Answer:
a. 0.1038 = 10.38% probability that the sample mean is more than 59 pounds.
b. 0.6772 = 67.72% probability that the sample mean is more than 56 pounds.
c. 0.2210 = 22.10% probability that the sample mean is between 56 and 57 pounds.
d. 0.0146 = 1.46% probability that the sample mean is less than 53 pounds.
e. 0% probability that the sample mean is less than 49 pounds.
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 z-score 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 p-value, 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.
The Aluminum Association reports that the average American uses 56.8 pounds of aluminum in a year. The population standard deviation of annual usage is 12.3 pounds.
This means that [tex]\mu = 56.8, \sigma = 12.3[/tex]
Sample of 50:
This means that [tex]n = 50, s = \frac{12.3}{\sqrt{50}} = 1.74[/tex]
a. More than 59 pounds
This is 1 subtracted by the pvalue of Z when X = 59.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{59 - 56.8}{1.74}[/tex]
[tex]Z = 1.26[/tex]
[tex]Z = 1.26[/tex] has a pvalue of 0.8962
1 - 0.8962 = 0.1038
0.1038 = 10.38% probability that the sample mean is more than 59 pounds.
b. More than 56 pounds
This is 1 subtracted by the pvalue of Z when X = 56. So
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{56 - 56.8}{1.74}[/tex]
[tex]Z = -0.46[/tex]
[tex]Z = -0.46[/tex] has a pvalue of 0.3228
1 - 0.3228 = 0.6772
0.6772 = 67.72% probability that the sample mean is more than 56 pounds.
c. Between 56 and 57 pounds
This is the pvalue of Z when X = 57 subtracted by the pvalue of Z when X = 56.
X = 57
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{57 - 56.8}{1.74}[/tex]
[tex]Z = 0.11[/tex]
[tex]Z = 0.11[/tex] has a pvalue of 0.5438
X = 56
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{56 - 56.8}{1.74}[/tex]
[tex]Z = -0.46[/tex]
[tex]Z = -0.46[/tex] has a pvalue of 0.3228
0.5438 - 0.3228 = 0.2210
0.2210 = 22.10% probability that the sample mean is between 56 and 57 pounds.
d. Less than 53 pounds
This is the pvalue of Z when X = 53.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{53 - 56.8}{1.74}[/tex]
[tex]Z = -2.18[/tex]
[tex]Z = -2.18[/tex] has a pvalue of 0.0146
0.0146 = 1.46% probability that the sample mean is less than 53 pounds.
e. Less than 49 pounds
This is the pvalue of Z when X = 49.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{49 - 56.8}{1.74}[/tex]
[tex]Z = -4.48[/tex]
[tex]Z = -4.48[/tex] has a pvalue of 0
0% probability that the sample mean is less than 49 pounds.
please help me with this ASAP
Answer:
32
Step-by-step explanation:
15x+19=2(10x+2)
15x+19=20x+4
19-4=20x-15x
15=5x
x=3
PQ=QN
10x+2=
10(3)+2=
30+2=
32
PLEASE HELP ME ANYONE ???????????!!!
Answer:
A x>9
Step-by-step explanation:
add 4 to both sides and ta da
Answer:
x>9
Step-by-step explanation:
you move the negative 4 to the other side to get it away from x so then you can find the answer.
Hope this helps:)
If you are asked to complete 5 sit-ups for every 9 push-ups you complete, answer each of the following questions:
Write the ratio of push-up’s to sit-ups three different ways.
_____________ ____________ ____________
If you complete 36 push-ups, how many sit-ups did you complete?
____________
If you complete 95 sit-ups, how many push-ups did you complete?
_____________
Answer:
1)5:9 ,5 of 9 5/9 2) 36x5 3) 95x5
Which graph shows a proportional relationship between X and y
i can’t figure this one out.
Answer:
5
Step-by-step explanation:
3/12=x/20
cross multiply
12x=3(20)
12x=60
x=60/12
x=5
50 POINTS BRAINLIEST
Answer:
31 degrees
Step-by-step explanation:
Measure angles 1 and 3 are vertical angles, meaning they are equal which means 3 = 149 degrees
Angles 2 and 3 are adjacent and supplementary, meaning that their angles add up to 180.
180 - 149 = 31 degrees
Answer:B would be right so you are right!(give other user brainliest)
Step-by-step explanation:
can 8 go into 3? plz answer
Answer:no
Step-by-step explanation:it would not be possible as 8 is a larger number then 3 unless u would be multiplying by decimals which in which case might be possible
Help please?? Thank you
Answer:
Isosceles right
Step-by-step explanation:
And isosceles triangle has 2 congruent sides, and since 90° is a right angles, it is a right triangle.
Answer:
isosceles acute I believe, since the two even sides are acute angles, however it could also be right since the top angle is a right angle and therefore the other two equal a right angle sorry if this didn't come in very useful
50 POINTS QUICK Given that ab = x, evaluate the following:
1.) [tex]a^{2b}[/tex]
2.)[tex]a^{b+2}[/tex]
Answer:
2)The answer is x*a^2 because the equation is saying a^b*a^2. And if we knew that a^b = x, then the answer is x*a^2
Step-by-step explanation:
What is the equation of the line that is perpendicular to y=-3x+1 that passes through the point (9,0)?
y=1/3x-3
y=-1/3x+3
y=3x+9
y=-3x+3
Answer:
Step-by-step explanation:
the correct answer of the question is y=x/3-3 b.c
m1.m2 = -1 But m1=-3
so -3.m2=-1
-3.m2/-3=-1/-3
m2=1/3 therefore
Y=1/3x-3
Find the slope of the line that passes through (10, 2) and (1, 6).
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
what value from the set makes x/6 =18
true?
A.3
B.12
C.54
D.108
Answer:
D
Step-by-step explanation:
Plug it in 108 divide by 6
What is the value of f(x) when x=3?
0 -3
0-2
0 1
04
The value of the function when x=3 is approximately 18.83.
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.
Linear function is a function whose graph is a straight line
We are given that;
The function
Now,
we need to substitute x=3 into the function and simplify it. We get:
3(3)−1+(1+3)2
=8+16
≈2.83+16
=4
Therefore, by the given function answer will be 4.
Learn more about function here:
https://brainly.com/question/2253924
#SPJ7
A program to restore an endangered frog species began 8 months
ago. The table shows the population of the species at various
times since the program began.
Month
Number of Frogs
0
11
2
69
4
195
6
547
8
1,231
On average, what has been the monthly change in the frog
population over the last 4 months?
Answer:
195
Step-by-step explanation:
Therefore, the monthly change in the frog population over the last four months is [tex]195[/tex].
What is the simplification?
Simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.
As per the given information,
The monthly change in the frog population over the last four months is [tex]195[/tex].
Hence, the monthly change in the frog population over the last four months is [tex]195[/tex].
To know more about the simplification
https://brainly.com/question/12795317
#SPJ2
what is the equation for the graph below?
Answer:
ummmm, i cant see the graph
Step-by-step explanation:
Suppose that the Celsius temperature at the point (x, y) in the xy-plane is T(x, y) = x sin 2y and that distance in the xy-plane is measured in meters. A particle is moving clockwise around the circle of radius 1 m centered at the origin at the constant rate of 2 m/sec.How fast is the temperature experienced by the particle changing in degrees Celsius per meter at the point?
Missing information:
How fast is the temperature experienced by the particle changing in degrees Celsius per meter at the point
[tex]P = (\frac{1}{2}, \frac{\sqrt 3}{2})[/tex]
Answer:
[tex]Rate = 0.935042^\circ /cm[/tex]
Step-by-step explanation:
Given
[tex]P = (\frac{1}{2}, \frac{\sqrt 3}{2})[/tex]
[tex]T(x,y) =x\sin2y[/tex]
[tex]r = 1m[/tex]
[tex]v = 2m/s[/tex]
Express the given point P as a unit tangent vector:
[tex]P = (\frac{1}{2}, \frac{\sqrt 3}{2})[/tex]
[tex]u = \frac{\sqrt 3}{2}i - \frac{1}{2}j[/tex]
Next, find the gradient of P and T using: [tex]\triangle T = \nabla T * u[/tex]
Where
[tex]\nabla T|_{(\frac{1}{2}, \frac{\sqrt 3}{2})} = (sin \sqrt 3)i + (cos \sqrt 3)j[/tex]
So: the gradient becomes:
[tex]\triangle T = \nabla T * u[/tex]
[tex]\triangle T = [(sin \sqrt 3)i + (cos \sqrt 3)j] * [\frac{\sqrt 3}{2}i - \frac{1}{2}j][/tex]
By vector multiplication, we have:
[tex]\triangle T = (sin \sqrt 3)* \frac{\sqrt 3}{2} - (cos \sqrt 3) \frac{1}{2}[/tex]
[tex]\triangle T = 0.9870 * 0.8660 - (-0.1606 * 0.5)[/tex]
[tex]\triangle T = 0.9870 * 0.8660 +0.1606 * 0.5[/tex]
[tex]\triangle T = 0.935042[/tex]
Hence, the rate is:
[tex]Rate = \triangle T = 0.935042^\circ /cm[/tex]
Please I’m dying to know the answer can anyone help me?
Answer:
-1/3x+2y=4
Step-by-step explanation:
Substitute the negative reciprocal.
-1/3x+2y=4
The average number of televisions per family is numbered in the tens.
A. True
B. False
Answer:
False!
~The Average number of TVs in a house is 2 - 3
Hope this helps!
Answer:
False.
The average number of televisions per family would have to be more than ten for it to be true, and I find this very hard to believe.
Hope I helped!
Will 3in,4in,7in form a triangle.
Will 3in, 4in, 6in form a triangle
Will 1m, 2m, 3m form a triangle
Yes or no
Answer:
No, Yes, No
Step-by-step explanation:
3in by 4in by 5in will not make a triangle.
3in by 4in by 6in will make a triangle.
1m by 2m by 3m will not make a triangle.
The reason two of these triangles cannot be form is because the side lengths do not adhere to the triangle inequality theorem. This theorem states that the sum of the side lengths of any 2 sides of a triangle must exceed the length of the third side.
Juan threw a dart onto the board. Which of the following is most likely?
A. Juan scored 0 points.
B. Juan scored at least 2 points.
C. Juan scored at least 4 points.
D. Juan scored at least 8 points.
Answer:
I think the answer should be.
B
Answer:
B
Step-by-step explanation:Edg 2021
a map has a scale of 1 cm :15.5 km two cities are 2.3 cm apart on the map. to the nearest tenth of a kilometer,whatis the actual distance corresponding to the map distance
Pls help. Sorry if its blurry
Answer:
5 divided by some number.
Step-by-step explanation:
Hope this helps!
Answer:
third option
Step-by-step explanation:
Aaron currently earns $1,400 per month working. Each year he will get a $150 per month raise. How much money will Aaron earn per month in 7 years?
the correct answer is 10290000
Answer:
130,200
Step-by-step explanation:
Earnings for 7yrs= $1,400 × 12 months × 7yrs
= $117,600
Raise for 7 yrs= $150 × 12 months × 7yrs
=$ 12,600
Earnings in 7yrs= $117,600 + $12,600
= 130,200
Is this a complementary, supplementary, vertical, or adjacent
ill give brainly
Answer:
its complemtary
Step-by-step explanation:
check this photo
I need help on this asap
Answer: 13.7ft (1 decimal place)
Step-by-step explanation:
For this question you will have to use Pythagoras theorem.
The formula for the short side is x²=c²-b² and when you put the numbers from this question into it you get x²=15²-6²
15²=225
6²=36
x²=225-36
x²=189
Then, as you want to find x on its own, you would have to square root 189 which is 13.7 (1 decimal place).
Hope this helps :)
What is the common denominator for 4/10 and 1/5
Answer:
10
Step-by-step explanation:
1/5 = 2/10
need help asap provide explanation
Answer:
B is the correct answer
8 The length of Adriana's chicken coop is 3x + 12 feet. The length of her garden is
6x – 16 feet. The garden is the length of the chicken coop.
What is the length of the chicken coop? Enter the number of feet only.
What is the length of the garden? Enter the number of feet only.
Answer:
Rounded down to the nearest foot, the length of the garden is nine feet.
Step-by-step explanation:
We're told that the length of the chicken coop, 3x + 12 feet, is equal to the length of the garden, 6x - 16 feet. Let's put them together then and solve for x:
3x + 12 = 6x - 16
First, we'll subtract 6x from both sides
3x - 6x + 12 = 6x - 6x - 16
-3x + 12 = -16
Now we subtract 12 from both sides:
-3x + 12 - 12 = -16 - 12
-3x = -28
Finally divide both sides by -3
-3x / -3 = -28 / -3
x = 28/3
x = 9 and 1/3
As the question asks for the number of feet only (not inches), the answer is nine feet.
A third of a foot though is four inches, so the more exact answer is nine feet and four inches, or 9'4"
Branliest to correct answer no guessing explain how you got your answer
Answer:
the answer is 1771! good luck!
Step-by-step explanation:
i attached an image with the steps!
What is the common denominator of 4/12
Answer:
lcm of
Step-by-step explanation:
it is 12and 2.........