

This means that [tex]\mu = 60, \sigma = 8[/tex]

Calculate the test score above which 2.5% of all test scores lie.

Above the 100 - 2.5 = 97.5th percentile, which is the value of X when Z has a pvalue of 0.975, so X when Z = 1.96.

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

[tex]1.96 = \frac{X - 60}{8}[/tex]

[tex]X - 60 = 8*1.96[/tex]

[tex]X = 75.7[/tex]

Test score of 75.7.


Related Questions

What is the difference, in hours and minutes, between these times?
a)
13 40 and 17 15
hours
minutes
b)
11 25 and 14 10
hours
minutes
c)
2:50 am and 7:20 am
hours
minutes
d)
10:35 am and 2:40 pm
hours
minutes

Answers

Answer:

a) 3 hrs 35 mins

b) 2 hrs 45 mins

c) 4 hrs 30 mins

d) 4 hrs 5 mins

Step-by-step explanation:

The difference, in hours and minutes, between these times are;

a) 3 hrs 35 mins

b) 2 hrs 45 mins

c) 4 hrs 30 mins

d) 4 hrs 5 mins

What is Algebra?

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The difference, in hours and minutes, between these times can be calculated as;

a) 13 40 and 17 15

13 :40 - 17 : 15

= 3 hrs 35 mins

b) 11 :25 and 14: 10

11 :25 - 14: 10

= 2 hrs 45 mins

c) 2:50 am and 7:20 am

2:50 am - 7:20 am

=  4 hrs 30 mins

d) 10:35 am and 2:40 pm

10:35 am - 2:40 pm

= 4 hrs 5 mins

More about the Algebra link is given below.

brainly.com/question/953809

#SPJ2

value digit of 468, 204, 459 , 964, 468​

Answers

Answer:

964 = 4

204 = 4

459 = 400

468 = 400

b=3(3,1) find the equation

Answers

Answer:

Are you asking, given b = 3, write an equation that passes through the point (3,1)?

Which expression results from using the Distributive Property?
16. 3(6 +r)
A. 6+r
B. 6 + 3r
C. 181
D. 18 + 3r

Answers

The answer is D because you would multiply 3 * 6 and 3 * r, getting you 18+3r


Elmer is purchasing 2 4/5 pounds of candy that cost $1.85 per pound.
If he pays with $10, how much will he get in change? HELP I WILL MARK BRAINIEST

Answers

Answer:

hi

Step-by-step explanation:

Daniel bought 1 pound of jelly beans and 2 pounds of chocolates for $2.00. ... for $1.50. How much would he have to pay on his next trip to the candy store if he bought 1 pound of each of the 4 kinds ... How many are there? Assign ... Multiply each equation by a factor, so that all equations will have the same total price: 3(1j +.

The candy is $1.85 per pound so you would multiply that by 2 4/5 which equals 5.18. 10 - 5.18 = 4.82
Hope this helps!

what is Z x-2, when x=2 and z=2

Answers

Answer:

2

Step-by-step explanation:

2x2-2=2

2 x 2-2 because everytbing is just two

how many seconds are there in 8 minutes 12seconds​

Answers

Answer:

1 minute has 60 seconds

therefore 8 minutes will have 60 × 8 seconds = 480 seconds

480 + 12 = 492

hence 8 minutes 12 seconds will have 492 seconds

Answer: 492 seconds

Step-by-step explanation:

1min = 60sec

therefore, 8min 12sec = [8 x 60] + 12

= 480 + 12

= 492 sec

Hope it helped u,

pls mark as the brainliest        - Ayaan707 for help :) -

^_^

1. The nominal rate on Sandra's loan is 7.125%. If the interest is compounded monthly, what rate of

interest is Sandra actually paying? (use the formula)

Answers

Answer:

She is actually paying a rate of 7.36% of interest.

Step-by-step explanation:

The real interest rate, as a decimal, is given by:

[tex]I = (1 + \frac{r}{n})^{n}[/tex]

In which r is the interest rate and n is the number of compoundings during an year.

