Answer:
0% probability that the mean score for the B group will be at least five points higher than the mean score for the A group
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution, the central limit theorem, and subtraction of normal variables:
Normal probability distribution
When the distribution is normal, we use 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.
Subtraction of normal variables:
When we subtract two normal variables, the mean is the subtraction of the mean of each variable, while the standard deviation is the square root of the sum of each variance.
Method A:
One student: N(75,30), so [tex]\mu = 75, \sigma = 30[/tex]
Samples of 100 students: [tex]n = 100, s = \frac{30}{\sqrt{100}} = 0.3[/tex]
Method B:
One student: N(74,40), so [tex]\mu = 74, \sigma = 40[/tex]
Samples of 100 students: [tex]n = 100, s = \frac{40}{\sqrt{100}} = 0.4[/tex]
What is the probability that the mean score for the B group will be at least five points higher than the mean score for the A group?
This is the probability that B - A >= 5. So
[tex]\mu_{B-A} = \mu_B - \mu_A = 74 - 75 = -1[/tex]
[tex]s_{B-A} = \sqrt{s_A^{2}+S_B^{2}} = \sqrt{(0.3)^2+(0.4)^2} = 0.5[/tex]
We have to find 1 subtracted by the pvalue of Z when X = 5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{5 - (-1)}{0.5}[/tex]
[tex]Z = 12[/tex]
[tex]Z = 12[/tex] has a pvalue of 1
1 - 1 = 0, so
0% probability that the mean score for the B group will be at least five points higher than the mean score for the A group
18 = 3 (3x - 6) help please!
Answer: 4
Step-by-step explanation:
What are the next three terms in the following sequence 3 6 12 24 plz help
Answer:
3 6 12 24 48 96 192
Step-by-step explanation:
The answer is 48 96 192
Answer:it equals 96 hope this helps
Step-by-step explanation:
What is the solution to the inequality
below?
X+3> 7
A X 4
B x 4
C3x7
PLEASE HELP !
Answer:
[tex]x+3>7\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x>4\:\\ \:\mathrm{Interval\:Notation:}&\:\left(4,\:\infty \:\right)\end{bmatrix}[/tex]
The solution line graph is also attached.
Step-by-step explanation:
Given
The inequality is given by
[tex]x+3>7[/tex]
To determine
What is the solution to the inequality?
Solving the given inequality
[tex]x+3>7[/tex]
Subtract 3 from both sides
[tex]x+3-3>7-3[/tex]
Simplify
[tex]x>4[/tex]
Thus,
[tex]x+3>7\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x>4\:\\ \:\mathrm{Interval\:Notation:}&\:\left(4,\:\infty \:\right)\end{bmatrix}[/tex]
The solution line graph is also attached.
20x=-58-2y
17x=-49-2y
Answer:
20x = -58 - 2y( Ans~ x= -29/11)
17x = -49 - 2y (Ans~ x = -49/19)
Step-by-step explanation:
(1) 20x = -58 2x
20x + 2x = -58
22x = -58
x = -29/11
(2) 17x = -49 - 2x
17x + 2x = -49
19x = -49
x = -49/19
U WELCOME!!
Answer:
y=1
x=-3
Step-by-step explanation:
20x=-58-2y
20x/20=(-58-2y)/20
x=(-58-2y)/20
17x=-49-2y
17x/17=(-49-2y)/17
x=(-49-2y)/17
(-58-2y)/20=(-49-2y)/17
17(-58-2y)=20(-49-2y)
-986-34y=-980-40y
add 40y to both sides
6y-986=-980
add 986 to both sides
6y=6
divide both sides by 6
y=1
substitute
20x=-58-2(1)
20x=-60
x=-3
Proof: (substituting x & y values in original equations)
20(-3)=-58-2(1)
-60=-60
17(-3)=-49-2(1)
-51=-51
Natalie completed 56 sit-ups. Natalie completed 4 times as many sit-ups as Matthew. How many sit-ups did Matthew complete?14 sit-ups
24 sit-ups
52 sit-ups
224 sit-ups
Answer:
224 sit-ups
Step-by-step explanation:
multiply 56 by 4
Which represents the inverse of the function f(x) = 4x?
