X ~ N(70, 14). Suppose that you form random samples of 25 from this distribution. Let X be the random variable of averages. Let ?X be the random variable of sums. Find the 10th percentile. (Round your answer to two decimal places.)

Answers

Answer 1

Answer:

The 10th percentile is 66.42.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

X ~ N(70, 14).

This means that [tex]\mu = 70, \sigma = 14[/tex]

Suppose that you form random samples of 25 from this distribution.

This means that [tex]n = 25, s = \frac{14}{\sqrt{25}} = 2.8[/tex]

Find the 10th percentile.

This is X when Z has a pvalue of 0.1, so X when Z = -1.28.

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

By the Central Limit Theorem

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

[tex]-1.28 = \frac{X - 70}{2.8}[/tex]

[tex]X - 70 = -1.28*2.8[/tex]

[tex]X = 66.42[/tex]

The 10th percentile is 66.42.


Related Questions

A basketball player has a 60% chance of making each free throw. What is the probability that the player makes exactly
three out of six free throws?

Answers

It has 27.648 percent

Find the value of x in the triangle shown below 3 6

5

√18

√27

4

Answers

a^2 + b^2 = c^2

In this case we're looking for C

so

(3)^2 +  b^2 = (6)^2

9 + b^2 = 36

b^2 = 36-9

√b^2 = √27

b = 3√3

Answer:

the answer is actually d= 27

Step-by-step explanation:

What is the answer to this please????

Answers

Answer:

your answer will be

y=40 x +20

Step-by-step explanation:

have a nice day/night ^_^

If you divide me by 9, the remainder is 4. I am a multiple of 10. What two-digit number am I?​

Answers

Answer:

40?

Step-by-step explanation:

i tried

Highest common factor of 15 30 and 45

Answers

Step-by-step explanation:

I believe it is 15...all the numbers can be divided by 15, since 15 is the smallest number it is also the highest common factor only because 30 and 45 can be divided by 15

.......hope it helps!

Answer:

15

Step-by-step explanation:

Find the prime factors for each number as:

45 =3 × 3 × 5

30 = 2 × 3 × 5

15 = 3 × 5

Now identify the common factors and determine the GCF:

Therefore:

HCF = 3 × 5 = 15

Answer choices please help
240
200
240
280

Answers

It’s just blank I’m sorry :( I can’t see the photo
The answer is A: 240

if ABCA-QRS, what must be the measure of <A​

Answers

Answer:

m<A is 33

Step-by-step explanation:

126+21+x=180

147+x=180

180-147=x

x=33

Name the two congruent triangles

Answers

Answer:

∆ABE ≅ ∆DCE by SAS Congruence Theorem.

Step-by-step explanation:

The diagram given indicates the following:

<E ≅ <E (vertical angles)

AE ≅ DE

BE ≅ CE

Thus, an included angle, <E, and two side lengths, AE and BE, in ∆ABE are congruent to an included angle, <E, and two corresponding side lengths, DE and CE, in ∆DCE. By the SAS Congruence Theorem, both angles are congruent to each other.

Therefore:

∆ABE ≅ ∆DCE by SAS Congruence Theorem.

Help please!
Factoring Quadratics
Factor the following quadratic expressions into two binomials. Show your work.

1. x + 34x + 64
2. x - 14x + 40
3. X2 + 8x - 48
4. x2 - 17% - 60
5. 2x + 13x + 20
6. 5x? - 13x + 6
7. 8x + 14x - 15
8.-8x? - 20x + 12

Answers

Answer:

Step-by-step explanation:

Sry but I only did 1,2,5,6,7&8

But am not sure if am correct just try

ags of sugar come in 3 sizes.

Small bag: A 250 g bag costs 64p.
Medium bag: A 575 g bag costs £1.25.
Large bag: A 1.25 kg bag costs £2.54.

Find the cost per gram for each bag of sugar.
Round your answers to 3dp.
Write which size of bag is best value for money in the comment box.

Answers

Answer:1 gram of the small bag costs 0.256p ,1 gram of the medium bag costs 0.217p and 1 gram of the big bag costs 2. 032p

Step-by-step explanation:

Which equation can be used to describe the pattern in the table

Answers

Answer:

I feel like its C.

Step-by-step explanation:

Answer:

the answer is C

Step-by-step explanation:

because all the a values are 5 more than b

Help please!! I’ll give best answer brainliest!!

Answers

Answer:

D, The last one

Step-by-step explanation:

What fraction is equivalent to 8%

Answers

2/25

4/50

8/100

this are the smallest fractions equivalent to 8%

Answer:

8/100

Step-by-step explanation:

8% = 0.08 = 8/100

let me know if you need more of an explaination <33

PLAZ HELPPP PWETRYYY PSLOD

Answers

Answer:

=

Step-by-step explanation:

whatever comes out of an absolute value is always positive so 8=8

Ms. Smith mixes orange juice with seltzer in a ratio of 3:1. If she uses 48 ounces of orange juice, how many ounces of seltzer does she need?

