The grades on a language midterm at Oak Academy are roughly symmetric with = 67 and 0 = 2.5. Ishaan scored 70 on the exam. Find the z-score for Ishaan's exam grade. Round to the nearest tenth.

Answers

Answer 1

Answer:  1.2

Step-by-step explanation:

Let X denotes the grades on a  language midterm at Oak Academy.

As per given ,

X follows normal distribution ( because it has symmetric graph)

[tex]\mu=67,\ \ \ \ \sigma= 2.5[/tex]

Formula for z : [tex]z=\dfrac{X-\mu}{\sigma}[/tex]

For X = 70, we have

[tex]z=\dfrac{70-67}{2.5}=\dfrac{3}{2.5}=1.2[/tex]

Hence, the z-score for Ishaan's exam grade = 1.2

Answer 2

z-scores are the corresponding standard normal variate's values for normal variates' values. The z-score for Ishaan's grade is 1.2

How to get the z scores?

If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z score.

If we have

[tex]X \sim N(\mu, \sigma)[/tex]

(X is following normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] )

then it can be converted to standard normal distribution as

[tex]Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)[/tex]

(Know the fact that in continuous distribution, probability of a single point is 0, so we can write

[tex]P(Z \leq z) = P(Z < z) )[/tex]

Also, know that if we look for Z = z in z tables, the p-value we get is

[tex]P(Z \leq z) = \rm p \: value[/tex]

For the given case, if we suppose the random variable X's values as scores of the grades on given language midterm at Oak Academy, then, as it is symmetric around value 67, with σ = 2.5, thus,

[tex]X = N(\mu = 67, \sigma = 2.5)[/tex]

Its given that Ishaan scored X = 70

The standard normal variate conversion of X is given by:

[tex]Z = \dfrac{X- \mu}{\sigma} = \dfrac{X - 67}{2.5}[/tex]

Thus, z-scores for Ishaan's score is: [tex]Z = \dfrac{70 - 67}{2.5} = \dfrac{3}{2.5} = 1.2[/tex]

Learn more about standard normal distribution here:

https://brainly.com/question/10984889


Related Questions

Can someone one at least help me with Part A?

Answers

13x + 42 < 81

X represents the number of cheeseburgers. 42 is the combined grams from the onion rings and shake.
This all combine can be no more than, meaning less than, 81.

Write an equation of a parabola with a vertex at the origin and the focus at (0,3). Please helpppp meeee???!!

Answers

Answer:

y= [tex]\frac{1}{12}[/tex] · x²

Step-by-step explanation:

[tex]\frac{1}{4 times P}[/tex] ·x²

p=3

[tex]\frac{1}{4times3}[/tex] ·x²

94.89 x 3.11 ≈
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Answer:

295.1079

Step-by-step explanation:

Sally went to the clearance rack at a department store and found a shirt she wanted to buy. The shirt was $36.00 and is on sale for $24.00. What is the percent of the decrease?

Answers

Answer:

33.34%.

Step-by-step explanation:

Given that,

The actual price of the shirt = $36

Price on sale = $24

We need to find the percent of the decrease. The formula for the percentage is given by :

[tex]\%=\dfrac{|\text{actual value-estimated value}|}{\text{actual value}}\times 100[/tex]

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9. Consider f(x) = x³+x¹. Would the function be even, odd, neither, or not enough information to determine? A. even B. Odd C. Neither D. Not Enough Information​

Answers

The function is odd, since

f(-x) = (-x)³ + (-x)

… = (-1)³ x³ - x

… = -x³ - x

= -(x³ + x)

… = - f(x)

so the answer is B.

c=(q+k/3)m for q Solve for q.

Answers

Answer:

(3 -mk)/3m=q

Step-by-step explanation:

you have been saving money to buy a new pair of shoes. Three different stores are having sales on them. Which store has the best deal. Order from lowest price to the highest price.

Original Price $70
Take 10% off
Then take 10% off that price

Original Price $80
Take 15% off
Then take 10% off

Original Price $90
Take 10% off
Then take $25 of

Answers

Answer:

Store 1 has the best deal at $56.70. The order goes as shown below!

Step-by-step explanation:

Store 2 - $61.20

Store 3 - $60.75

Store 1 - $56.70

Hope this helped :)

18) If Holstein cows produce milk that is on average 3.66% butterfat and Jersey
cows produce milk that is on average 4.5% butterfat, how many gallons of Jersy milk
should be added to every 100 gal of Holstein milk to have milk that is 4% butterfat?

