Answer:
Okay, anything else along with that or was it just a statement?
Step-by-step explanation:
Given a test that is normally distributed with a mean of 100 and a standard deviation of 12, find:
(a) the probability that a single score drawn at random will be greater than 110
(b) the probability that a sample of 25 scores will have a mean greater than 105
(c) the probability that a sample of 64 scores will have a mean greater than 105
(d) the probability that the mean of a sample of 16 scores will be either less than 95 or greater than 105
Answer:
(a) 0.2033
(b) 0.0188
(c) 0.0004
(d) 0.095
Step-by-step explanation:
(a) the probability that a score at random is greater than 110 is obtained with a normal distribution of mean 100 and standard deviation 12 can be estimated using the z-table for Z = (110 - 100)/12 = 0.83
So P (X > 110) = P (Z > 0.83) = 0.2033
(b) Probability that a sample of 25 scores will have a mean greater than 105:
we use a standard distribution with the same mean (100) but the standard distribution reduced by a factor of [tex]\sqrt{25} = 5[/tex]. That is a standard deviation of 12/5 = 2.4. which gives a Z-value of (105-100) / 2.4 = 2.08
P (X> 105) = P (Z > 2.08) = 0.0188
(c) Probability that a sample of 64 scores will have a mean greater than 105:
we use a standard distribution with the same mean (100) but the standard deviation reduced by a factor of [tex]\sqrt{64} = 8[/tex]. That is a standard deviation of 12/8 = 1.5. which gives a Z-value of (105-100) / 1.5 = 3.33
P (X> 105) = P (Z > 3.33) = 0.0004
(d) the probability that the mean of a sample of 16 scores will be either less than 95 or greater than 105
This will be the addition of the two probabilities. We use a standard distribution with the same mean (100) but the standard distribution reduced by a factor of [tex]\sqrt{16} = 4[/tex]. That is a standard deviation of 12/4 = 3. which gives us two different Z values to study:
(105-100) / 3 = 1.67
and for X= 95 ==> Z = (95 - 100)/3 = - 1.67
P (X > 105) = P (Z > 1.67) = 0.0475
P (X < 95) = P (Z < -1.67) = 0.0475
which add up to: 0.095.
Using the normal distribution and the central limit theorem, it is found that there is a:
a) 0.2033 = 20.33% probability that a single score drawn at random will be greater than 110.
b) 0.0188 = 1.88% probability that a sample of 25 scores will have a mean greater than 105.
c) 0.0004 = 0.04% probability that a sample of 64 scores will have a mean greater than 105.
d) 0.095 = 9.5% probability that the mean of a sample of 16 scores will be either less than 95 or greater than 105.
In a normal distribution 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]
It 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, which is the percentile of X. By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem:
Mean of 100, hence [tex]\mu = 100[/tex].Standard deviation of 12, hence [tex]\sigma = 12[/tex].Item a:
This probability is 1 subtracted by the p-value of Z when X = 110, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{110 - 100}{12}[/tex]
[tex]Z = 0.83[/tex]
[tex]Z = 0.83[/tex] has a p-value of 0.7967.
1 - 0.7967 = 0.2033
0.2033 = 20.33% probability that a single score drawn at random will be greater than 110.
Item b:
Sample of 25, hence [tex]n = 25, s = \frac{12}{\sqrt{25}} = 2.4[/tex].
This probability is 1 subtracted by the p-value of Z when X = 105, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{105 - 100}{2.4}[/tex]
[tex]Z = 2.08[/tex]
[tex]Z = 2.08[/tex] has a p-value of 0.9812.
1 - 0.9812 = 0.0188
0.0188 = 1.88% probability that a sample of 25 scores will have a mean greater than 105.
Item c:
Sample of 64, hence [tex]n = 64, s = \frac{12}{\sqrt{64}} = 1.5[/tex].
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{105 - 100}{1.5}[/tex]
[tex]Z = 3.33[/tex]
[tex]Z = 3.33[/tex] has a p-value of 0.9996.
1 - 0.9996 = 0.0004
0.0004 = 0.04% probability that a sample of 64 scores will have a mean greater than 105.
Item d:
Sample of 16, hence [tex]n = 16, s = \frac{12}{\sqrt{16}} = 3[/tex].
Both 105 and 95 are the same distance of the mean, so we find one probability, and multiply by 2.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{105 - 100}{3}[/tex]
[tex]Z = 1.67[/tex]
[tex]Z = 1.67[/tex] has a p-value of 0.9525.
1 - 0.9525 = 0.0475.
2 x 0.0475 = 0.095
0.095 = 9.5% probability that the mean of a sample of 16 scores will be either less than 95 or greater than 105.