The nominal rate on Sandra's loan is 7.125%, compounded monthly:

This means that [tex]r = 0.07125, n = 12[/tex]

So

[tex]I = (1 + \frac{0.07125}{12})^{12} = 1.0736[/tex]

As a percentage: 1.0736*100 = 107.36% - 100% = 7.36%

She is actually paying a rate of 7.36% of interest.

What is the y-intercept of the line with the equation 4y = -3x + 10?

Answers

Step-by-step explanation:

Given

4y = - 3x + 10

y = ( - 3x + 10 ) / 4

y = - 3/4 x + 10 / 4

y = - 3/4 x + 5 / 2

Comparing the given equation with y = mx +c Then

y - intercept (c) = 5/2

Hope it will help :)

Imagine that Dr. Jones publishes a study that claims that drinking while pregnant is dangerous for the health of the unborn baby. He surveys 200 women and finds that of the 100 women in his study who drank when pregnant, 78 had children who experienced problems with attention. Of the 100 women in his study who did not drink when pregnant, only 29 children experienced problems with attention. Your neighbor says that Dr. Jones is wrong because she drank when pregnant and her child is perfectly healthy. Explain why Dr. Jones is NOT wrong.

Answers

Answer:

Kindly check explanation

Step-by-step explanation:

Dr. Jones conclusion was based on probability which measures the degree of likelihood of an occurrence or event. In his experiment, the result could be interpreted using point estimate to mean that ; 78/100 = 0.78 or 78% of those who drank while pregnant has problem with attention while only 29/100 = 0.29 or 29% of those who did not drink.

This conclusion means that pregnant women who drink have a higher likelihood of giving birth to a child with attention problem than pregnant women who do not drink. Hence, the fact that someone who drank gave birth to a perfectly healthy child does not discredit or annull Dr. Jones study.

Solve (x - 2)^2 - 3 = 1 graphically. That is graph y = (x - 2)^2 - 3 and y = 1 on the same set of axes and find the x-value(s) of any points of intersection. Then use algebraic strategies to solve the equation and verify that your graphical solutions are correct.

Answers

Check the attachment(s) for the graphs pertaining to the question

No. 1) Check graph [first attachment]

No. 2) y = (x - 2)^2 - 3, y = 1

           (x - 2)^2 - 3 = 1,

           (x - 2)^2 = 4

            x - 2 = √4, x - 2 = - √4

            x = 4, x = 0

Substitute back to determine the respectively y-value:

y = (4 - 2)^2 - 3 = (2)^2 - 3 = 4 - 3 = 1

Check: y = (0 - 2)^2 - 3 = (-2)^2 - 3 = 4 - 3 = 1

So the points of intersection are (4, 1) and (0, 1). According to the graph, that is correct.

35% of students take spainsh or engineering. 30% of students take Spanish. 25% of students take engineering. What is the probability that a student takes Spanish and engineering?

Answers

Answer:

0.2 = 20% probability that a student takes Spanish and engineering

Step-by-step explanation:

We solve this question treating the probabilities as Venn sets.

I am going to say that:

Event A: Student takes Spanish

Event B: Student takes Engineering.

35% of students take spainsh or engineering.

This means that [tex]P(A \cup B) = 0.35[/tex]

30% of students take Spanish.

This means that [tex]P(A) = 0.3[/tex]

25% of students take engineering.

This means that [tex]P(B) = 0.25[/tex]

What is the probability that a student takes Spanish and engineering?

This is [tex]P(A \cap B)[/tex].

These probabilities are related by the following formula:

[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]

So

[tex]P(A \cap B) = P(A) + P(B) - P(A \cup B)[/tex]

Replacing the values

[tex]P(A \cap B) = 0.3 + 0.25 - 0.35 = 0.2[/tex]

0.2 = 20% probability that a student takes Spanish and engineering

you bought 12 red apples and 15 green apples to make a pie?
what is the ratio of the number of red apples to the total number of apples simplified?​

Answers

Answer:

4:9

Step-by-step explanation:

12 red apples and 27 apples in total so it would be 12:27. Just divided it by 3

I think that's what the question is asking...

