The researcher wants to estimate the number of hours that 5 year old children spend watching television. A sample of 50 five year old children was observed to have a mean viewing time of 3 hours. The population is normally distributed with a population standard deviation 0. 5,find the best point of the population mean and the 95& confidence interval of the population mean
Answers
We can be 95% confident that the true population mean of hours spent watching television by 5 year old children lies between 2.804 and 3.196 hours.
Plugging in the values, we get:
CI = 3 ± 1.96 * (0.5/√50)
CI = 3 ± 0.196
CI = (2.804, 3.196)
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The population from which sample is selected is normally distributed with a population standard deviation 0. 5. The best point of the population mean is equals to the 3 hours and the 95% confidence interval of the population mean is equals to the (2.8614, 3.1386).
A researcher wants to estimate the number of hours that 5 year old children spend watching television so that he consider a sample of 5 year old children with Sample size, n = 50
Sample Mean hours for watching tv
= 3 hours
The population of sample is normally distributed. Population standard deviations = 0.5
A point estimate of the population mean is determined by calculating the sample mean drawn from population. The sample mean is calculated by the sum of all sample values divided by the number of values and denoted by \( \bar X \).
The larger the sample the more accurate the estimate. If n equals the number of items in the population the same formula calculates the population mean, μ.Using the definition, the best estimate of population mean, μ = 3 hours.
Now, we have to determine the 95% confidence interval of the population mean.
Level of significance, α = 1 - 0.95 = 0.05
or α/2 = 0.025
Using the standard normal distribution table, the value of Z₀.₀₂₅ is 1.96. The 95% of confidence interval is a range of values above and below the point estimate. That is \(CI = \bar X - Z_{α/2} \frac{\sigma}{\sqrt{n}} < μ < \bar X + Z_{α/2} \frac{\sigma }{ \sqrt{n}} \\ \)
So, \(CI = 3 - 1.96 \times \frac{0.5}{\sqrt{50}} < μ < 3 + 1.96× \frac{0.5}{\sqrt{50}} \\ \)
=> CI = 3 - 0.1386 < μ < 3 + 0.1386
=> CI = 2.8614 < μ < 3.1386
Hence, the required confidence interval is ( 2.8614, 3.1386).
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Related Questions
Please solve both questions
Answers
The total amount of money that Mike made during summer by solving the equation formed is $3360. And the time that Mike worked whole summer at Six flags was 360 hours.
What exactly does the term "equation" mean?An equation, like 6 x 4 = 12 x 2, is used to demonstrate that two amounts or values are equal. Numerical noun An equation is a circumstance in which two or more components must be taken into account in order to perceive or comprehend the circumstance as a whole.
a) Let's denote the number of hours that Milk worked at Six Flags as x. Then, the amount of money he earned from Six Flags is given by:
9x
The amount of money he earned from babysitting his sister is given by:
120
Therefore, the total amount of money he made over the summer is:
9x + 120= $3360
b) We are given that the total amount of money Milk earned over the summer is $3,360. Setting this equal to the equation for the total amount of money he made above, we get:
9x + 120 = 3360
Subtracting 120 from both sides:
9x = 3240
Dividing both sides by 9:
x = 360
Therefore, Mike worked 360 hours at Six Flags over the summer.
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36) A new car dealership celebrated its grand opening by awarding prizes to 10 buyers. Five of
the buyers received a cash prize of $500, and 3 buyers received a cash prize of $1000. Two
buyers received $2500. If one of the buyers receiving a prize is selected at random, what is the
probability that the buyer received $2500?
Answers
Answer:
.20
Step-by-step explanation:
a six foot man standing 200 feet from a tower observes the angle of elevation to the top of the tower to be 67 degrees. how high is the tower?
Answers
So, the height of the tower is approximately 363.6 feet.
You can use trigonometry to solve this problem.
If we call the height of the tower "h" and the distance between the man and the base of the tower "d", then the angle of elevation is defined as the angle between the line of sight from the observer to the top of the tower and the horizontal line.
