The Intelligence Test Scale in a school is composed of a number of subtests. On one subtest, the raw scores have a mean of 35 and a standard deviation of 6. Assuming these raw scores form a normal distribution: a) What number represents the 65th percentile (what number separates the lower 65% of the distribution)? b) What number represents the 90th percentile? c) What is the probability of getting a raw score between 28 and 38? d) What is the probability of getting a raw score between 41 and 44?.

Answers

Answer 1

Using the normal distribution, it is found that:

a) The 65th percentile is of 37.31.

b) The 90th percentile is of 42.68.

c) There is a 0.5705 = 57.05% probability of getting a raw score between 28 and 38.

d) There is a 0.0919 = 9.19% probability of getting a raw score between 41 and 44.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

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

It 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, which is the percentile of X.

In this problem:

The mean is of 35, hence [tex]\mu = 35[/tex]The standard deviation is of 6, hence [tex]\sigma = 6[/tex]

Question a:

The 65th percentile is X when Z has a p-value of 0.65, so X when Z = 0.385.

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

[tex]0.385 = \frac{X - 35}{6}[/tex]

[tex]X - 35 = 0.385(6)[/tex]

[tex]X = 37.31[/tex]

The 65th percentile is of 37.31.

Question b:

The 90th percentile is X when Z has a p-value of 0.9, so X when Z = 1.28.

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

[tex]1.28 = \frac{X - 35}{6}[/tex]

[tex]X - 35 = 1.28(6)[/tex]

[tex]X = 42.68[/tex]

The 90th percentile is of 42.68.

Question c:

The probability is the p-value of Z when X = 38 subtracted by the p-value of Z when X = 28, hence:

X = 38:

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

[tex]Z = \frac{38 - 35}{6}[/tex]

[tex]Z = 0.5[/tex]

[tex]Z = 0.5[/tex] has a p-value of 0.6915.

X = 28:

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

[tex]Z = \frac{28 - 35}{6}[/tex]

[tex]Z = -1.17[/tex]

[tex]Z = -1.17[/tex] has a p-value of 0.121.

0.6915 - 0.121 = 0.5705.

There is a 0.5705 = 57.05% probability of getting a raw score between 28 and 38.

Question d:

The probability is the p-value of Z when X = 44 subtracted by the p-value of Z when X = 41, hence:

X = 44:

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

[tex]Z = \frac{44 - 35}{6}[/tex]

[tex]Z = 1.5[/tex]

[tex]Z = 1.5[/tex] has a p-value of 0.9332.

X = 41:

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

[tex]Z = \frac{41 - 35}{6}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a p-value of 0.8413.

0.9332 - 0.8413 = 0.0919

There is a 0.0919 = 9.19% probability of getting a raw score between 41 and 44.

A similar problem is given at https://brainly.com/question/24663213


Related Questions

Find the constant(s): 12x - 8 - 12​

Answers

Hello there!

-8 and -12 are constants

A constant is any real number.

Hope this helps!

~Just a determined gal

#CarryOnLearning

[tex]MysteriousNature[/tex]

Help I am stuck I will give brainlist

Answers

Answer:  I think it is B

Step-by-step explanation:

What is the midpoint of the segment shown below?
10
O A. (6.3)
(2,3)
(10,3)
B. (6,3)
- 10
10
C. (5,3)
-10
D. (533)
SUE

Answers

Answer:

b. (6,3)

Step-by-step explanation:

10+2=12

12/2=6

The line is always on 3, so that will be the y coordinate!

The midpoint of the line segment are (6, 3). Therefore, option B is the correct answer.

What is the midpoint of a line segment?

A midpoint of a line segment is the point on a segment that bisects the segment into two congruent segments.

The formula to find the midpoint of line segment is (x, y) = [(x₁+x₂)/2, (y₁+y₂)/2]

From the graph, the coordinate points of ends of line segment are (2, 3) and (10,3).

