2.
Select the correct answer.
The national apple growers organization recently released its first crop of a new apple variety. It gathered data on the weight of the new apples.
It found a population mean of 4.85 ounces and a standard deviation of 0.92. Each sample size was 500 apples. By the central limit theorem,
which interval do 99.7% of the sample means fall within?
OA.
4.81 and 4.89
OB.
4.73 and 4.97
Ос. .
4.84 and 4.86
OD
4.77 and 4.93
Answers
Answer:
B. 4.73 and 4.97
Step-by-step explanation:
To solve this question, we need to understand the Empirical Rule and the Central Limit Theorem.
Empirical Rule:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
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.
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.
Standard deviation of 0.92, sample of 500:
This means that [tex]\sigma = 0.92, n = 500, s = \frac{0.92}{\sqrt{500}} = 0.04[/tex]
By the central limit theorem, which interval do 99.7% of the sample means fall within?
Within 3 standard deviations of the mean. So
4.85 - 3*0.04 = 4.85 - 0.12 = 4.73
4.85 + 3*0.04 = 4.85 + 0.12 = 4.97
So, option B.
Answer:
4.73 and 4.97
Please give me brainliest, I really need it.
Related Questions
Which statement does not describe the graph of f(x) = -3
3 (*)*-+2?
A As x→ 00, f(x) +0.
B As x→-0, f(x) →-0.
© The y-intercept is (0, -13).
D The asymptote is y = 2
Answers
Suppose that you have a bowl of 500 m&m candies, and each day you eat 1/4 of the candies you have. Is the number of candies left changing linearly or exponentially? Write an equation to model the number of candies left after n days.
Answers
Answer:
[tex]500(.75)^{n}[/tex]
Step-by-step explanation:
It is changing exponentially because if you are eating a fraction of the left over m & m's, that is a different amount each time so it can't be linear.
500(1-(1/4))^n
[tex]500(.75)^{n}[/tex]
Initial quantity of the candies = 500
If we eat [tex]\frac{1}{4}[/tex] candies each day, number of candies after one day
= 500 - [tex]\frac{1}{4}\times 500[/tex]
= 500 - 125
= 375
Number of candies after two days
= 375 - [tex]\frac{1}{4}\times (375)[/tex]
= 281.25
Therefore, sequence formed will be.
500, 375, 281.25.......n days
Ratio of 2nd and 1st term = [tex]\frac{375}{500}[/tex] = 0.75
Ratio of 3rd and 2nd term = [tex]\frac{281.75}{375}[/tex] = 0.75
Therefore, there is a common ratio of 0.75 in each successive and previous term.
And the sequence will be a geometric sequence.
Expression for the exponential decay is,
[tex]A=A_0(1-r)^n[/tex]
Here, A = Final amount
[tex]A_0=[/tex] Initial amount
r = percentage decrease
n = duration
From the given question,
[tex]A_0=500[/tex]
r = [tex]\frac{1}{4}=\frac{25}{100}[/tex]
Therefore, equation for the decrease in number of candies will be.
[tex]A=500(1-0.25)^n[/tex]
[tex]A=500(0.75)^n[/tex]
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May you please help me figure out every angle?
Answers
Answer:
<D = 82°
<E = 49°
<F = 49°
Step-by-step explanation:
This is an isosceles triangle because two of the sides are the same length which means the 2 bottom angles are the exact same which means we can set them equal to each other to solve for it.
ITS AN EMERGENCY PLEASE HELP
Answers
Answer:
$9.80
Step-by-step explanation:
Remember that the way to find the mean of a data set is by adding together all the values, and dividing by the number of the values. So, in this case, you add the 5 values together and get 49. Since there are 5 values, you divide 49 by 5 and get 9.8, or in a real world-money situation $9.80.
A school band performed a concert on four different days. The band sold tickets and snacks each day of the concert for a fundraiser. The first table shows the numbers of tickets sold and the amounts of money collected from ticket sales. The second table shows the numbers of snacks sold and the amounts of money collected from snack sales. If each snack costs the same price, what is the price per snack?
Answers
Answer:
$1.25
Step-by-step explanation:
There is a lot of unnecessary extra information we can ignore here. Simply divide the amount collected on any given day by the number of snacks sold.
53.75 / 43 = $1.25
Double check via another day:
45 / 36 = $1.25 ~ yup!
The price per snack is $1.25.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
From the table,
We see that,
43 snacks = $53.75
This means,
1 snack = 53.75/43 = 1.25
Similarly,
36 snacks = 45
1 snack = 45/36 = 1.25
Thus,
The price per snack is $1.25.