O h(x) = X + 4
• h(x) =X- 4
O h(x) = =x
O h(x) = ÷x
PLEASEE HELP
Answer:
f^(-1) = x/4
Step-by-step explanation:
1. Starting with f(x) = 4x, replace 'f(x)' with y: y = 4x
2. Interchange x and y: x = 4y
3. Solve for y: y = x/4
4. Replace this y with 'f^(-1) = ": f^(-1) = x/4
Amy and Joey are situated on a circular track 400 feet around. Joey starts running at a rate of 10 feet per second. Amy waits for a full minute, then starts running from the same point (in the same direction) at 12 feet per second. How many seconds elapse before Amy passes Joey on the track?
Answer: 15 second
Step-by-step explanation:
Amy to be at the start point is 400 seconds and for Joey to be at the start point is 333.3 seconds, in that time Joey finished the 10 turns, and Amy had ended the 12.
How many seconds elapse before Amy passes Joey on the track?Joey starts running at v₁ = 10 m/sec
Amy starts running at v₂ = 12 m/sec
we know that d = v [tex]*[/tex] t then t = d/v
Joey will take 400 / 10 = 40 seconds
Amy will take 400 / 12 = 33.33 seconds
To check Joey 10 [tex]*[/tex] 40 = 400
And the Amy 12 [tex]*[/tex] 33.33 = 333.3
That means that time required for Amy to be at the start point is 400 seconds and for Joey to be at the start point is 333.3 seconds, in that time Joey finished the 10 turns, and Amy had ended the 12.
Therefore, 12 seconds elapse before Amy passes Joey on the track.
To learn more about arithmetic operations
https://brainly.com/question/1098659
#SPJ2
Find the greatest common factor of 16 17 20
Answer:
1
Step-by-step explanation:
As you can see when you list out the factors of each number, 1 is the greatest number that 16, 17, and 20 divides into.
brainliet, please? hee hee
1/2x -5-1/3y when x =48 and y=15
what is B? b-1/4=3 1/2
Answer:
hello! :) have a good day!
Exact Form:
b =15/4
Decimal Form:
b =3.75
Mixed Number Form:
b =3 3/4
4.0681 to the nearest thousand
A farmer sells 6.3 kilograms of pears and apples at the farmer's market. 4 5 of this weight is pears, and the rest is apples. How many kilograms of apples did she sell at the farmer's market?
Answer:
1.8 Kilograms
Step-by-step explanation:
Since the farmer sells 6.3 Kilograms of fruit in total and 4.5 Kilograms of this weight is pears, you have to subtract 4.5 from 6.3.
6.3-4.5 = 1.8
So, there are 1.8 Kilograms of apples.
Solve each system of equations using any method.
y = 5x +7
y = 4x - 3
Answer:
x= -10
y= -43
Step-by-step explanation:
since both of your equations equals y just plug it into each other and than make the equation: 5x+7=4x-3
and than you can just start with the variables OR numbers and then simplify
5x+7=4x-3
5x+10=4x
10= -x
x= -10
so -10 for x
plug it in to one of your 2 equations to get y
5(-10)+7= y
-50+7=y
y= -43
Two of the angles are 90 degrees and 40 degrees. What is the measure of the missing angle? *
Enter only a two digit number.
Purple paint is made by mixing red paint and blue paint in the ratio 5:2
Yan has 30 litres of red paint and 9 litres of blue paint.
What is the maximum amount of purple paint he can make?
Write 383 in expanded form
Answer:
300 + 80 + 3
PLease mArk me brainliest
helpsjdjdjdjcjcjfjfjfjcjfjfjxjff
Answer:
that is right what u have right there
Step-by-step explanation:
Tell whether a triangle can have the given angle measures. 5 2/3∘, 64 1/3∘, 87∘
sooo
5 2/3+64 1/3+87 = 157
that aint right- a triangles angles has to add up to 180
this triangle b trippin
What is 264*675+1239-56+887
Answer:
180270
Step-by-step explanation:
Do Pemdas to find order of operations:
(264*675)+ 1239-56+887
So it is:
(178200)+2070
This equals: 180,270
4. A bakery used 30% more butter this month than last month. If the bakery used 300 kilograms of
butter last month, how much did it use this month? Explain or show your reasoning.
they used 500 kilograms because since it is thirty percent will not be 600 it is 500 so there is the answer
there are 20 girls and 16 boys in a classroom. complete the table of ratios below.
Answer:
The ratio of boys to girls is [tex]\frac{16}{20}[/tex]
The simplified ratio of boys to girls is [tex]\frac{4}{5}[/tex]
So the ratio of girls to total students is [tex]\frac{20}{36}[/tex]
The simplified ratio of girls to total students is [tex]\frac{5}{9}[/tex]
Step-by-step explanation:
Ratio of a to b:
The ratio of a to b is given by:
[tex]\frac{a}{b}[/tex]
Boys to girls:
There are 16 boys and 20 girls.