Here, midpoint = [(2+10)/2, (3+3)/2]

= (6, 3)

Therefore, option B is the correct answer.

To learn more about the formula of midpoint visit:

https://brainly.com/question/4728902.

#SPJ7

A baseball tournament begins with 128 teams. After each round of games, only half of the teams are left. How many teams will be left after four rounds of games?

Answers

Answer:

128 ÷ 2 = 64

64 ÷ 2 = 32

32 ÷ 2 = 16

16 ÷ 2 = 8

answer is 8

what is the lateral surface area of a right circular cylinder with height 10cm and base area 154cmsquare (use pi = 22/7)​

Answers

Answer:

Lateral surface area = 154cm²

Step-by-step explanation:

h = 10cm

pi = 22/7

base area = 154cm²

2πrh = 154cm²

2 × 22/7 × r × 10 = 154

440/7 × r = 154

r = 154 ÷ 440/7 = 2.45

r = 2.45

LSA of right circular cylinder = 2πrh

2 × 22/7 × 2.45 × 10

44/7 × 24.5 = 1078/7

1078/7 = 154

Therefore, lateral surface area = 154cm²

Hope it helps:)

Mr. Gooddeal sells cars. He gets to keep 1/6 of his sales commission. How much must he sell in order to earn $1500.

Answers

if he sells about 8 cars he will get above 1500

Craig wants to create a right triangle with side lengths 4 centimeters, 6 centimeters, and 8 centimeters. Is this possible? Why or why not?

Answers

Answer:

It's not possible

Step-by-step explanation:

In right triangle hipotenuse must be the longest side so it'll be 8 and legs will be 4 and 6.

So

[tex]4 {}^{2} + 6 {}^{2} [/tex]

Doesn't equal to

[tex]8 {}^{2} [/tex]

16+36=52 not 64

Which number makes this number sentence true?

q: 7.05<____<7.2

o:A:7.016
B:7.182
C:7.206
D:7.241

Answers

Answer:

A: 7.016

Step-by-step explanation:

this is the answer. I'm 100% sure.

Solve 2^2x-3 = 128. X =

Answers

Answer:

x=131/4

Step-by-step explanation:

ANYONE CAN HELP ME ?? :)​

Answers

Answer:

12[tex]\frac{2}{3}[/tex] cm

Step-by-step explanation:

Have a nice day

I need help pls I'll give brainliest!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

[tex]\sqrt{32}[/tex]

Step-by-step explanation:

4^2+ 4^2=c

16+16=32

[tex]\sqrt{32}[/tex]

=5.65685424949

How to subtract? how can we minus 7 from 2 how can we maintain sign​

Answers

Answer:

a² - b² = (a+b)(a-b)

Step-by-step explanation:

= 2x² - 7x²

=(2x + 7x)(2x - 7x)

Answer:

-5x²

Step-by-step explanation:

combine like terms in 2x²-7x²

If Jada runs 5 laps around the track in 6 minutes how many minutes per lap is that

Answers

Answer:

1.2 minutes

Step-by-step explanation:

5 laps >> 360 ( 6×60)

1 lap >> x

cross multiplication

5x = 360

x = 360/5

x= 72 second

x = 72/60 = 1.2 minute

A gopher lives in an underground burrow. It starts at a certain point, p, underground and digs straight down to triple its distance under
the surface. It then climbs straight down another 2 feet. Its final position is deeper than 8 feet under the surface.
What was the gopher's original position, p, relative to the surface?
Enter your answer in the box to complete the inequality

Answers

Answer:

<-2

Step-by-step explanation:

Find the perimeter. Simplify your answer.

Answers

add all the sides!

[side one] + [side two] + [side three]

[7y + 10] + [7y + 10] + [y - 4]

= 14y + 20 + y - 4

= 15y + 16

hope this helps :) !!