I really need help plz

Answers

Answerwhat do you need help with?

Step-by-step explanation:

Find the area please :)))

Answers

Answer:

area would be 98.35

Step-by-step explanation:

the area is 98.35 units squared

PLSSS PLSSS I NEED HELPP

Answers

Answer:

Step-by-step explanation:

Perpendicular (p) = 8

base(b) = 7

Tan A = p/b

tan A = 8/7

A = tan ^-1(8/7)

A = 48.81°

Please help me with this question

Answers

Answer:

An equation is y=-3x+7 (I chose slope-intercept form because they already showed us the slope). When y =13 x=-2

Step-by-step explanation:

plugin 13 for y and subtract 7 from both sides, this lets you get 6=-3x then divide 6 by -3 which makes x=-2

3.3.4 Practice: Angle Relationships in Triangles

Practice

Math 8 Sem 2

Tips for Success
Read the assignment carefully and make sure you answer each part of the question or questions.
Check your work when you're done.
Your Assignment
Answer the questions to find the measures of ∠2 and ∠3.


1. What is the measure of ∠4? Explain how you know.


Write your answer in the space below.


2. What is the sum of the measures of the angles in a triangle?


Write your answer in the space below.


3. ∠1 is in a triangle with ∠4 and a 53° angle. What is the sum of the measures of those two angles?


Write your answer in the space below.


4. What is the measure of ∠1? Explain.


Write your answer in the space below.

5. Find the measure of ∠2. Explain how you found its measure.


Write your answer in the space below.


6. What is the measure of ∠3? Explain.


Write your answer in the space below.

Answers

For question 1 and 2, you should keep in mind that the sum of all angles in a triangle is 180°. 1. If the measure of one angle of a triangle is 90 degrees, you can assume that the sum of the other two triangles should be 90 degrees. Because

180 - 90 = 90

The sum of the three angles of any triangle is equal to 180 degrees.

Angle 2=127 because 180-53=127.

Angle 3=23 because 180-30-127=53

Angle 1=37 because 90-53=37

Angle 4=90

Angle 1+4=127

The measure of ∠1 is 125° .

Next x+64=110. The reason why you can do this is because ∠R is going to be an opposite interior angle. Subtract 64 from the left and right sides. x=46

Answer:

Good luck!

Step-by-step explanation:

Are these answers right

Look at pictures

Complementary angles

Answers

Answer:

1) correct

2) correct

3) incorrect, x = 11

4) incorrect, x = 50

Step-by-step explanation:

3) 90-35 = 5x

5x = 55

x = 11

4) 90-56 = (x-16)

x-16 = 34

x = 50

Answer:

Step-by-step explanation:

3) 5x +  35 = 90 {Complementary angles}

          5x = 90 - 35

          5x = 55

            x = 55/5

             x = 11

4) 56 +x - 16 = 90 {Complementary angles}

         x + 40 = 90

                x = 90 - 40

               x = 50

calcule a área lateral de uma pirâmide regular quadrangular de altura 6 cm e área da base 64 cm2​

Answers

Answer:

bam

Step-by-step explanation:

bam

Find angle picture below

Answers

Answer:

T=62

U=33

V=85

Step-by-step explanation:

i really really need the answer plz help this is the fourth time im asking this question plz help.

Answers

Answer:

5g-4/4your answer right answer

Step-by-step explanation:

we have to find value of g ????

We roll two fair 6-sided dice. If a fair dice is rolled, the probability of it landing on any number between [1-6] is equi- probable (i.e., 1 6 ). (a) Find the probability that doubles are rolled. (Rolling doubles mean both dices land in the same number, e.g., 3 and 3.) (b) Given that the roll results in a sum of 6 or less, nd the conditional probability that doubles are rolled. (c) Find the probability that the larger of the two die's outcomes is at least 4.

