Answer:
0.9484 = 94.84% probability that the sample proportion of girls will be greater than 41%
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]
Suppose 44% of the children in a school are girls.
This means that [tex]p = 0.44[/tex]
Sample of 727 children
This means that [tex]n = 727[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.44[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.44*0.56}{727}} = 0.0184[/tex]
What is the probability that the sample proportion of girls will be greater than 41%?
This is 1 subtracted by the p-value of Z when X = 0.41. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.41 - 0.44}{0.0184}[/tex]
[tex]Z = -1.63[/tex]
[tex]Z = -1.63[/tex] has a p-value of 0.0516
1 - 0.0516 = 0.9884
0.9484 = 94.84% probability that the sample proportion of girls will be greater than 41%
The figure shows trapezoid ABCD on a coordinate plane.
Which of the following represents the area of this figure, rounded to the nearest square unit?
99
121
198
231
Answer:
121 unit^2.
Step-by-step explanation:
The area = height/2 * ( sum of the opposite parallel lines)
= h/2(BC + AD
h = BF = 14 - 3 = 11 units.
BC = 13 - 5 = 8 units.
AD = 16 - 2 = 14 units.
Area = (11/2)(8 + 14)
= 5.5 * 22
= 121 unit^2.
Answer:
121
Step-by-step explanation:
=
The solution set is
1/2(10x+16)-13=-3/5(15x-35)
Answer: 13/7 or as a decimal 1.857142857
How did i get the answer:
Step 1: Simplify both sides of the equation.
so 1/2 of 10 is 5, 1/2 of 16 is 8
-3/5 of 15 is -9 and -3/5 of -35 is POSITIVE 21
all together should look like 5x+8+−13=−9x+21
(now we have to combine like terms)
8+ -13= -5
5x -5 = -9x+21
Step 2: Add 9x to both sides
5x + 9x= 14x
14x -5 = 21
Step 3: Add 5 to both sides.
21+5= 26
14x=26
Step 4: Divide both sides by 14.
26/14= 1.85714286 or 13/7
Simplify. v80
A. 16v5
B. 5v4
C. 4v5
D. 20v4
Hi!
√80 = √(16 • 5) = √(4² • 5) = 4√5
A square has an area of 25 yd^2. What is the length of each side?
Answer:
5 yd
Step-by-step explanation:
Formula to find area of a square is a² where each side is a,
So, a²=25
or, a=√25
or, a=±5
since a side can't be negative, so a = 5 yd
Answered by GAUTHMATH
solve the inequality 4t^2 ≤ 9t-2 please show steps and interval notation. thank you!
Answer: [tex]t\in [\dfrac{1}{4},2][/tex]
Step-by-step explanation:
Given
Inequality is [tex]4t^2\leq9t-2[/tex]
Taking variables one side
[tex]\Rightarrow 4t^2-9t+2\leq0\\\Rightarrow 4t^2-8t-t+2\leq0\\\Rightarrow 4t(t-2)-1(t-2)\leq0\\\Rightarrow (4t-1)(t-2)\leq0[/tex]
Using wavy curve method
[tex]t\in [\dfrac{1}{4},2][/tex]
The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing (in mm3/s) when the diameter is 60 mm?
Answer:
22608 mm³/s
Step-by-step explanation:
Applying chain rule,
dV/dt = (dV/dr)(dr/dt)............... Equation 1
Where dV/dr = rate at which the volume is increasing
But,
V = 4πr³/3
Therefore,
dV/dr = 4πr²............... Equation 2
Substitute equation 2 into equation 1
dV/dt = 4πr²(dr/dt).............. Equation 3
From the question,
Given: dr/dt = 2 mm/s, r = 60/2 = 30 mm
Consatant: π = 3.14
Substitute these values into equation 3
dV/dt = 4×3.14×30²×2
dV/dt = 22608 mm³/s
A sample of 1300 computer chips revealed that 50% of the chips do not fail in the first 1000 hours of their use. The company's promotional literature claimed that more than 47% do not fail in the first 1000 hours of their use. Is there sufficient evidence at the 0.05 level to support the company's claim
Answer:
The p-value of the test is 0.015 < 0.05, which means that there is sufficient evidence at the 0.05 level to support the company's claim.
Step-by-step explanation:
The company's promotional literature claimed that more than 47% do not fail in the first 1000 hours of their use.
At the null hypothesis, we test if the proportion is of 47% or less, that is:
[tex]H_0: p \leq 0.47[/tex]
At the alternative hypothesis, we test if the proportion is of more than 47%, that is:
[tex]H_1: p > 0.47[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.47 is tested at the null hypothesis:
This means that [tex]\mu = 0.47, \sigma = \sqrt{0.47*0.53}[/tex]
A sample of 1300 computer chips revealed that 50% of the chips do not fail in the first 1000 hours of their use.
This means that [tex]n = 1300, X = 0.5[/tex]
Value of the statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.5 - 0.47}{\frac{\sqrt{0.47*0.53}}{\sqrt{1300}}}[/tex]
[tex]z = 2.17[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a sample proportion above 0.5, which is 1 subtracted by the p-value of z = 2.17.
Looking at the z-table, z = 2.17 has a p-value of 0.9850
1 - 0.985 = 0.015
The p-value of the test is 0.015 < 0.05, which means that there is sufficient evidence at the 0.05 level to support the company's claim.
Joyce paid $60.00 for an item at the store that was 50 percent off the original price. What was the original price?
$
Give your answer to the nearest cent.
What type of line is PQ⎯⎯⎯⎯⎯⎯⎯⎯?
Answer:
median
Step-by-step explanation:
Q is at the midpoint of RS and so PQ is a median
A median is a segment from a vertex to the midpoint of the opposite side.
We want to define what type of line is PQ (the line that passes through points P and Q) by looking at the given image, one can easily see that the line PQ is a median, now let's explain why.
First, let's analyze the image:
In the image, we can see that P is one vertex of the triangle, and Q is the midpoint of the segment RS (you can see that RQ = 4 and QS = 4) , where R and S are the other two vertexes of the triangle.
Particularly, we can define a median of a triangle as the line that passes through the midpoint of one side of the triangle and by the vertex that does not belong to that side.
With that definition, we can see that PQ is a median because Q is the midpoint of one side of the triangle and P is the vertex that does not belong to that side.
If you want to learn more, you can read:
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Two functions, A and B, are described as follows: Function A y = 9x + 4 Function B The rate of change is 3 and the y-intercept is 4. How much more is the rate of change of function A than the rate of change of function B?
2
3
6
9
Answer:
[tex]{ \tt{rate \: of \: change \: in \: A = 9}}[/tex]
Rate of change in function A is two times than that in function B
The speed (S) an object falls varies directly with time. If the speed is 49.0m/s after 5 seconds, then what is the speed after 3 seconds
9514 1404 393
Answer:
29.4 m/s
Step-by-step explanation:
Speed is proportional to time, so we have ...
speed / time = s/3 = 49/5
s = 3/5(49) = 29.4
The speed of the object is 29.4 m/s after 3 seconds.
B
13 ft.
5 ft.
A
C
12 ft.
Find the value of Cos (B) =
Answer: the answer is 12/13
what type of number cannot be written as a fraction p/q, where p and q are intergers and q is not equal to zero
Answer:
irrational numbers
Step-by-step explanation:
An irrational number is a number that cannot be expressed as a fraction p/q for any integers p and q.
Hi there!
»»————- ★ ————-««
I believe your answer is:
Irrational Number
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
The definition that is given in the question was the definition of a irrational number.A number that cannot be written as a fraction with two integers is called a irrational number. Some examples of irrational numbers are non-terminating decimals that do not repeat and non-perfect squares. A number that CAN be written as a fraction with two integers is called a rational number.⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the self-service island at a particular time, and let Y denote the number of hoses on the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying tabulation.
p(x, y) y
0 1 2
x 0 0.10 0.03 0.01
1 0 08 0.20 0.06
2 0.05 0.14 0.33
(a) Given that X = 1, determine the conditional pmf of Y�i.e., pY|X(0|1), pY|X(1|1), pY|X(2|1).
(b) Given that two hoses are in use at the self-service island, what is the conditional pmf of the number of hoses in use on the full-service island?
(c) Use the result of part (b) to calculate the conditional probability P(Y ? 1 | X = 2).
(d) Given that two hoses are in use at the full-service island, what is the conditional pmf of the number in use at the self-service island?
Answer:
(a): The conditional pmf of Y when X = 1
[tex]p_{Y|X}(0|1) = 0.2353[/tex]
[tex]p_{Y|X}(1|1) = 0.5882[/tex]
[tex]p_{Y|X}(2|1) = 0.1765[/tex]
(b): The conditional pmf of Y when X = 2
[tex]p_{Y|X}(0|2) = 0.0962[/tex]
[tex]p_{Y|X}(1|2) = 0.2692[/tex]
[tex]p_{Y|X}(2|2) = 0.6346[/tex]
(c): From (b) calculate P(Y<=1 | X =2)
[tex]P(Y\le1 | X =2) = 0.3654[/tex]
(d): The conditional pmf of X when Y = 2
[tex]p_{X|Y}(0|2) = 0.025[/tex]
[tex]p_{X|Y}(1|2) = 0.150[/tex]
[tex]p_{X|Y}(2|2) = 0.825[/tex]
Step-by-step explanation:
Given
The above table
Solving (a): The conditional pmf of Y when X = 1
This implies that we calculate
[tex]p_{Y|X}(0|1), p_{Y|X}(1|1), p_{Y|X}(2|1)[/tex]
So, we have:
[tex]p_{Y|X}(0|1) = \frac{p(y = 0\ n\ x = 1)}{p(x = 1)}[/tex]
Reading the data from the given table, the equation becomes
[tex]p_{Y|X}(0|1) = \frac{0.08}{0.08+0.20+0.06}[/tex]
[tex]p_{Y|X}(0|1) = \frac{0.08}{0.34}[/tex]
[tex]p_{Y|X}(0|1) = 0.2353[/tex]
Using the format of the above formula for the rest, we have:
[tex]p_{Y|X}(1|1) = \frac{0.20}{0.34}[/tex]
[tex]p_{Y|X}(1|1) = 0.5882[/tex]
[tex]p_{Y|X}(2|1) = \frac{0.06}{0.34}[/tex]
[tex]p_{Y|X}(2|1) = 0.1765[/tex]
Solving (b): The conditional pmf of Y when X = 2
This implies that we calculate
[tex]p_{Y|X}(0|2), p_{Y|X}(1|2), p_{Y|X}(2|2)[/tex]
So, we have:
[tex]p_{Y|X}(0|2) = \frac{p(y = 0\ n\ x = 2)}{p(x = 2)}[/tex]
Reading the data from the given table, the equation becomes
[tex]p_{Y|X}(0|2) = \frac{0.05}{0.05+0.14+0.33}[/tex]
[tex]p_{Y|X}(0|2) = \frac{0.05}{0.52}[/tex]
[tex]p_{Y|X}(0|2) = 0.0962[/tex]
Using the format of the above formula for the rest, we have:
[tex]p_{Y|X}(1|2) = \frac{0.14}{0.52}[/tex]
[tex]p_{Y|X}(1|2) = 0.2692[/tex]
[tex]p_{Y|X}(2|2) = \frac{0.33}{0.52}[/tex]
[tex]p_{Y|X}(2|2) = 0.6346[/tex]
Solving (c): From (b) calculate P(Y<=1 | X =2)
To do this, where Y = 0 or 1
So, we have:
[tex]P(Y\le1 | X =2) = P_{Y|X}(0|2) + P_{Y|X}(1|2)[/tex]
[tex]P(Y\le1 | X =2) = 0.0962 + 0.2692[/tex]
[tex]P(Y\le1 | X =2) = 0.3654[/tex]
Solving (d): The conditional pmf of X when Y = 2
This implies that we calculate
[tex]p_{X|Y}(0|2), p_{X|Y}(1|2), p_{X|Y}(2|2)[/tex]
So, we have:
[tex]p_{X|Y}(0|2) = \frac{p(x = 0\ n\ y = 2)}{p(y = 2)}[/tex]
Reading the data from the given table, the equation becomes
[tex]p_{X|Y}(0|2) = \frac{0.01}{0.01+0.06+0.33}[/tex]
[tex]p_{X|Y}(0|2) = \frac{0.01}{0.40}[/tex]
[tex]p_{X|Y}(0|2) = 0.025[/tex]
Using the format of the above formula for the rest, we have:
[tex]p_{X|Y}(1|2) = \frac{0.06}{0.40}[/tex]
[tex]p_{X|Y}(1|2) = 0.150[/tex]
[tex]p_{X|Y}(2|2) = \frac{0.33}{0.40}[/tex]
[tex]p_{X|Y}(2|2) = 0.825[/tex]
The awnser for this question
Find the volume of the cone. Round to the nearest hundredth.
Answer:
Step-by-step explanation:
volume of cone=1/3 πr²h
=1/3×π×5²×11
=275/3 ×3.14
≈287.33 in³
The sum of an a.p is 340. the first term is 7 and the common difference is 6. Cal the number of terms in the sequence.
anyone?
Common difference: 6
First term: 7
Second term: 13
Third term: 19
Fourth term: 25
Fifth term: 31
I hope this is correct and helps!
Answer to the following question is as follows;
Number of term in AP (N) = 10
Step-by-step explanation:
Given:
Sum of arithmetic progression (Sn) = 340
First term of AP (a) = 7
Common difference of AP (d) = 6
Find;
Number of term in AP (N)
Computation:
Sn = [n/2][2a + (n-1)d]
340 = [n/2][2(7) + (n-1)6]
340 = [n/2][14 + 6n - 6]
680 = n[6n + 8]
6n² + 8n - 680
Using Quadratic Formula
n = 10
Number of term in AP (N) = 10
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How to find the surface area of a cuboid
Answer:
To find the surface area of a cuboid we can also label the length, width and the height of the prism and use the formula SA=2LW+2LH+2HW to find the area of a cuboid
Answer:
202 cm²
Step-by-step explanation:
The opposite faces of a cuboid are congruent , then
SA = top/bottom + front/ back + sides , that is
SA = 2(9 × 4) + 2(9 × 5) + 2(4 × 5)
= 2(36) + 2(45) + 2(20)
= 72 + 90 + 40
= 202 cm²
Question 8 of 9
Use a calculator to find the correlation coefficient of the data set.
у
2
15
6
13
7
8
12
X
15
13
9
8
5
A. -0.909
B. 0.909
C. 0.953
D. -0.953
Actual data table :
X __ y
2 15
6 13
7 9
8 8
12 5
Answer:
0.953
Step-by-step explanation:
The question isnt well formatted :
The actual data:
X __ y
2 15
6 13
7 9
8 8
12 5
Using a correlation Coefficient calculator, the correlation Coefficient obtained by fitting the data is 0.953 which depicts a strong linear correlation between the x and y variable. This shows that the value of y increases with a corresponding increase in x values and vice versa.
The house-numbers on a certain street go from 1 to 88. The function B(n) models the type of the building whose number is n according to the following key:
(GRAPH ATTATCHED)
What number type is more appropriate for the domain of B?
A. Integer
B. Real Number
What's the appropriate domain?
Hello,
Answer A
[tex]dom (B(n)) =\{0,1,2,3\} =\{ z\ in \ \mathbb{Z} \ |\ 0 \leq z \leq 4\}[/tex]
Solve the equation −96=3(8x)^(5/3).
Answer:
x= - 1
Step-by-step explanation:
The average of 6,10,x,20 and 30 is 18. what is the value of x
Answer:
24
Step-by-step explanation:
18 times 5 is 90 so that means that the given numbers have to add up to 90 (including x)
so,
6+10+20+30=66
90-66=24
I hope this helps!
Answer:
[tex]x = 24[/tex]
Step-by-step explanation:
[tex]6 + 10 + x + 20 + 30 = 18[/tex]
There are 5 numbers that we must add to average out to get 18 so let set this equation up
[tex] \frac{6 + 10 + x + 20 + 30}{5} = 18[/tex]
[tex]6 + 10 + x + 20 + 30 = 90[/tex]
[tex]x = 24[/tex]
The following data was collected from a survey in which people identified their average salaries over the past ten years. Identify the number of classes in the histogram.
Answer:
nine 9 classes in the histogram
In the given figure, find m_RST, if m RSU = 43° and m_UST = 23°.