Answer:

15y + 16

Step-by-step explanation:

2(7y + 10) + y - 4

14y + 16 + y

15y + 16

A recipe for a batch of muffins calls for 13 cup of sugar, 34 cup of flour, and 12 cup of milk. How many total cups of sugar, flour, and milk will be needed for three batches of muffins?

Answers

Answer:

177 total cups

Step-by-step explanation:

13×3=39 sugar

34×3=102 flour

12×3=63 milk

total 177

Simplify the exponential expression 48 Superscript one-half.

Answers

Your answer should be 4 3 (1/2

x + 8 less than or equal to 6

Answers

If this is an equality question:
x is less than or equal to -2
x is less than or equal to -2

PLS HELP ASAP ILL GIVE BRAINLKEST THANKS

Answers

Answer:

d>-7

Step-by-step explanation:

first answer
d = greater than or equal to 7

3/5 + (-4/11)...........

Answers

Answer:

13/55

Step-by-step explanation:

(3/5) + -(4/11) = (3/5) - (4/11) = (33/55) - (20/55) = (13/55)

Tell me if I'm wrong :)

[tex]\dfrac 35 + \left( -\dfrac 4{11} \right) \\\\\\=\dfrac35 - \dfrac{4}{11} \\\\\\=\dfrac{13}{55} \approx 0.24[/tex]

The elevators in an office building have been approved for a maximum load of 3,600 pounds.

Can the elevator hold a weight of exactly 3,600 lbs? If w = weight in elevator, what should the inequality look like?

Plz help thx.

Answers

Answer:

w [tex]\leq[/tex] 3,600

Step-by-step explanation:

[tex]\leq[/tex]  means less than or equal to.

Can someone please give me the answer​

Answers

Answer:

6/10

Step-by-step explanation:

30/50=3/5

3/5=3/5

15/25=3/5

3/5*2/2=6/10

Write 63 as the product of prime factors
HOW AM I WRONG???

Answers

Answer:

It says in ascending order, and I don't think exponents will work.

Step-by-step explanation:

I think the correct answer would be 3 x 3 x 7, or 3² x 7

The only mistake that I can see is that it is not in ascending order.

-Chetan K

Answer:

3*3*7 or 3^2*7

Step-by-step explanation:

Do you need to have the exponent of 2?

If not, then write it as 3*3*7 or 3^2*7

can i have help please

Answers

(y + 1)^3 would just be dividing the two

If you want it completely simplified, then it’s the following:

(y + 1)(y + 1)(y + 1)

= y^2 + y + y + 1 (y + 1)

= y^2 + 2y + 1 (y + 1)

= y^3 + y^2 + 2y^2 + 2y + y + 1

= y^3 + 3y^2 + 3y + 1

Complete the equation of the line through (-6,-5)(−6,−5)left parenthesis, minus, 6, comma, minus, 5, right parenthesis and (-4,-4)(−4,−4)left parenthesis, minus, 4, comma, minus, 4, right parenthesis.
Use exact numbers.

Answers

Answer:

d

Step-by-step explanation:

Answer:

Hint #33 / 3

The equation is y=\dfrac{1}{2}x -2y=

2

1

x−2y, equals, start fraction, 1, divided by, 2, end fraction, x, minus, 2.

Step-by-step explanation:on kan

TRUE OR FALSE , When you divide the numerator of a fraction by the denominator you always get a terminating decimal?

Answers

Answer: false.

Step-by-step explanation:

it's only a terminating decimal if you end up with a remainder of 0.

It takes Billy 40 minutes to drive to his friend's house at his normal speed but it takes two hours if he drives 20 mph slower how far away is Billy's friend's house. How far does his friend live?

Answers

Answer:

20 miles

Step-by-step explanation:

O 8) Translate the point and give the resulting coordinates.
(-9,6); (5,-2)

Answers

Answer:

- 4/7

Step-by-step explanation:

The resulting point is 5 units right and 2 units down, and the resulting coordinates are (- 4, 4).