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whats the area of a circle if the diameter 6
Answer:
28.27
Step-by-step explanation:
Answer:
18.84
Step-by-step explanation:
6x3.14 = 18.84. multiply by pi
how many eights are there in three and a quater
The expression 63 × 42 is equivalent to which of the following numerical expressions?
18 x 8
B.
(6 x 4) 5
C.
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D.
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please answer
Answer:
2646
Step-by-step explanation:
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The required equivalent expression is (216 x 16).
The correct is D.
What is Expression?In mathematics, an expression is a phrase that has at least two numbers or variables and at least one maths operation. Addition, subtraction, multiplication, or division are all examples of maths operations. An expression's structure is as follows:
(Number/variable, Math Operator, Number/variable) is an expression.
We have the Expression as,
6³ x 4²
Now, expand the exponents as
6³
= 6 x 6 x 6
= 216
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Your answer is 96.5606 Kilometers.
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Mark as brainliest if it's correct!
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What is the chance of rolling two dice and the dice add up to six?
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Step-by-step explanation:
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Francine has a picture with a length 5/3 its width. She wants to enlarge the picture to have an area of 240 in2. What will the dimensions of the enlarged picture be?
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Answer:
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Explain why 3( + 4) = 3( − 5) has no solution. Choose the best response below. I NEED THIS ASAP!!!
a. The coefficients of are the same, but the constant terms are different.
b. The coefficients of are the same, and the constant terms are same.
c. The coefficients of are different, but the constant terms are the same.
d. The coefficients of are different, and the constant terms are different.
Answer:
a. The coefficients of are the same, but the constant terms are different.
Step-by-step explanation:
it makes the most sence to me, but appoligise if I'm wrong
LMC given numbers 60 and 80
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LCM : least common factorLet V=ℝ2 and let H be the subset of V of all points on the line 4x+3y=12. Is H a subspace of the vector space V?
Answer:
No, it isn't.
Step-by-step explanation:
We have [tex]V=IR^{2}[/tex] and let [tex]H[/tex] be the subset of [tex]V[/tex] of all points on the line
[tex]4x+3y=12[/tex]
We need to find if [tex]H[/tex] is a subspace of the vector space [tex]V[/tex].
In [tex]IR^{2}[/tex] all the possibilities for own subspace of the vector space [tex]IR^{2}[/tex] are :
[tex]IR^{2}[/tex] itself.The vector [tex]0_{IR^{2}}=\left[\begin{array}{c}0&0\end{array}\right][/tex]All lines in [tex]IR^{2}[/tex] that passes through the origin ( [tex]0_{IR^{2}}=\left[\begin{array}{c}0&0\end{array}\right][/tex] )We know that [tex]H[/tex] is the subset of [tex]IR^{2}[/tex] of all points on the line [tex]4x+3y=12[/tex]
If we look at the equation, the point [tex]\left[\begin{array}{c}0&0\end{array}\right][/tex] doesn't verify it because :
[tex]4x+3y=12\\4(0)+3(0)=12\\0=12[/tex]
Which is an absurd. Therefore, [tex]H[/tex] doesn't contain the origin (and [tex]H[/tex] is a line in [tex]IR^{2}[/tex]). Finally, it can't be a vector space of [tex]V=IR^{2}[/tex]
A Ferris wheel can accommodate 55 people in 30 minutes. How many people could ride the Ferris wheel in 5 hours? What was that rate per hour?
Answer:
i believe your answer is 550 people, which would be 110/hr
Step-by-step explanation:
Hope that helps!
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suponiendo que dispone de $100 pesos extras para comprar
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A car travels 2,347 feet in 10 seconds. At that speed, how far can this car travel in 50 seconds?
Answer: 11,735
Step-by-step explanation:
2,347 x 5 = 11,735
Answer:
play car games and find out
Step-by-step explanation:
Help me on this Algebra 2
Graph the greatest integer, f(x) = [x]
Answer:
Step-by-step explanation:
how do u find the third side
Answer:
Square root of 49
The missing side is 7
Step-by-step explanation:
With the Pythagorean theorem.
25^2= 625
24^2= 576
Square root of 49=7
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Solve for f: (-1/8)f - (3/4) -
(1/4)f = 11
Answer: The answer is f= –31 1/3.
Step-by-step explanation: To solve for f, you’ll need to simplify the both sides of the equation, and then isolating the variable. Use online advanced calculators to calculate the equation to view all the steps.
Select the correct answer.
The surface area of a cube is 600 square inches. What is the area of one of its faces?
A 6 square inches
B. 36 square inches
C. 75 square inches
D. 100 square inches
Answer:
D=100 square inches
Step-by-step explanation:
Area of a square=side^2
Area of a cube=6xside^2
let the side be a
6a^2=600
a^2=600/6
a^2=100
Answer:
im on it its d
Step-by-step explanation:
Help me with this please
Answer:
The First Table
Step-by-step explanation:
The y-values increase inconsistently, while the other tables are constant.