Answer:
66
Step-by-step explanation:
Add both of the angles given together
43 + 23
Find the missing term in the pattern.
Answer:
1/108
Step-by-step explanation:
each denominator triples, so just triple 36.
Answer:
1/108
Step-by-step explanation:
This is a geometric sequence, where each number is 3 times the previous. Normally you would use the actual formula, however you're just asked to pick up on a pattern so just multiplying the second number by 3 works.
You are dealt one card from a 52-card deck.
a) Find the odds in favor of getting a red king.
b) Find the odds against getting a red king.
Answer:
(a)So, there are 2 kings in red- one of hearts and the other of diamonds. Therefore, the probability of selecting a red king from a deck of cards= 2/52 or 1/26.
(b) There are 6 red face cards in a 52-card deck (so 46 other cards). PROBABILITIES compare the number of favorable outcomes to the total number of possible outcomes: The PROBABILITY of getting a red face card is 6/52 = 3/26.
The odds in favor of getting a red king will be 1/26. And the odds against getting a red king will be 25/26.
What is probability?Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
You are dealt one card from a 52-card deck.
Total events = 52
The odds in favor of getting a red king will be
Favorable events = 2
Then the probability will be
P = 2/52
P = 1/26
The odds against getting a red king will be
q = 1 – P
q = 1 – 1/26
q = 25/26
More about the probability link is given below.
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Can someone help me with this an my other work please?
vention 1 of 10
These box plots show daily low temperatures for a sample of days in two
different towns
TWINA
M
41
41
Town 1
1620
MI
D
10
152025 M3540
Degrees (0)
Which statement is the most appropriate comparison of the centers?
O A. The median temperature for both towns is 20"
B. The mean for town A, 30", is greater than the mean for town 8,25"
C. The median temperature for both towns is 30'
D. The median for town A, 30', is greater than the median for town B,
25
PREVIOUS
9 M
What is the scale factor from ALMN to AOPQ?
M
P
3
3
3
3
2
4
N
0
4
A. 4
(
B. 0
c
C. 3
D. 1
Answer:
D
Step-by-step explanation:
There 2 ways to interpret this problem.
From the info given:
These two triangles are congruent by SSS and congruent triangles have congruent or equal side lengths so the answer have to be 1.
If the triangles are similar, the side lengths form a proportion of that
[tex] \frac{3}{3} = \frac{3}{3} [/tex]
So the ratio or scale factor is 1.
The scale factor in the figure is 1.
What is a scale factor?A scale factor in math is the ratio between corresponding measurements of an object and a representation of that object.
Given that two triangles, LMN and OPQ, we need to find the scale factor,
We can see triangles are congruent, and we know that
Two triangles are congruent, by the SSS congruence criterion, if they are similar and the scale factor happens to be 1,
Hence, the scale factor in the figure is 1.
Learn more about scale factors, click;
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Help please!!!!! I’m using Plato
Answer:
[tex]\frac{y^{6} }{ x^{2} }[/tex]
Step-by-step explanation:
[tex]y^{6} x^{-2}[/tex]
Answer and Step-by-step explanation:
When there is a set of values within parenthesis, and an exponents on the values and on the parenthesis, you multiply the outer exponent with the inner exponent.
When a value has a negative exponent, the value that has the negative exponent will become a fraction and go to the denominator of the fraction (or go immediately to the denominator), or if it is already a fraction, goes to the denominator. If the value that has the negative exponent is in the denominator, the value will go to the numerator. In both instances, the negative exponent will then change to positive.
First, we need to simplify the expression inside the parenthesis.
[tex]y^{\frac{3}{2} } x^{-\frac{1}{2} } --> \frac{y^{\frac{3}{2} } }{x^{\frac{1}{2}} }[/tex]
Now we multiply the 4 to the exponents.
[tex]\frac{y^{\frac{3}{2} *\frac{x4}{1} } }{x^{\frac{1}{2}}*\frac{4}{1} } = \frac{y^{\frac{12}{2}} }{x^{\frac{4}{2}}} = \frac{y^6}{x^2}[/tex]
[tex]\frac{y^6}{x^2}[/tex] is the answer.
#teamtrees #PAW (Plant And Water)