Guys please help me with this question I’m using all my points for this please just help me

Answers

Answer:

68 gallons

Step-by-step explanation:

Milk of Holstein cows ⇒ 3.66% butterfatMilk of Jersey  cows ⇒ 4.5% butterfat

If we add x gal of 4.5% milk, then we have below equation:

100*0.0366 + x*0.045 = (100 + x)*0.043.66 + 0.045x = 0.04x + 40.045x - 0.04x = 4 - 3.660.005x = 0.34x = 0.34/0.005x = 68 gal

Xochitl has saved $201.60. Yamka has saved LaTeX: \frac{2}{3}2 3 the amount Xochitl saved. Zack has saved 1.5 times the amount Yamka saved. How much have they saved all together?

Answers

Answer:

$537.60

Step-by-step explanation:

Xochitl has saved $201.60.

Yamka has saved 2/3 the amount Xochitl saved.

The amount Yamka has saved us calculated as:

2/3 × $201.60

= $134.40

Zack has saved 1.5 times the amount Yamka saved.

The amount Zack has saved is

1.5 × $134.40

= $201.60

How much have they saved all together?

This is calculated as:

$201.60 + $134.40 + $201.60

= $537.60

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Answers

Answer:

x = 30°

Step-by-step explanation:

Since m and n are perpendicular, then

y + 70° = 90° ( subtract 70° from both sides )

y = 20°

thus 40 + y = 40° + 20° = 60°

Then

x + 60° = 90° ( subtract 60° from both sides )

x = 30°

Francis is 9 years older than Vincent. Francis is 17 years old. Let v represent how old Vincent is.

Which equation shows an equality between two different ways of expressing how old Francis is?

A. v + 9 = 17
B. v – 9 = 17
C. v x 9 = 17
D.

Answers

Answer: A

Step-by-step explanation:

Francis = v+9

17 = v +9 so A

Answer:

it would be a

A passenger train has 12 cars with a total of 204 people on it. How many people per car?

Answers

Answer:

17

Step-by-step explanation:

204 / 12 = 17

which ordered pair is a solution to the equation y=3x-10​

Answers

Answer:

(4,2)

As you plug the coordinates into an equation and it equals

(3x4)-2= 12-2 =10

Have a beautiful day! v(⌒o⌒)v♪

Geppetto is a puppet maker. When the month started, Geppetto had 6 puppets ready to sell. On the ninth day, he had 69 puppets finished.

Answers

He made 7 puppets per day for nine days plus that 6

2.4 x 10^2 and 2.4 x 10^3 expressed in scientific notation?

Answers

Answer:

.024 and .0024

Step-by-step explanation:

move the decimal over the amount of spaces that is the exponent.

how would I go about Simplify 2⁵ ÷ 2³​

Answers

Answer:

2^8

Step-by-step explanation:

A manufacturer wants to construct a box whose base length is 4 times the base width. The material to build the top and bottom cost 8 dollars per ft.2 and sides 5 dollars per ft.2. If the box must have a volume of 72 ft.3, determine the dimensions that will minimize cost.

Answers

Answer:

width = 1.77845 ft

length = 7.1138 ft

height = 5.691 ft

total cost = $759.09

Step-by-step explanation:

volume = length x width x height

length = 4 width

base of the rectangle = 4 x 1 w = 4w²

72 (volume) = 4w²h

18 = w²h

f(c) = (2 x 4w² x $10) + (2 x wh x $5) + (2 x 4wh x $5)

f(c) = 80w² + 10wh + 40wh

f(c) = 80w² + 50wh

since we need only 1 variable (width), we have to substitute h:

h = 18/w²

f(c) = 80w² + 50w(18/w²) = 80w² + 900/w

f'(c) = 160w + 900/w²

0 = (160w³ + 900)/w²

0 = 160w³ + 900

0 = 20(8w³ + 45)

0 = 8w³ + 45

8w³ = -45

w³ = -45/8

w = ∛-45/8 = -1.77845 and 1.77845

since w cannot be negative, then it must be 1.77845

Can some pls help me with one question I will brainlest

Answers

Answer:

whats the question

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

whwieiwisijwjdjejeusjsjs

please hurry

what’s the slope of the line that passes through the points (-5,6) and (11,2)??

Answers

Answer:

-0.25Step-by-step explanation:11 - (-5) is 16 and 2 - 6 is -4 and -4 divided by 16 is -0.25

Answer:

-0.25

Step-by-step explanation:

This is because when calculating the slope of given points, we must use this simple formula:

Slope= rise/run = Δy/Δx

(simplified version)

The actual formula is

slope = (y₂ - y₁) / (x₂ - x₁)PROCESS:

1. Find the difference of the x axis'

ANSWER: The difference of the x axis should be 11-(-5)= 16

2. Find the difference of the y axis'

ANSWER: The difference of the y axis should be 2-(6)= -4

3.  Substitute these new values into the formula Δy/Δx

ANSWER: You should get -4/16 which is -0.25

4. Your answer will be -0.25

The length of a rectangle is 4 yd less than three times the width, and the area of the rectangle is 55 ya? Find the dimensions of the rectangle. Length: Width : ​

Answers

Answer:

length = 11 yard

width =  5 yard

Step-by-step explanation:

Area of a rectangle = L W

where A = 55 yard

           L = 3W - 4

find: Length

        width

solution:

A = L W

55 = (3W - 4) W

55 = 3W² - 4W

3W² - 4W - 55 = 0

use quadratic equation to solve for W:

W = - (-4) ± √(-4)² - 4(3)-55

                    2(3)

W = 5,  W = -11/3

substitute W=5 to equation L = 3W - 4 to solve for L

L = 3W - 4

L = 3(5) - 4

L = 15 - 4

L = 11

therefore, the dimensions of a rectangle:

length = 11 yard

width =  5 yard

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Answers

Answer:

I would say that the percentage is 2  since

90=100\%(1)

x=95\%(2)

x=85.5

so the answer for this equation is 2% of percentage tax

and will save 85.5

A rectangle is 12 feet long and 5 feet wide. If the length of the rectangle is increased by 25% and the width is decreased 20%, what is the change in the area of the rectangle?​

Answers

Answer:

36 ft squared

Step-by-step explanation:

12*5=60 Original Size

12+25% of 12= 16

5+ 20% of 5= 6

6*16=96

The difference between the two:

96-60=36 ft squared difference

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Answers

the answer is 5. (B)

What is 12r + 5 + 3r - 19

Answers

Ниже прикреплено фото с объяснением

What is the equation in slope-intercept form for the graph shown? *
N
0
F. y + x = -3
G. y = 3x + 1
H. y - 3x = 1
I. y = - 3x + 1

Answers

Answer:

I

Step-by-step explanation:

The answer is y = -3x+1. If you need an explanation, just ask.  

What is the value of x in the equation 5(3x + 4) = 23?

start fraction 43 over 15 end fraction
start fraction three over 15 end fraction
start fraction 15 over 43 end fraction
start fraction two over five end fraction

Answers

Answer:

5(3x+4)=23

5*3=15 5*4=20

15x+20=23

      -20=-20

15x=3

divide by 15 from both sides

x=0.2

Step-by-step explanation:

Answer:

5(3x+4)=23

5*3=15 5*4=20

15x+20=23

     -20=-20

15x=3

divide by 15 from both sides

x=0.2

Explanation: In a fraction, the number of equal parts being described is the numerator (from Latin: numerātor, "counter" or "numberer"), and the type or variety of the parts is the denominator (from Latin: dēnōminātor, "thing that names or designates"). As an example, the fraction 8/5

amounts to eight parts, each of which is of the type named "fifth". In terms of division, the numerator corresponds to the dividend, and the denominator corresponds to the divisor.

Informally, the numerator and denominator may be distinguished by placement alone, but in formal contexts they are usually separated by a fraction bar. The fraction bar may be horizontal (as in 1/3), oblique (as in 2/5), or diagonal (as in 4⁄9). These marks are respectively known as the horizontal bar; the virgule, slash (US), or stroke (UK); and the fraction bar, solidus, or fraction slash. In typography, fractions stacked vertically are also known as "en" or "nut fractions", and diagonal ones as "em" or "mutton fractions", based on whether a fraction with a single-digit numerator and denominator occupies the proportion of a narrow en square, or a wider em square. In traditional typefounding, a piece of type bearing a complete fraction (e.g. 1/2) was known as a "case fraction", while those representing only part of fraction were called "piece fractions".

PLEASE HELP ME ASAP!!

Answers

the answer would be y= -2/5x +2 :)

Please Help ASAP - 10 Points!

What is the value of f(g) at f(21)?

Answers

Answer:

46.2

Step-by-step explanation:

if you plug the value given for g into g in the equation, it should look like

2.2(21) which you multiply the two together. and you get 46.2.

hope this helps you...sorry just seen  your question now.

Simplify -8xy + 7xy

is the answer xy?

Answers

-8 + 7 = -1

so the answer would be:

-xy or -1xy

Answer:

-xy

Step-by-step explanation:

Add -8xy and 7xy= -xy

Hope this helped! :)

May i have brainliest!

please help me and pls do both

Answers

Answer:

7/36

Step-by-step explanation:

find the LCD   write all the numerators above the least common denominator

LCD is 36

4 +3 /36 =7/36

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