The snow is now 52 inches deep. If this was a 77%
decrease, what was the initial depth
Answer:
29.3785310734 is the exact answer but you can estimate
Step-by-step explanation:
Let’s say the initial depth was 100%.
A 77% decrease would mean that 77% of the 100% was added to the hole so then it final result would be 177% of the initial hole which is also 52 as given. 177% is the same as 1.77 so we would divide 52 by 1.77 to get that x = 29.3785310734. Still confusing? Just look here:
In the model for exponential growth or decay, the amount, or size, at t=0 is represented by __ the amount, or size, at time t is represented by __
In the model for exponential growth or decay, the amount, or size, at t=0 is represented by [tex]N=N_{0}[/tex]. and at time t is represented by [tex]N=N_{0}e^{kt}[/tex]
Let us consider that [tex]N_{0}[/tex] is the initial amount and N is represent that amount after growth or decay in time t .
Model for exponential growth or decay is,
[tex]N=N_{0}e^{kt}[/tex]
Amount at t=0 is,
[tex]N=N_{0}e^{k*0}=N_{0}[/tex]
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Mario paid $30 to activate his cellular phone plus $50 per month. Type an equation:_
Answer:
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Answer:
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Step-by-step explanation:
What is the exact value of sin(75°)?
Step-by-step explanation:
sin 75°: Now using the formula for the sine of the sum of 2 angles, sin(A + B) = sin A cos B + cos A sin B, we can find the sine of (45° + 30°) to give sine of 75 degrees.
Answer:
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Step-by-step explanation:
Edge
Please help me as soon as possible! :)
1 1/8 + b ≥ 7/16
Answer: 42
Step-by-step explanation:
Example:
Solve x + 7 < 15
Solution:
x + 7 < 15
x + 7 – 7 < 15 – 7
x < 8
Inequalities Of The Form “x – a < b” or “x – a > b”
Please mark me brainliest if this helped you ! (by clicking the little crown on my answer) it helps a lot thnx! (*≧∀≦*)
The solution of the inequality 1 1/8 + b ≥ 7/16 will be;
⇒ - 11/16 ≤ b
What is Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The inequality is,
⇒ 1 1/8 + b ≥ 7/16
Now,
Solve the inequality as;
The inequality is,
⇒ 1 1/8 + b ≥ 7/16
Solve for b as;
⇒ 9/8 + b ≥ 7/16
Subtract 9/8 as,
⇒ 9/8 + b - 9/8 ≥ 7/16 - 9/8
⇒ b ≥ (7 - 18) / 16
⇒ b ≥ - 11/16
⇒ - 11/16 ≤ b
Thus, The solution of the inequality 1 1/8 + b ≥ 7/16 will be;
⇒ - 11/16 ≤ b
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help me answer this question please
Answer:
f'(2) = 8
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASCalculus
The definition of a derivative is "the slope of the tangent line".
Derivatives of constants are 0.
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
f(x) = 3x² - 4x + 2
Step 2: Find 1st Derivative
Basic Power Rule: f'(x) = 2·3x²⁻¹ - 1·4x¹⁻¹Simplify: f'(x) = 6x - 4Step 3: Find tangent slope
Define: f'(x) = 6x - 4, x = 2Substitute: f'(2) = 6(2) - 4Multiply: f'(2) = 12 - 4Subtract: f'(2) = 8Step 4: Identify
f'(2) = 8 tells us that at x = 2, the slope of the tangent line is 8.
Can someone help me plz
Answer:
i think the answer is 7
Solve for x: 5x + 15 = 28
Answer:
x= 2 [tex]\frac{3}{5}[/tex]
Step-by-step explanation:
5x + 15 = 28
5x + 15 (-15) = 28 (-15)
5x = 13
5/5x = 13/5
x= 2 [tex]\frac{3}{5}[/tex]
Answer:
x=2.6
Step-by-step explanation:
1)write equation
2)put line through equal sign(if on paper, its way easier to put a line through.)
3)subtract 15 from 15
4)subtract 15 from 28(13)
If it were to be a negative 15 youd add 15. Never add or subtract to a number with a letter!
5)what's left over is 5×=28 divide 5 on both sides.
6)13÷5=2.6
Help no troll answer plz
Answer:
Step-by-step explanation:
Q 4. (25m + 25m) ÷ 25 sec. = 2 m/sec.
Q 5. This question belongs to Physics and not Mathematics!!!
Wavelength (lambda) = Velocity (v) ÷ Frequency ( [tex]sec^{-1}[/tex] or Hz )
f = v / (lambda)
f = 3 / 2 = 1.5 (Hz)
Q 6. 0.060 ÷ 2 = 0.030 m