Answers

Answer:

a.) [tex]\frac{1}{6}[/tex]

b.) [tex]\frac{3}{15}[/tex]

c.) [tex]\frac{27}{36}[/tex]

Step-by-step explanation:

Given - We roll two fair 6-sided dice. If a fair dice is rolled, the probability

             of it landing on any number between [1-6] is equi- probable

             (i.e., [tex]\frac{1}{6}[/tex]).

To find - (a) Find the probability that doubles are rolled.

               (b) Given that the roll results in a sum of 6 or less, and  

                    the conditional probability that doubles are rolled.

               (c) Find the probability that the larger of the two die's outcomes

                    is at least 4.

Proof -

As given , two fair 6-sided dice is rolled.

The sample space is as follows :

S = { (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)

        (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)

        (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)

        (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)

        (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)

        (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)  }

Total number of outcomes = 36

a.)

Sample space that double are rolled = { (1, 1), ( 2, 2), ( 3, 3) , ( 4, 4), ( 5, 5), ( 6, 6) }

Total number of possible outcomes = 6

So, Probability = [tex]\frac{6}{36}[/tex] = [tex]\frac{1}{6}[/tex]

b.)

Sample space that roll shown sum of 6 or less = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (4, 1), (4, 2), (5, 1)}

Now,

Total outcomes = 15

Total possible outcome that doubles are rolled = 3 ( i.e (1,1), (2, 2), (3, 3) )

So, Probability = [tex]\frac{3}{15}[/tex]

c.)

Sample space that larger of the two die's outcomes is at least 4 = { (1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6) }

Total possible outcomes = 27

So, Probability = [tex]\frac{27}{36}[/tex]

What is the total cost of 1.2 Cubic yards of soil if it sells for $24 per cubic yard?

Answers

Answer:

$28.80 I hope that helps if not I'm sorry if it's wrong

Step-by-step explanation:

we write "dollars per cubic yard" as "dollars/yd^3" so that the units "yd^3" will cancel when multiplying by "1.2 yd^3", leaving an answer in units of dollars

24 dollars / yd^3 * 1.2 yd^3 = 28.80

the cost would be $28.80

24/ yd^3 * 1.2yd^3= 28.80

the cost would be $28.80

Describe the characteristics of metal in which metal converts into sheet.​

Answers

Answer:

a solid material that is typically hard, shiny, malleable, fusible, and ductile, with good electrical and thermal conductivity ( iron, gold, silver, copper, and aluminum, and alloys such as brass and steel)

Step-by-step explanation:

1) If Donkey Kong is on a bridge 638 feet in the air, 6 seconds after a shell
was released, which shell hit Donkey Kong and how do you know?
+

Answers

Answer:

5000inches

Step-by-step explanation:

i think is that!

PLEASE HELP, I WILL MARK BRAINLIEST TO THE ONE WHO ANSWERS FIRST

The perimeter of the base of a square prism is 16cm. The height of the prism is 5 cm. Find the volume of the prism.

(Hint: use the perimeter to find the length of the side)

Answers

Answer: Down Below

Step-by-step explanation:

Surface Area(rectangular prism) = 192 cm^2

Area(square) = 16cm^2

Area(square) = LW or S^2

Area = 16cm^2

Question 11

A rectangle with a perimeter of 12 inches is enlarged by a scale factor of 3. What is the perimeter of the enlarged

rectangle?

Answers

Answer:

The perimeter of the enlarged rectangle is 36 inches.

Step-by-step explanation:

Perimeter of an enlarged figure:

To find the perimeter of an enlarged figure, we multiply the perimeter of the original figure by the scale factor.

In this question:

Perimeter of the original rectangle: 12 inches

Scale factor: 3

Perimeter of the enlarged rectange:

12*3 = 36 inches

For the function f(x)=-7x-5, evaluate f(6)

Answers

Answer:

f(x)=-7x-5

f(6)=-7(6)-5

f(6)=-42-5

f(6)=-47

Simplify completely and find the restrictions on the variable.​

Answers

Answer:

[tex]\displaystyle \frac{8}{x - 11}, x \neq 2, 11[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Terms/CoefficientsFactoring

Algebra II

DiscontinuitiesDomain Restrictions

Step-by-step explanation:

Step 1: Define

[tex]\displaystyle \frac{8x - 16}{x^2 - 13x + 22}[/tex]

Step 2: Simplify

[Fraction] Factor numerator:                                                                          [tex]\displaystyle \frac{8(x - 2)}{x^2 - 13x + 22}[/tex][Fraction] Factor denominator:                                                                       [tex]\displaystyle \frac{8(x - 2)}{(x - 11)(x - 2)}[/tex][Fraction] Divide:                                                                                            [tex]\displaystyle \frac{8}{x - 11}[/tex]

We know that x cannot equal 11, because that would give us a divide by 0 error and we know that x cannot equal 2 because it was canceled out when simplifying.

Other Questions
Can someone help me with two geometry questions? They are in a PDF document that I attached. The temperature at 12 am was 44 degrees. The temperature dropped steadily for the next 8 hours to reach the daytime low of 20 degrees. Create an equation for the relationship between temperature and the time. In each of the following transactions ( a ) through ( c ) for Romney's Marketing Company, use the three step process illustrated in the chapter to record the adjusting entry at year-end December 31, 2015. The process includes (1) determining if revenue was earned or an expense incurred, (2) determining whether cash was received or paid in the past or will be received or paid in the future, and (3) computing the amount of the adjustment. a. Estimated electricity usage at $450 for December; to be paid in January of next year. b. On September 1 of the current year, loaned $6,000 to an officer who will repay the loan principal and interest in one year at an annual interest rate of 14 percent. c. Owed wages to 10 employees who worked four days at $200 each per day at the end of the current year. The company will pay employees at the end of the first week of next year. What is the tone like in this and feel free to add any more notes x What is the interquartile range (IQR) of the data set represented by this boxplot?3239446169 . 22 . 17 C. 39D. 44 What are the multiplication sentences for factors of 6? Write the correct conjugation. (By the way, how would I figure this out because it doesn't make sense to me?) Thanks. WILL GIVE BRAINLIEST, NEED HELP ASAP ----------------------------------------------------------------------------------------------------------------------------Based on the section "A country full of mountains," how did deserts and mountains affect Chinese civilization?AThey attracted people from around the world who wanted to hike and ski.BThey became oases where large populations created huge farming settlements.CThey created barriers that forced the people to focus on improving what they had.DThey formed rivers and worked as boundaries to keep them from overflowing. In the early days of the Internet, most access was done via a modem over an ________.Question 10 options:Analog telephone lineFaxTelegramNone of the above Write an equation in slope-intercept form of the line that passes through the given points. 0,4 4,2 What does it mean to be "somebody" and what does it mean to be "nobody"?Which is better in the context of this poem? Which is better in your opinion?Write a 5 sentence paragraph response. Solve the equation. Graph the solution on a number line. (You dont have to graph it, I just need the equation answer.)5x = 20; x = ? Does anyone know?? I'll give a brainliest For the correct answer. 38:5A point is on a circle if the distance from the center of the circle to the point is equal to theCEarea.circumference.o radius.O diameter. When you recant something, what are you doing?O A. Spreading a new ideaO B. Making a good decisionO C. Taking back what you saidO D. Describing it in accurate detail DESCRIBE a food chain for a temperate forest community that contains at least four links. the intersection of parallel lines b and c and transversal line d form several special angle relationships. which pairs of angles and vertical angles? 2. On the Internet, you find an Latin quiz with 10 matching vocabulary questions. Your 3 year old niece randomly matches thewords with the definitions. What is the probability that she makes 100 on the quiz?Does the order matter? Yes -This is a permutationWill all of the words be matched? Yes -Can we use factorials? Yes -How many different ways can the answer key be arranged?P(all correct)(Enter your answer as a reduced fraction using/ for the fraction bar.) Mr. Voytko wants to know how high in meters he can lift an 0.3 kg apple with 7.35 joules? Find y in the parallelogram