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Can please someone help me out and explain it step by step. Thank you
Answers
Answer:[tex]x=7, \ y=-2[/tex]
Step-by-step explanation:
Given
Equations are [tex]3x-y=23[/tex] and [tex]2x+3y=8[/tex]
take [tex]3x-y=23[/tex]
[tex]y=3x-23[/tex]
Put the value of y in another equation
[tex]\Rightarrow 2x+3(3x-23)=8\\\Rightarrow 2x+9x-69=8\\\Rightarrow 11x=77\\\Rightarrow x=7[/tex]
Put the value of x in y
[tex]y=3(7)-23=21-23=-2[/tex]
Hence, [tex]x=7, \ y=-2[/tex]
What number is in between 1.89 and 1.11
Answers
Answer:
Any number between 1.88-1.12
Step-by-step explanation:
1.88 or 1.12
for instance 1.9 , 1.92 ,1.93 1.94 ,1.95,1.96,1.97,1.98,1.99,1.1,1.2,1.3,1.4,1.5,1.6,1.7,1.8,1.9,1.91
There are infinite numbers because it is real number
PLEASE ANSWER ASAP FOR BRAINLEST !!!!!!!!!!!!!!!!!!!!
Answers
Answer:
197 in²
Step-by-step explanation:
TOP 5x5=25
BOTTOM 9x5=45
BACK 5x5=25
SLOPED FRONT 6.4x5=32
TRAPEZOID SIDE (9+5)/2x5=35 (each), so 70
25+45+25+32+70=197
A man who is 2m tall stands on horizontal ground 30m from a tree. The Angel of elevation of the top of the tree from his eyes is 28 . Fine the distance between the men eyes to the top of the tree
Answers
Answer:33.95 m
Step-by-step explanation:
Given
The height of the man is 2 m
Distance between man and tree is 30 m
the angle of elevation of the top from the eyes is [tex]28^{\circ}[/tex]
from the figure,
[tex]\Rightarrow \tan 28^{\circ}=\dfrac{h}{30}\\\\\Rightarrow h=30\tan 28^{\circ}=15.91\ m[/tex]
Using Pythagoras we can write
[tex]\Rightarrow AD^2=ED^2+AE^2\\\Rightarrow AD^2=30^2+15.91^2\\\Rightarrow AD=33.95\ m[/tex]
Thus the distance between the men eyes to the top of the tree is 33.95 m
What is the value of this expression? {18÷(2+4)}+3×2 Enter your answer in the box.
Answers
Answer:
The value of the expression is 78
Step-by-step explanation:
Answer:
Step-by-step explanation:
{18÷(2+4)}+3×2 = {18÷6}+3×2
= 3+3×2
= 3+6
= 9
Find the surface area of a basketball with a diameter of 10 in.
400π in²
10π in²
100π in²
25π in²
Answers
Answer:
100 pie
Step-by-step explanation:
Find the surface area of a basketball with a diameter of 10 in.
100π in²
10π in²
400π in²
25π in²
The surface area of the basketball is 100π square inches.
The correct option is C.
What is the surface area of a sphere?The area of the outer surface of a sphere is the surface area of a sphere.
And its formula:
The surface area of the sphere is 4πr².
Where r is the radius of the sphere.
Given:
The shape of the basketball is spherical.
The diameter of the basketball is 10 inches.
So, the radius of the basketball = 10/2 = 5 inches.
The surface area of the basketball,
= the surface area of the sphere.
= 4πr²
= 4π(5)²
= 2π25
= 4 x 25π
= 100π square inches.
Therefore, the surface area is 100π square inches.
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buna seara ce faceti eu sunt un om
Answers
Answer:
5
Step-by-step explanation:
Answer:
Sunt și bărbat, ești foarte înfiorător
Step-by-step explanation:
How much time will it take for an amount of Rs900 to yield Rs81 as interest at 4.5% per annum of simple interest
Answers
Answer:
T=2 years.hope it will help u.
nine times the difference between 4 and a number is24.what is the number.
Answers
Answer:
9×24-4
216-4
212
Step-by-step explanation:
I am not sure, but it might help you
Answer:
n = [tex]\frac{4}{3}[/tex]
or (because the wording is kind of confusing)
n = [tex]\frac{20}{3}[/tex]
Step-by-step explanation:
9(4 - n) = 24
36 - 9n = 24
-9n = -12
n = [tex]\frac{4}{3}[/tex]
or (because the wording is kind of confusing)
9(n - 4) = 24
9n - 36 = 24
9n = 60
n = [tex]\frac{20}{3}[/tex]
1. x²+2xy+y²
2. x²-8x+16
3. 16a⁴_24a²b²+9b
Answers
Answer:
1.(x+y)²
2. (x-4)²
3. (4a²-3b²)²
cost price of television is Rs 40000.The profit is 1/9 of selling price ,find the selling price .