Answers

Answer:

16 oz

Step-by-step explanation:

the ratio is 3 oz of oj to 1 oz of seltzer.

I pretty much just divided 48 by 3.

I hope this is correct and I hope it helps you!

How do I solve 5x/6=-8 to get the answer

Answers

Answer:

Download photo math

Step-by-step explanation:

Need help please help me​

Answers

the answer is c not tha

Help fast pleaseeeee

Answers

we will find the area of triangle with sides 5y,6y and 9y using herons formula

Your business loan has a variable interest rate. Next month the annual rate will jump from 6.3% to 7.8%. Your balance is
$1,620,000. How much will your monthly payment go up?

Answers

Answer:

$2,025

Step-by-step explanation:

The monthly payment will be increased by $‭2,025‬.

What is an amount?

The quantity of money anyone has is termed as the amount. Your monthly payment based on the rate of 6.3% per annum is:

= (6.3% * 1,620,000 ) / 12 months

= 102,060‬ / 12

= $‭8,505‬

Now that the rate has gone up to 7.8% per annum, the payment is:

=  (7.8% * 1,620,000 ) / 12 months

= ‭126,360‬ / 12

= $‭10,530‬

Payment went up by:

= ‭10,530‬ - 8,505

= $‭2,025‬

Therefore the monthly payment will be increased by $‭2,025‬.

To know more about the amount follow

https://brainly.com/question/25109150

#SPJ2

The graph of triangle ABC is shown below:



What is the area, in square units, of triangle ABC?

Answers

Answer:

36 square units

Step-by-step explanation:

Height = 9

Base = 8

Area of a triangle = A = 1/2bh

Plug in

1/2 (8) (9) = 4 x 9 = 36

Kate’s father is a baker at the Morning Muffin Bakery. This morning the oven wasn’t working correctly and 2 dozen muffins burned. Kate’s father gave ¼ of what was left to Kate to take to school. He wrapped up ½ of the remaining muffins and sold them to the grocery store down the street. He then wrapped ⅓ of what was remaining and gave them to the coffee shop to sell. That left Kate’s father with a dozen muffins to sell at the bakery. How many muffins did Kate’s dad bake?

Answers

Answer:

64

Step-by-step explanation:

Step 1: 12 divided by 3 = 4. 12+4 = 16.

I need to know what ⅓ of 12 is so I can continue the problem without messing up.

Step 2: 16*2 = 32.

Half of however many are left is 16.

Step 3: 32 divided by 4 is 8. 32+8 is 40. Two dozen is 24. 40 + 24 = 64.

Now we know the answer.

Boom.

Solve the equation. The symbol "^" mean "raised to the second power"

C^2=28.2+42.1​

Answers

Answer:

Step-by-step explanation:

c^2=28.2 + 42.1

SOLVE FOR A

A=logc (703/20), c ≠ 1 and C > 0

SOLVE FOR C

{ c = - (700/20) 1/a, A ≠ 0 and Numberator (A) bmod 2 = 0 and denominatior (A)bmod 2=1 SOOOOOOO a ≠ 0

Ava bought 2 sandwiches for a total of $5.25, a bowl of soup for $3.00, and a bag of chips for $1.25. How much change did she get back if she paid with a $20.00 bill?​

Answers

Answer:

Step-by-step explanation:

5.25

3.00

1.25

_____

$ 9.50

- 20.00

_______

$10.5

What is the area of this shape

Answers

46

i think im not sure

Pleasee helppp it’s due todayyy

Answers

Answer:

88 is a solution to 1/8 x =11, since a solution means that x is equal to that number, so in this scenario, x=88. When substituted(88*0.125), the same answer, 11, is obtained.

Step-by-step explanation:

Calculate the area, in terms of x and in simplest form, of the rectangle shown below.
5x + 4
2x - 5

Answers

I know the answer but let me just make sure that it is correct

5x +4 the x is 2 the answer to this is 14

2x-5 the x is 4 the answer to this is 13

A rectangular prism has a length of 1 1/4 centimeters, a width of 4 centimeters, and a heigh of 3 1/4 centimeters What is the volume of the prism? Enter your answer in the box as a simplified mixed number or a decimal​

Answers

Answer:

Step-by-step explanation:

V=lbh=1 1/4×4×3 1/4

=5/4×4×13/4

=65/4

=16 1/4 cm³

=16.25 cm³

Volume of a rectangular prism can be found by multiplying all three dimensions of the prism together:   V = lwh

WILL MARK BRAINLIEST!!!

(03.03)
The description below represents Function A and the table represents Function B:

Function A

The function is 2 more than 5 times x.

Function B

x
y
−1
2
0
5
1
8

Which statement is correct about the slope and intercept of the two functions? (1 point)

Select one:
a. Their slopes are equal but y-intercepts are not equal.
b. Their slopes are not equal but y-intercepts are equal.
c. Both slopes and y-intercepts are equal.
d. Neither slopes nor y-intercepts are equal.

Answers

Function b? Honestly, I need these points.

solve for x: -3(x+7)=5 . Explain how you solved for x and how you know your answer is correct​

Answers

Answer:

Step-by-step explanation:

-3(x+7)=5

1. Multiply 3 and x+7 , you will get -3x-21=5

2. Add 21 on both sides, you will be left with -3x=26

3. Divide both sides with -3, and x will equal to -26/3

The length of a rectangle is increasing at a rate of 4 meters per day and the width is increasing at a rate of 1 meter per day. When the length is 10 meters and the width is 23 meters, then how fast is the AREA changing

Answers

Answer:

[tex]\displaystyle \frac{dA}{dt} = 102 \ m^2/day[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Geometry

Area of a Rectangle: A = lw

l is lengthw is width

Calculus

Derivatives

Derivative Notation

Implicit Differentiation

Differentiation with respect to time

Derivative Rule [Product Rule]:                                                                              [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]

Step-by-step explanation:

Step 1: Define

[tex]\displaystyle l = 10 \ meters[/tex]

[tex]\displaystyle \frac{dl}{dt} = 4 \ m/day[/tex]

[tex]\displaystyle w = 23 \ meters[/tex]

[tex]\displaystyle \frac{dw}{dt} = 1 \ m/day[/tex]

Step 2: Differentiate

[Area of Rectangle] Product Rule:                                                                 [tex]\displaystyle \frac{dA}{dt} = l\frac{dw}{dt} + w\frac{dl}{dt}[/tex]

Step 3: Solve

[Rate] Substitute in variables [Derivative]:                                                    [tex]\displaystyle \frac{dA}{dt} = (10 \ m)(1 \ m/day) + (23 \ m)(4 \ m/day)[/tex][Rate] Multiply:                                                                                                [tex]\displaystyle \frac{dA}{dt} = 10 \ m^2/day + 92 \ m^2/day[/tex][Rate] Add:                                                                                                      [tex]\displaystyle \frac{dA}{dt} = 102 \ m^2/day[/tex]

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Implicit Differentiation

Book: College Calculus 10e

Other Questions
A fruit fly somatic cell contains 8 chromosomes. How many chromosomes will each fruit fly gamete contain? 2.11.2 project: performance task: the parallax problem help needed pls!! Gina and her friends postponed their trip to the moviesbecause a thunderstorm was brewing, Gina helped hermother with the laundry, Christopher decided to followthe updates about the thunderstorm on his computer,Rodney took a shower, and Pablo read a book in hisroom. Which person would likely be the most safe from thethunderstorm?O GinaO ChristopherRodney0 Pablo please help 10 points per person 2 pounds 13 ounces = how many ounces? *Please help i will give brainliest :P Read article then give me 2 facts and a question you have for the author about birds. Select the factorsthat, according to research, determine the snack food eaten by consumers.moodsimplicitydietDeasehungerpricetaste The ________________________ option allows one to start a numbered list on any number desired. [Set Starting Number Values]Question 7 options:Number FormatsChange List LevelDefine New Number FormatSet Numbering Value When future historians examine our contemporary age, they will likely be perplexed by many things. Of course, change is a constant throughout history. The past flows into the present, which in turn the future.Fill in the blank with the correct answer.A) destroysB) controlsC) merges withD) rallies around Some of the Pygmies of the Congo are the____and the____ Patty and Bob were in a romantic relationship. While they were seeing each other, Patty and Bob acquired an electronics service center, Bob paying $60,000 and Patty running all facets of the center. The center becomes very profitable. Two years later, when the romantic relationship ended, Bob goes to court for a declaration that they had no partnership because they did not have a written partnership agreement and Patty contributed no cash, she was merely an employee. Did they have a partnership plsssss help right now pls pls pls pls pls PLEASE HELP ME: Strawberries cost $1.24 per pound. What is the cost for 3.16 pounds of strawberries? 20s, 140e what continent is this How did the U.S. military hope to win the war in Vietnam? Which artwork didPicasso make duringhis Classical Period? Please help me need this today before 11:00pmThe fight - John Montague poem summarize the poem in sentences , Identify one example where the author used connotation and explain how, What are the speakers and poets attitudes (or tone) in the poem, Where is there a shift ( or change) in attitude, What is the theme of the poem, What does the title mean to you now. Solve to x to the nearest foot How did Caesar change the Roman Senate?He increased its membership by adding members who were loyal to him.He loosened its membership requirements so more people could run for election.He gave the people of the nation more representation than people from conquered lands.He created new rules that made representation more equal between patricians and plebeians. True or false?All quadrilaterals are also rhombuses.