Used the concept of coordinate that states,

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

Given that;

The coordinate is (- 9, 6) and (5, - 2).

Now the value of the resulting coordinate is found as,

(- 9 + 5, 6 - 2)

= (- 4, 4)

Therefore, the resulting point is 5 units right and 2 units down, and the resulting coordinates are (- 4, 4).

To learn more about the coordinate visit:

https://brainly.com/question/24394007

#SPJ3

Your current salary is $32,000 per
year. If you get a 4% raise, how
much will you make now per year?

Answers

Answer:

$128,000 per year

Step-by-step explanation:

32,000

×. 4

Answer:

$33,280

Step-by-step explanation:

Since your salary is $32,000, you would take 4% from $32,000 and add it to the current salary. 4% can be shown as .04 in decimal form. If you multiply 32,000 by .04 you get 1280. Add 1,280 to 32,000 and you get 33,280.

can someone give me the answer and please explain this to me because i really don't understand what this means at all, I need someone to help me with this because i'm going to be asking multiple of these questions. So if u have friends or family who know this answer then please tell/ask them these questions so they can help understand fractions. Not asking in a mean way i am just really cuious because i never learned how to do this so just let your family / or friends know what these answers are to all of the questions that i am going to ask about fractions because these are really hard for me!

Answers

Step-by-step explanation:

the one is the middle top the one in the middle bottom and the one in the bottom right

Other Questions
Describe in words a sequence of transformations that maps ABC to A' B' CWrite an ordered-pair rule for this sequence of transformations. what are languages distributed the way they are? 5. Using the equation y=2x+5, construct a table and graph the line HELP ME PLEASE! PICTURE IS HERE Will mark brainliestWhich type of conflict does Theseus face with Procrustes in "The Adventures of Theseus"?1.man vs. society2.man vs. man3.man vs. himself4.man vs. nature Write a function rule for the statement.The output is the cube of the input.y= ? What happens to the price and quantity of churro waffles if the price of brown sugar decreases?. Earth orbits the Sun because there is a:a) strong magnetic interaction between the Sun and the Earth. the gravitational interaction between the Sun and the Earth is small. b) gravitational pull from the Sun on the Earth. The Sun pulls the Earth in the direction of the Earth's orbit path.c) gravitational pulls from the Sun on the Earth. the Earth is pulled towards the sun, rather than going off in a straight line.d)gravitational force from the Sun on the Earth. The Sun part is the Earth away so it does not crash into the sun. what is 15/2 into a mixed number Solve for x in terms of y if 3x - 5 = y. Essay: What is the election process? Attempt an explanation on the rainfall regime of a station experiencing Arid climate type. Carrie loves carrots so much that she ate 30 of them for lunch. Her sister doesnt like carrots as much and only ate 5 of them for lunch. The number of carrots Carrie ate is how many times greater than the number that her sister ate? Use properties to evaluate (-25) HIS O A. 15 5 O B. 5 C. - OC. 15 O D. 1 Harvey is studying the polynomial f(x) = (4x 3)(x 3)(x2 +5) and determines that the polynomial has four real roots. Do you agree or disagree with Harveys statement? Explain your reasoning.A.yes because there are 4 roots B.yes because complex solutions do not matter C.yes because when I solve he gets 4 x intercepts D.no because there are two complex solutions Calculate the volume of the pyramid. Round your answer to the nearest hundredth 10in 7in Is the equation y + 1 = 5(x + 3) in point-slope form? Justify your answer. What is the y-intercept of the graph of the equation 6x + 3y = 18? Where does the chemical energy to produce ATP come from?The use of chemicals fro the environment to make sugarsThe conversion of ATP to ADPThe breakdown of carbon-based molecules into smaller moleculesThe addition of a phosphate group to ATP Peyton facilitates an empowerment oriented program based on the philosophy of restorative justice. Peyton is most likely employed by a _____.