Answers
Answer:
₹45000
Step-by-step explanation:
Let the selling price (SP) of the television be ₹x.
Therefore,
Profit [tex] =\frac{1}{9}x[/tex]
Cost price (CP) = ₹ 40000
[tex]Profit = SP - CP \\ \\ \frac{1}{9}x = x - 40000 \\ \\ \frac{x}{9} - x = - 40000 \\ \\ \frac{x - 9x}{9} = - 40000 \\ \\ - \frac{8}{9} x = - 40000 \\ \\ x = 40000 \times \frac{9}{8} \\ \\ x = 5000 \times 9 \\ \\ x = 45000[/tex]
Find the missing value(s) in this ratio table. Pens: 3 6 ? Pencils: 4 ? 12
Answers
Pen is 3 x 2 = 6
Pencils s 4 x 3 = 12
Daniel is making cupcakes for a school bake sale. He wants to make 120 cupcakes. So far he has made 65% of them. How many more cupcakes does he need to make?
Answers
0.65*120=78
First divide 65 and 100 you will get 0.65.
Then just multiply your whole number.
I will send a pic to you
Answers
Answer:
agreed
Step-by-step explanation:
agreed...............................
ABCDEFGHIJKLMNOPQRSTUVWXYZ
In a particular library, 18% of the books are children's books, 53% of the books are adult fiction, and the rest are adult nonfiction. You select 3 books at random; what is the probability That none of them are children's books?
Answers
Answer:
3321 / 12500
Step-by-step explanation:
P (not child, not child, not child) = 82/100 × 81/100 × 80/100
Which of the following is in the solution set to 3x - y = 12? (hint: what
makes the equation true)
(3,2)
(0,4)
(-4,0)
(8,12)
Answer(8,12)
Answers
24-12=12
The fourth choice.
Yeah I think you already got it
choose the correct equation please
Answers
Answer:
y=3×+6
Step-by-step explanation:
bla bla bla bla bla bla bla hhhhhhhhhhhh
need help with this ‼️
Answers
GO to math-way it’s a algebra calculator it works type this problem in
PLEASE HELP I DONT GET THIS ASAP! IS THIS 21??
Answers
The difference between three times a number and 5 is 10.
Answers
Answer:
Equation: 3x-5=10
Answer: X=5
Step-by-step explanation:
3 times a number (represented as X) and 5 (means subtract by 5)
3x-5=10
Add 5 on both sides
3x=15
X=5
Answer:
3(5) - 5 = 10
15 - 5 = 10
10 = 10 x = 5
Step-by-step explanation:
Three times a number is 3x because you do not know the number.
Add five to both sides of the equation.
Divide both sides of the equation by 3 and the solution is x = 5
Can anyone help me I would really appreciate it.
Answers
Answer:
7c + 4 = 8
7c = 8 -4
7c = 4
c=4/7
Mrs. Stephens bought 3 pounds of tomatoes.How many ounces are equal to 3 pounds?
Answers
Answer:
48 ounces
Step-by-step explanation:
16 ounces per pound
3 x 16 = 48 ounces
Rory earned an 84% on his test. He answered 21 questions correctly. How many total questions were on the
test? Round to the nearest tenth if necessary
Answers
Answer:
25 questions,
$18.75
Step-by-step explanation:
Remember, to change percents to decimals, divide the number by 100 and remove the parentheses.
1. 84%, or 21 questions of Roy's test were correct.
Let's set the number of questions on the test as "x". We can then write this equation:
84% * x = 21
Simplify.
0.84 * x = 21
Divide both sides by 0.84
x = 25
There were 25 questions on the test.
2. Cheesecake Factory question
We need to find 15% of 125.
15% * 125 =
0.15 * 125 =
18.75
They need to leave a $18.75 tip.
I hope this helps! Feel free to ask any questions!
20. The top layer of a circular wedding cake has a
diameter is 15 inches. The bottom layer of the circular
wedding cake has radius is 30 inches. How many times
greater is the circumference of the bottom layer than
the top layer?
Answers
Answer:
4 times
Explanation:
tc = 15×π = 47.12.. in
bc = 2×30×π = 188.49.. in
bc = 188.5/47.12 = 4 times
what is the value of x?
Answers
Answer:
40
Step-by-step explanation:
135-95
im not 100% sure tho