So the ratio of boys to girls is [tex]\frac{16}{20}[/tex]
Both these numbers can be simplified by 4, 16/4 = 4, 20/4 = 5. So the simplified ratio of boys to girls is [tex]\frac{4}{5}[/tex]
Girls to total students
There are 20 girls and 20 + 16 = 36 total students.
So the ratio of girls to total students is [tex]\frac{20}{36}[/tex]
Both these numbers can be simplified by 4, 20/4 = 5, 36/4 = 9. So the simplified ratio of girls to total students is [tex]\frac{5}{9}[/tex]
The 95% confidence interval for these parts is 56.98 to 57.05 under normal operations. A systematic sample is taken from the manufacturing line to determine if the production process is still within acceptable levels. The mean of the sample is 56.96. What should be done about the production line
Answer:
Stop the line of production since the sample mean (56.96) is outside the confidence interval [[tex]CI_{0.95}[/tex] = ( 56.98, 57.05 )]
Step-by-step explanation:
Given that;
95% confidence interval for these parts is 56.98 to 57.05
[tex]CI_{0.95}[/tex] = ( 56.98, 57.05 )
Sample mean = 56.96
We know that;
If the sample mean is within the confidence interval then, our decision is to keep the line operating as it is inside the confidence interval.
But if the sample mean is not within the confidence interval them, our decision is to stop the line of production as it is outside the confidence interval.
Now since our mean sample (56.96) does not lie between with the 95% confidence interval [tex]CI_{0.95}[/tex] = ( 56.98, 57.05 ).
Therefore, Stop the line of production since the sample mean (56.96) is outside the confidence interval [[tex]CI_{0.95}[/tex] = ( 56.98, 57.05 )]
A body of mass 2 kg moves in a (counterclockwise) circular path of radius 3 meters, making one revolution every 5 seconds. You may assume the circle is in the xy-plane, and so you may ignore the third component.
A. Compute the centripetal force acting on the body.
B. Compute the magnitude of that force.
Answer:
a) [tex]\vec{F_{c}}=mR\omega^{2}[/tex]
[tex]\vec{F_{c}}=9.53 \: N \vec{r}[/tex]
b) [tex]|\vec{F_{c}}|=9.53 \: N [/tex]
Step-by-step explanation:
a) The centripetal force equation is:
[tex]\vec{F_{c}}=m\vec{a_{c}}[/tex]
[tex]\vec{F_{c}}=mR\omega^{2}[/tex]
Now, we know that the body makes one revolution every 5 seconds, so we can find the angular velocity:
[tex]\omega=\frac{1 rev}{5 s}=0.2\: \frac{rev}{s}=1.26\: \frac{rad}{s}[/tex]
[tex]\vec{F_{c}}=2*3*1.26^{2}=9.53 \: N \vec{r}[/tex]
The centripetal force is a vector in the radius direction.
b) The magnitude of that force will be:
[tex]|\vec{F_{c}}|=9.53 \: N [/tex]
who wants a slushie ?
Answer:
i want a slushie what's your favorite slushie flavor
What is BD? BC=x DC=x+5
Answer:
BD is just equal to the sum of BC and CD.
So we have: BD = x + x + 5
Simplifying, we have BD = 2x+5
Let me know if this helps!
13.6z - 11 = -1.48.
can u please show the work for it
Step-by-step explanation:
13.6z - 11 = -1.48.
13.6z=-1.48+11
z=9.52/13.6=0.7
What is the value of x in the equation 3×=1
Answer:
x=1/3
Step-by-step explanation:
What is the solution to the system of equations below?
x = 5y - 2 AND 3x - 4y = 27 *
Answer:
x = 13, y = 3
Step-by-step explanation:
3(5y - 2) - 4y = 27
15y - 6 - 4y = 27
11y = 33
y = 3
x = 15 - 2
x = 13
Pls help I’ll brainlest for the right answer
Answer:
29110.87
Step-by-step explanation:
mt might is 20,401.5 ft high, and tall mountain is 8709.37 ft higher than mt might, so add their those numbers together
The slope and y-intercept of the equation y – 5x = 7.
Graph points
Answer:
The slope is 5
the y-intercept is (0,7)
Step-by-step explanation:
