Answer:
The probability that the sample mean will be between 82.5 and 86 years is 0.8351.
Step-by-step explanation:
According to the Central Limit Theorem if an unknown population is selected with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from this population with replacement, then the distribution of the sample means will be approximately normally.
Then, the mean of the sample means is given by,
[tex]\mu_{\bar x}=\mu\\[/tex]
And the standard deviation of the sample means is given by,
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
The information provided is:
[tex]\mu=85\\\sigma=6\\n=36[/tex]
As the sample size is large enough the Central Limit Theorem can be used to approximate the sampling distribution of sample mean life expectancy (M) in the United States.
Compute the probability that the sample mean will be between 82.5 and 86 years as follows:
[tex]P(82.5<\bar X<86)=P(\frac{82.5-85}{6/\sqrt{36}}<\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}<\frac{86-85}{6/\sqrt{36}})\\\\=P(-2.5<Z<1)\\\\=P(Z<1)-P(Z<-2.5)\\\\=0.84134-0.00621\\\\=0.83513\\\\\approx 0.8351[/tex]
Thus, the probability that the sample mean will be between 82.5 and 86 years is 0.8351.
The probability that the sample mean will be between 82.5 and 86 years is 0.8351.
Standard deviation σ = 6
Sample size n =36
What is the central limit theorem?The central limit theorem (CLT) states that the distribution of sample means approximates a normal distribution as the sample size gets larger, regardless of the population's distribution.
Since the sample size is significant i.e. large, so the given scenario can be treated as normally distributed as per the central limit theorem.
So, the standard deviation of sample means = σ/√n
The probability that the sample mean will be between 82.5 and 86 years:
[tex]P(82.5 < X < 86) = P(\frac{82.5-85}{\frac{6}{\sqrt{36} } } < Z < \frac{86-85}{\frac{6}{\sqrt{36} } } )[/tex]
[tex]P(-2.5 < Z < 1)=P(Z < 1)-P(Z < 2.5)[/tex]
[tex]P(-2.5 < Z < 1) =0.8413-0.0062=0.8351[/tex]
Therefore, the probability that the sample mean will be between 82.5 and 86 years is 0.8351.
To get more about the central limit theorem visit:
https://brainly.com/question/18403552
find the sum for(2x−6)+4(x−3)
Answer:
6x - 18
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Combining Like TermsStep-by-step explanation:
Step 1: Define expression
(2x - 6) + 4(x - 3)
Step 2: Simplify
Distribute 4: 2x - 6 + 4x - 12Combine like terms (x): 6x - 6 - 12Combine like terms (Z): 6x - 18An $800 couch is marked up 20%. (increase) What is the new price of the couch?
Answer:
The new price of the couch is $960
Step-by-step explanation:
Write the equation of the line that is parallel to the line y = -3x + 12 and passes through the point (-1, 6). (2 points)
Answer:
x=−9. Explanation: x=12 is a line parallel to the y-axis passing through all points in the plane with an x-coordinate of 12. therefore a line ...
x=−9 Explanation: x=12 is a line parallel to the y-axis passing through all points in the plane with an x-coordinate of 12 therefore a line parallel ... More
How long would 8 thousand trillion trillion trillion trillion trillion trillion trillion trillion years be if typed out?
Answer:
100 digits
Step-by-step explanation:
One trillion is 10¹², so it adds 12 zeros.
8000 adds 4 digits.
8 trillions add 8·12 = 96 zeros.
So in total you have 96+4 = 100 digits
This number would also be called 8 googol, since 1 googol is 10¹⁰⁰
Answer this please thanks
Answer:
No
Step-by-step explanation:
The first 3 boxes are proportional since they have a ratio of 1:3, but 6:21 is not proportional to the others.
Answer:
No it is not proportional.
Step-by-step explanation:
This is not proportional because
2 times 3 = 6
4 times 3 = 12
8 times 3 = 24
but,
6 times 3 = 18 not 21 so it is not proportional.
Hope this helped! Ask me any questions if needed!
DECA is putting in a t-shirt order for the school. At the Nike store you can get 3 t-shirts for $25.00. At the
Adidas store you can get 4 t-shirts for $29.00. At the Under Armour store you can get 5 t-shirts for $36.00. At
which store would the school get the better deal?
Answer:
Under Armour store you can get a better deal.
Step-by-step explanation:
25/3=8.33
29/4=7.25
36/5=7.2
(1, -7) slope = -1 writing linear equations given point and slope
Answer:
The answer is
[tex] \huge y = - x - 6[/tex]
Step-by-step explanation:
To find an equation of a line when given the slope and a point we use the formula
[tex]y - y_1 = m(x - x_1)[/tex]
From the question we have
[tex]y + 7 = - 1(x - 1) \\ y + 7 = - x + 1 \\ y = - x + 1 - 7[/tex]
We have the final answer as
[tex]y = - x - 6[/tex]
Hope this helps you
A sonographer is trying to determine the size of a gallstone. If
the stone is spherical and has a diameter of 12 millimeters, what
Is its volume?
Answer:
0.9 cubic centimeters
Step-by-step explanation:
Help?!
I dont understand this Help?!
Translate to algebra:
Tom has t dollars. He buys 5 packets of gum worth d dollars each. How much money does he have left?
Answer: t - 5d
Step-by-step explanation: Since you are buying 5 and they cost d dollars you would multiply 5 by d. Then since you have t dollars as a total you subtract 5d from t so you get t -5d.
Celeste wants to have her hair cut and
permed and also go to lunch. She knows
she will need $95. The perm costs twice
as much as her haircut and she needs $5
for lunch.
How much does the perm cost?
Answer:
the perm will cost $60
Step-by-step explanation:
take away $5 from the total because Its a set amount that's already known
which leaves 90 which if you take 30 away you are left with 60 its twice the amount of the haircut, I didn't really do any math techniques so I'm sorry that my explanation is weird, I hope this helped
Becky read 10 books in 4 days.Sarah reads 50 books in 20 days. Are the two girls reading at the same rate
Please help I’m stuck on this question
the answer is b. the rest is so it can be enough charecters so i can post this answer
if 5x+2y=20 and y=10, what is 3x?
Answer:
3x = 0
Step-by-step explanation:
Given,
y = 10
now,
5x+2y = 20
or, 5x+2×10=20
or, 5x = 20-20
or, 5x = 0
or, x = 0/5
or, x = 0
Again,
3x = 3×0 =0
Martinez bought 8 3/4 yd of fabric. She wants to make a skirt using 1 7/8 yd, pants using 2 3/8, and a vest using 1 2/3 yd. how much fabric will be left over?
Please help ASAP!!! :(
Answer:
The fabric left over will be [tex]2\frac{5}{6}[/tex]
Step-by-step explanation:
Total fabric bought= [tex]8\frac{3}{4} \ yd[/tex]
Fabric used for skirt = [tex]1\frac{7}{8} \ yd[/tex]
Fabric used for pants = [tex]2\frac{3}{8} \ yd[/tex]
Fabric used for vest = [tex]1\frac{2}{3} \ yd[/tex]
Total fabric used = Fabric used for skirt+Fabric used for pants+Fabric used for vest
Total fabric used=[tex]1\frac{7}{8}+2\frac{3}{8}+1\frac{2}{3}[/tex]
[tex]=\frac{15}{8}+\frac{19}{8}+\frac{5}{3}\\=\frac{15*3+19*3+5*8}{24}\\=\frac{45+57+40}{24}\\=\frac{142}{24} \\=\frac{71}{12}[/tex]
So, Total fabric used = [tex]\frac{71}{12}[/tex]
Total Fabric left= Total fabric bought-Total fabric used
Total Fabric left=[tex]8\frac{3}{4}-\frac{71}{12}[/tex]
[tex]=\frac{35}{4}-\frac{71}{12}\\=\frac{35*3-71}{12} \\=\frac{105-71}{12}\\=\frac{34}{12}\\=\frac{17}{6}\\=2\frac{5}{6}[/tex]
So, the fabric left over will be [tex]2\frac{5}{6}[/tex]
Each week, Mrs.Mack buys exactly 3 5/8 pounds of cheese for her mac-and-cheese recipe. She chooses from these kinds of cheese. Mrs.Mack buys as many packages as she needs— up to three packages of any kind. What packages of cheese (and how many of each kind) does Mrs.Mack buy? 7/8pounds of american cheese. 0.5 pounds of cheddar cheese. 0.2 pounds of swiss cheese. HELP PLEASE
9514 1404 393
Answer:
3 packages of American (7/8 lb)2 packages of cheddar (1/2 lb)Step-by-step explanation:
The amount of cheese Mrs Mack needs is an odd number of eighths of a pound. So, she must buy an odd number of the 7/8 pound packages.
If she were to buy any 1/5 pound packages, she would have to buy a multiple of 5 of them so as to have an integral number of eighths. The only suitable multiple is 0.
If Mrs Mack buys 1 of the 7/8 pound packages, she cannot make up the difference with half-pound packages. She must buy 3 of the 7/8 pound packages, for a total of 2 5/8 pounds of American cheese. The remaining pound can be bought as 2 of the 1/2 pound packages.
To buy 3 5/8 pounds, Mrs Mack must purchase ...
3 packages of American cheese (7/8 lb each)
2 packages of Cheddar cheese (1/2 lb each)
x2 + 5x +4=0
How do we do this
Answer: x=−1 or x=−4
Step-by-step explanation: Solve by factoring
Answer:
(x+1)(x+4)
Step-by-step explanation:
Please help I’m stuck on this question
Answer:
C. a => c
Step-by-step explanation:
a b c a => b a => c (not C)
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0 F F
1 0 1 F
1 1 0 F
1 1 1
¬a b c a => b ¬a => c (not B)
1 0 0 F F
1 0 1 F
1 1 0 F
1 1 1
0 0 0
0 0 1
0 1 0
0 1 1
a b c a => b c => a (not D)
0 0 0
0 0 1 F
0 1 0
0 1 1 F
1 0 0 F
1 0 1 F
1 1 0
1 1 1
¬a b ¬c a => b ¬a => ¬c
1 0 1
1 0 0 F
1 1 1
1 1 0 F
0 0 1 F
0 0 0 F
0 1 1
0 1 0
answer: everything is false lol
1+1 pls, help, I will give you brainliest answer!!! just hellllllp!!!!!
Answer:
2!!!
Step-by-step explanation:
PLS GIVE BRAINLIEST
Answer:
1+1=2
Step-by-step explanation:
Brainliest please!
What is the ones digit of 5120 + 2301 + 456?
Answer:
7
Step-by-step explanation:
Easier than you think. You do not have to add the numbers together to find your answer. You can just add 0+1+6, and you will get 7.
Answer:
7
Step-by-step explanation:
5120+2301=7421
7421+456=7877
Last # is 7
2.
If the sun is approximately 1.5 x 1011 meters from Earth, what is the approximate distance from Earth to Mars?
It was supposed to be 10 to the 11 power but it didn’t do it. It out 1011
Answer:
The distance from Earth to Mars is 8×10¹¹ m.
Step-by-step explanation:
Given that,
The speed of light is 3×10⁸ m/s. The sun is approximately 230,000,000,000 m from Mars. If the sun is approximately 1.5 x 10¹¹ meters from Earth, what is the approximate distance from Earth to Mars.
The sun is approximately 2.3 × 10¹¹ m from Mars.
The sun is approximately 1.5 x 10¹¹ m from Earth.
The distance between from Earth to Mars is :
d = 2.3 × 10¹¹ m - 1.5 x 10¹¹ m
= 8×10¹¹ m
Hence, the distance from Earth to Mars is 8×10¹¹ m.
Write an equation and solve. Round to the nearest hundredth where necessary. What is 35% of 63?
An annual pass to a park costs $120. Use a percent model to find 200% of the full price of the annual pass.
200% of the full price is $____
Given:
An annual pass to a park costs $120.
To find:
The 200% of the full price using percent model.
Solution:
In the percent model,
100% = 1 box
It means 1 box represents park costs $120.
200% = 2 box
[tex]120+120=240[/tex]
It means 2 box represents park costs $240.
Therefore, 200% of the full price is $240.
After simplifying the following expression, the coefficient of the m^2 term will be ______.
6mn^2 + 3m^2 + 16m^2 - 6m^2 - 5nm^2
The solution is ______
Answers:
After simplifying the following expression, the coefficient of the m^2 term will be 13
The solution is 13m^2 + 6mn^2 - 5nm^2
====================================================
Explanation:
Highlight all the terms that have m^2 in them and nothing else (so that means no variables of n or n^2)
You should highlight 3m^2, 16m^2 and -6m^2 as the three terms.
The coefficients 3, 16 and -6 combine to 3+16-6 = 13
Meaning that 3m^2+16m^2-6m^2 = 13m^2
----------------
There are no other like terms that pair up.
The 6mn^2 and -5nm^2 are different because the exponent 2 is over a different letter each time. Put another way: mn^2 is not the same as nm^2
So we cannot combine 6mn^2-5nm^2. We leave it as is.
Overall, the entire expression simplifies to 13m^2 + 6mn^2 - 5nm^2
What is the slops of this line? Enter your answer as a fraction in simplest term in the box.
Answer:
It is 1/4
Step-by-step explanation:
If you go from dot to dot on the line, starting with the first dot:
you go to the right 4 times and then up 1 to get to the next dot.
If you put that into a fraction it is [tex]\frac{rise}{run}[/tex] so going up (1) is ontop of going to the right (4), which is 1/4.
what is the equation of aline that passes through the point (4,-8) and has a slope of -1/2?
Answer:
The equation of the line will be:
[tex]y=-\frac{1}{2}x-6[/tex]
Step-by-step explanation:
Given
slope = m = -1/2point (4, -8)Point slope form:
[tex]y-y_1=m\left(x-x_1\right)[/tex]
substituting the values m = -1/2 and the point (4,-8)
[tex]y-\left(-8\right)=\frac{-1}{2}\left(x-4\right)[/tex]
[tex]y+8=\frac{-1}{2}\left(x-4\right)[/tex]
subtract 8 from both sides
[tex]y+8-8=\frac{-1}{2}\left(x-4\right)-8[/tex]
[tex]y=-\frac{1}{2}x-6[/tex]
Therefore, the equation of the line will be:
[tex]y=-\frac{1}{2}x-6[/tex]
does anyone like 4freakshow if so start a convo in comments 11-16 pleasee
Answer:
mhm
Step-by-step explanation:
Answer:
Bet
Step-by-step explanation:
Are these two triangles congruent? Use tracing paper to justify your answer
Answer:
no
Step-by-step explanation:
Answer:
Where's the pic shorty
Step-by-step explanation:
????????
Selecting which is the digit six is 10 times the value of the digit six in 3.161
Step-by-step explanation:
All the answers which apply are D and F
Answer:
I think it is d but I am now overthinking it so don't put too much trust in that
When two data sets are compared, what characteristics will give the most accurate prediction? Explain.
Answer:
If the trend line of scatterplots for two data sets are compared, the one more likely to provide an accurate prediction is the one with the stronger correlation.
Step-by-step explanation:
Answer:
If the trend line of scatterplots for two data sets are compared, the one more likely to provide an accurate prediction is the one with the stronger correlation.
Step-by-step explanation:
correct on edge