Answer:
This probability that the sample proportion is between 0.35 and 0.45 is the p-value of [tex]Z = \frac{0.45 - \mu}{\sqrt{\frac{p(1-p)}{160}}}[/tex] subtracted by the p-value of [tex]Z = \frac{0.35 - \mu}{\sqrt{\frac{p(1-p)}{160}}}[/tex]. These p-values are found looking at the z-table.
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 establishes 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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Estimate of the proportion:
This is p, and thus, we use [tex]\mu = p[/tex].
Sample of 160
This means that:
[tex]n = 160, s = \sqrt{\frac{p(1-p)}{160}}[/tex]
What is the probability that the sample proportion is between 0.35 and 0.45?
This probability that the sample proportion is between 0.35 and 0.45 is the p-value of [tex]Z = \frac{0.45 - \mu}{\sqrt{\frac{p(1-p)}{160}}}[/tex] subtracted by the p-value of [tex]Z = \frac{0.35 - \mu}{\sqrt{\frac{p(1-p)}{160}}}[/tex]. These p-values are found looking at the z-table.
What is 2/6 in simplest form? Find the greatest common factor of 2 and 6 and divide by that number. *
Answer:
[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
2 = 2 × 1
6 = 2 × 3
GCF = 2
[tex]\frac{2 /2 }{6/2} =\frac{1}{3}[/tex]
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]\boxed{\frac{1}{3}}[/tex]
»»————- ★ ————-««
Here’s why:
We would take the GCF of the two numbers in order to simplify.⸻⸻⸻⸻
[tex]\boxed{\text{Simplify:}}\\\\\frac{2}{6}\\\\\boxed{\text{Finding the Factors:}}\\\\2: 2\\6 : 2,3\\\\\boxed{\text{The GCF would be 2.}}\\\\\frac{2}{6} =\frac{2/2}{6/2}=\boxed{\frac{1}{3}}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Let XX be a random variable that is equal to the number of heads in two flips of a fair coin. What is \text E[X^2]E[X 2 ]
Answer:
Step-by-step explanation:
From the given information, it is likely that the random variable(X) have the values below:
Let head be H
Let tail be T
So;
X(HH) = 2;
X(HT) = 1;
X(TH) = 1;
X(TT) = 0
The distribution can now be computed as:
[tex]p(X= TT) = \dfrac{1}{4}[/tex]
[tex]p(X=TH) = \dfrac{1}{4}[/tex]
[tex]p(X=HT) = \dfrac{1}{4}[/tex]
[tex]p(X=HH)= \dfrac{1}{4}[/tex]
Now, the expected value that is equivalent to the number of heads when the coin is flipped twice is:
[tex]E(X) = p(TT)*X(TT)+p(TH)*X(TH)+p(HT)*X(HT)+p(HH)*X(HH)[/tex]
[tex]E(X) = \dfrac{1}{4}\times 0 + \dfrac{1}{4}\times 1 + \dfrac{1}{4}\times 1 + \dfrac{1}{4}\times 2[/tex]
[tex]E(X) = 0 + \dfrac{1}{4}+ \dfrac{1}{4} + \dfrac{1}{2}[/tex]
[tex]E(X) =\dfrac{1+1+2}{4}[/tex]
[tex]E(X) =\dfrac{4}{4}[/tex]
E(X) = 1
[tex]E(X^2) = p(TT)*X(TT)^2+p(TH)*X(TH)^2+p(HT)*X(HT)^2+p(HH)*X(HH)^2[/tex]
[tex]E(X^2) = \dfrac{1}{4}\times 0^2+ \dfrac{1}{4}\times 1^2 + \dfrac{1}{4}\times 1^2 + \dfrac{1}{4}\times 2^2[/tex]
[tex]E(X^2) = 0 + \dfrac{1}{4}+ \dfrac{1}{4} + \dfrac{4}{4}[/tex]
[tex]E(X^2) =\dfrac{1+1+4}{4}[/tex]
[tex]E(X^2) =\dfrac{6}{4}[/tex]
[tex]E(X^2) =1.5[/tex]
Finally; To compute E²[X]
E²[X] = E[X]²
E²[X] = 1²
E²[X] = 1
What is the mean of the data set shown below?
{10, 2, 8, 9, 5, 2, 6}
A. 42
B. 7
C. 6
D. 2
Answer:
6
Step-by-step explanation:
mean is the sum of them all followed by dividing how many there are, so 10 plus 2 plus 8 plus 9 plus 5 plus 2 plus 6 divided by 7 is 6
James invested £2000 for three years in an Internet Savings Account.
He is paid 5.5% per annum compound interest.
Work out the total interest earned after three years
Answer:
£2348.48
Step-by-step explanation:
We can use the “slow method” for this, seeing it’s only 3 years.
£2000 * 105.5% = 2110 * 105.5% = 2226.05 * 105.5% = 2348.48
(105.5% = 1.055, by the way)
After the initial calculation, you can use Ans * 1.055 until you’ve hit the three years.
I need help now plzzzzxz
Answer:
the last one
Step-by-step explanation:
there are 3 negative sings for that
You have a $50 coupon from the manufacturer good for the purchase of a cell phone. The store where you are purchasing your cell phone is offering a 20% discount on all cell phones. Let x represent the regular price of the cell phone. Use the word bank below to complete each blank. [Click on the phrase to fill in the blank. You do NOT need to type.] A.] Suppose only the 20% discount applies. Find a function \large f\left(x\right) that models the purchase price of the cell phone. f(x)
Answer:
[tex]f(x) = 0.80x[/tex]
Step-by-step explanation:
Given
[tex]x \to price[/tex]
[tex]discount \to 20\%[/tex]
[tex]coupon = \$50[/tex]
Required
The function f(x) if only the discount applies
20% discount implies that the price will be reduced by 20%.
So, the function is:
[tex]f(x) = Price - Price * Discount[/tex]
[tex]f(x) = x - x * 20\%[/tex]
Factorize
[tex]f(x) = x(1 - 20\%)[/tex]
Express percentage as decimal
[tex]f(x) = x(1 - 0.20)[/tex]
[tex]f(x) = x(0.80)[/tex]
[tex]f(x) = 0.80x[/tex]
Plz do.this for 20 points
Step-by-step explanation:
1 2 3 42 4 6 83 6 9 12You need to multiply the row and column to get the numbers
for example the block with row 3 column 3,the answer is 3 x 3= 9
each spinner can land on any of the points it has, thus each of the number have the same possibility.
Are the events independent or dependent. From a bag containing 10 marbles, 5 red, 3 black, 1 blue, and 1 white we pick two marbles:
Event A: Selecting a red marble first pick, and then without replacement
Event B: Selecting a white marble on the second pick
Answer:
Dependent
Step-by-step explanation:
The first draw has 10 marbles, the second draw has 9 marbles and the color of those 9 marbles depends on the marble picked in the first draw so the events are dependent.
Answer:
Dependant
Step-by-step explanation:
It would be independent if you put the marble BACK, because at first it was 1/10 to get the white marble and then it became 1/9.
For f(x) = 3x +1 and g(x) = x - 6, find (f- g)(x).
A. K - 3x-7
B. 3x - 17
c. -x + 3x + 7
D. -x + 3x - 5
SUBND
Answer:
c. -x + 3x + 7 = 2x+7
Step-by-step explanation:
f(x) = 3x +1 and g(x) = x - 6
f-g = 3x +1 - ( x - 6)
Distribute the minus sign
= 3x+1 - x+6
= 2x +7
Find the amount of money in an account after 9 years if $2,600 is deposited at 8% annual interest compounded monthly
Answer:
5328.78
Step-by-step explanation:
formula:
[tex]P(1+\frac{i}{n})^{n*t}\\2600(1+\frac{.08}{12})^{12*9}\\\\2600(1.006667)^{108}=5328.77861305[/tex]
this rounds to 5328.78
convert fraction to decimal 1/5 explanation
Answer: 0.2
Step-by-step explanation:
1 divided by 5 = 0.2
Answer:
0.2
Step-by-step explanation:
1/5 = 1 divided by 5.
This will also apply to any fraction
Fraction = Numerator divided by Denominator
is 3(6x + 1) and 21x
equivalent?
explain why
Answer: they are not equivalent be 3(6x+1) is 18x+3 and 21x stays the same so there for they are not equivalent to each other
Step-by-step explanation:
HELP WOULD BE APPRECIATED
Solve for n
n - 21 = 3
OA) n=45
OB) n=52
Oc) n= 24
OD) n= 19
Answer:
option C. n = 24
Step-by-step explanation:
n - 21 = 3
n - 21 + 21 = 3 + 21 [adding 21 on both sides ]
n + 0 = 24 [ -21 + 21 = 0 ]
n = 24
f(x)=-2x^2 -3, find f(0)
Answer:
Step-by-step explanation:
It's -3
4) 2 2/3 yards feet * O 8 feet O 6 feet O 2 feet O 7 feet
Answer:
your mom
Step-by-step explanation:
u gonna fail just give up on life
The Food Marketing Institute shows that 17% of households spend more than $100 per week on groceries. Assume the population proportion is p = 0.17 and a sample of 900 households will be selected from the population. Use z-table.
a. Calculate σ(p), the standard error of the proportion of households spending more than $100 per week on groceries (to 4 decimals).
b. What is the probability that the sample proportion will be within +/- 0.02 of the population proportion (to 4 decimals)?
c. What is the probability that the sample proportion will be within +/- 0.02 of the population proportion for a sample of 1,400 households (to 4 decimals)?
Answer:
The right answer is:
(a) 0.01252
(b) 0.8882
(c) 0.9544
Step-by-step explanation:
Given:
Population proportion,
P = 0.17
Sample size,
n = 900
(a)
The standard error of proportion will be:
⇒ [tex]SE_p=\sqrt{\frac{P(1-P)}{n} }[/tex]
By putting the values, we get
[tex]=\sqrt{\frac{0.17(1-0.17)}{900} }[/tex]
[tex]=\sqrt{0.000158}[/tex]
[tex]=0.01252[/tex]
(b)
We know that,
[tex]\hat{P}-P=\pm 0.02[/tex]
Now,
⇒ [tex]z=\frac{\hat{P}-P}{\sqrt{\frac{P(1-P)}{n} } }[/tex]
By substituting the values, we get
[tex]=\frac{\pm 0.02}{\sqrt{\frac{0.17(1-0.17)}{900} } }[/tex]
[tex]=\frac{\pm 0.02}{0.01252}[/tex]
[tex]=\pm 1.59[/tex]
⇒ [tex]P(I\hat{P}-PI<0,02)=P(-1.59<z<1.59)[/tex]
[tex]=1-2P(z<-1.59)[/tex]
[tex]=1-2(0.0559)[/tex]
[tex]=0.8882[/tex]
(c)
We know that,
[tex]\hat{P}-P=\pm 0.02[/tex]
[tex]n = 1400[/tex]
Now,
⇒ [tex]z=\frac{\hat{P}-P}{\sqrt{\frac{P(1-P)}{n} } }[/tex]
By substituting the values, we get
[tex]=\frac{\pm 0.02}{\sqrt{\frac{0.17(1-0.17)}{1400} } }[/tex]
[tex]=\frac{\pm 0.02}{0.01}[/tex]
[tex]=\pm 2[/tex]
⇒ [tex]P(I \hat P-PI<0.02)=P(-2<z<2)[/tex]
[tex]=1-2P(z<-2)[/tex]
[tex]=1-2(0.0228)[/tex]
[tex]=0.9544[/tex]
Think you can figure out the correct answer here
The answer would be 30 because the triangle is 10, the circle is 5, and each black triangle is 2 which would be 10 plus 5 which is 15 then times 2 which is 30.
Answer:
20?
Step-by-step explanation:
If 3 triangles = 30 they we could assume that each triangle = 10
10 + 10 + 10 = 30
If one triangle = 10 then the 2 circles would = 5 in the 2nd equation
10 + 5 + 5 = 20
If 1 circle = 5 then the 1 full squares would = 4
5 + 4 + 4 = 13
1 triangle = 10 , 1 circle = 5, Half a square = 2
10 + 5 * 2 = ?
Using PEMDAS we would multiply 2 and 5 first to get 10
10 + 10 = 20
Which word expression represents the algebraic expression shown?
12 – 3x
The difference between twelve and three times a number.
Hope this helps! :)
2) When Janet put her marble collection in groups of 7 there were two marbles left over, when she put them in groups of 5 there were 3 marbles left over. What is the fewest number of marbles that Janet could have had in her collection?
Answer:
23 marbles
Step-by-step explanation:
3 groups of 7 = 21 +2 = 23
4 groups of 5 = 20 +3 = 23
Complete the remainder of the table for the given function rule:
Y=3x-5
[X] -6 -3 0 3 6
[Y] -23 ? ? ? ?
answer is
(Y)=-23,-14, -5,4,13
hope this will help you
Can someone Help me please.?
Answer:
Option D
Hope this helps!
On a coordinate plane, a polygon has points (negative 3, 4), (3, 4), (3, negative 3), (negative 3, negative 2).
What points are the vertices of this polygon? Select all that apply.
(–3, –2)
(–2, –3)
(3, 4)
(–3, 4)
(3, 3)
(3, –3)
Answer:
(-3,-2)
(-3,4)
(3,4)
(3,-3)
Step-by-step explanation:
Answer:
cant see nun mind showing it
Analyze the diagram below and complete the instructions that follow.
Answer:
C).
[tex]= \sqrt{ {16}^{2} + {30}^{2} } \\ = \sqrt{1156} \\ = 34 \\= \sqrt{ {34}^{2} + {5}^{2} } \\ = \sqrt{1181} \\ = 34.37[/tex]
find the value of x. round your answer to the nearest tenth.
9514 1404 393
Answer:
x ≈ 13.7
Step-by-step explanation:
The relevant trig relation is ...
Tan = Opposite/Adjacent
tan(58°) = 22/x
x = 22/tan(58°) ≈ 13.747
The value of x is about 13.7 units.
I need help with this math question
Answer:
the scale factor is 3. hope this helps
Answer:
3
Step-by-step explanation:
you can set up a ratio using corresponding parts from each triangle.
or
notice the change from 3 to 9 is by multiplying 3 x 3
the change is the same for all : 3 x 4 = 12 , 3 x 5 = 15
ratio way
[tex]\frac{new}{old\\}[/tex] = [tex]\frac{9}{3}[/tex] = 3
a net ball team won 24 out of 40 matches. what percentage of the match did the team win
Answer:
60%
Step-by-step explanation:
[tex]percentage = \frac{24}{40} \times 100\% \\ = 60\%[/tex]
[tex]\Huge{\textbf{\textsf{{\purple{Ans}}{\pink{wer}}{\color{pink}{:}}}}} \\ [/tex]
[tex]percentage = \frac{24}{40} \times 100\% \\ = 60\%[/tex]
so answer is 60%
. Seja (G, ·) um grupo tal que para todo x ∈ G temos x
2 = eG. Mostre
que G ´e abeliano.
Please help Time limit
Answer:
n = 11. 6n - 4 = 5n + 7.
Step-by-step explanation:
Also, if you've ever read Romeo and Juliet, please help me! I just need a general answer on my questions, and I'll give brainliest.
A right cone has a radius of 5 cm and an altitude of 12 cm. Find its volume.
A)
300 cm3
B)
64.1 cm3
C)
942.5 cm3
D)
314.2 cm3
Answer:
D. V=314.2cm³
Step-by-step explanation:
The volume of the cone is:
V=pi×r²×h/3=pi×5²×12/3=100×pi=314.2cm³
Answer: D) 314.2 [tex]cm^3[/tex]
Step-by-step explanation:
The formula for finding the volume of a right cone is [tex]V=\pi r^2\frac{h}{3}[/tex]
r is the radius and h is the height/altitude.
We can sub these values in and solve
[tex]V=\pi (5^2)(\frac{12}{3} )\\V=\pi (25)(4)\\V=100\pi[/tex]
Let's sub in 3.14 for [tex]\pi[/tex] since that is a close estimate
[tex]V=(100)(3.14)\\V=314[/tex]
The volume is about 314.
Our closest answer to that is D so that is the correct choice.
I was wondering if anyone could answer this :)
Step-by-step explanation:
The sides with the variables are the same length, so make them equal.
x+2=2x-3
Get x alone on one side.
5=3x
Simplify.
5/3 = x
Answer:
5
Step-by-step explanation:
x+2 = 2x-3
+3 +3
x+5 = 2x
-x -x
x=5
Hope this helps! :)