We can use the tangent function to relate the angle of elevation to the height and distance.
tan(67) = h/d
We know that the distance between the man and the tower is 200 feet. We can use this information to find the height of the tower.
h = d * tan(67)
h = 200 * tan(67)
The height of the tower is approximately 363.6 feet.
Please note that due to the approximation of the trigonometric functions, the answer may not be exactly as calculated.
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Find the horizontal asymptote of the function
A. none
B. x = 0
c.y=0
D.y = 1
Reset Selection
(x-1)(x-3)²(x+1)²
(x-2)(x+2)(x-1)(x+3)*
Answers
Horizontal asymptote y = 1.
What is meant by horizontal asymptote?A slant asymptote has a specific instance known as a horizontal asymptote. A "recipe" for locating a rational function's horizontal asymptote is as follows: Let deg D(x) and deg N(x) represent the degree of the denominator and the numerator, respectively. No horizontal asymptote exists.1) If the degree of the numerator is smaller than the degree of the denominator, the horizontal asymptote is y = 0. 2) The horizontal asymptote is y = c, where c is the ratio of the leading terms or their coefficients if the degree of the numerator and denominator are equal.The denominator of the function, n(x), can be used to find vertical asymptotes by solving the equation n(x) = 0 (note that this only works if the numerator, t(x), is not zero for the same x value). Find the function's asymptotes. The graph exhibits a vertical asymptote at x = 1.Find the horizontal asymptote of the function:
Horizontal asymptotes are the lines perpendicular to the y-axis and meet the curve at infinity.
Horizontal asymptote y = 1.
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How far apart are the points (0,-1) and (6,5)?
Answers
Answer:
(6, 6)
Step-by-step explanation:
Answer:
The distance is 8.4853
Step-by-step explanation:
Input Data :
Point 1 (xA, yA) = (0, -1)
Point 2 (xB, yB) = (6, 5)
Objective :
Find the distance between two given points on a line?
Formula :
Distance between two points = √(xB − xA) ^ 2 + (yB − yA) ^ 2
Solution :
Distance between two points = √ (6 − 0)^2 + (5− −1) ^ 2
= √6^2 + 6^2
= √36 + 36
= √72
= 8.4853
Distance between points (0, -1) and (6, 5) is 8.4853
hope this helps and is right :)
Which of the following ordered pairs are solutions to the system of equations below?
s 4x + 4y = -9
y = 2x - 13
Answers
Answer:
x = 43/12
y = - 35/6
Step-by-step explanation:
4x + 4y = -9
y = 2x - 13
4x + 4(2x - 13) = - 9
4x + 8x - 52 = - 9
12x = 52 - 9
12x = 43
x = 43/12
y = 2×43/12 - 13
y = 86/12 - ¹²⁾13
y = (86 - 156)/12
y = - 70/12
y = - 35/6
what will A scale factor that is less than one produce
Answers
Answer:
When the absolute value of the scale factor is less than one, a compression occurs. When the absolute value of the scale factor is equal to one, neither an expansion nor a compression occurs.
Step-by-step explanation:
:)
b. Hazel is a member of one of these organizations. What is the probability that she is a
member of FFA?
Answers
The probability that Hazel is a member of the FFA , given the number of organizations is 1 / 3.
How to find the probability ?Three potential organizations in which Hazel could participate are the Future Farmers of America (FFA), 4-H, and Students Against Destructive Decisions (SADD). It is established that Hazel is a constituent of one of the aforementioned groups.
Hence, it may be posited that every organization holds an equi-probable likelihood of accommodating Hazel as a member.
This then means that the probability that Hazel is a member of the FFA would then be:
Probability = Number of possible outcomes / Number of desired outcomes
Probability = 1 / 3
Probability = 33. 3333 %
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The full question is:
Hazel is a member of one of these organizations : FFA, 4-H, and SADD. What is the probability that she is a member of FFA?
simplify
(8p^6)^1/3
simplifyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy
Answers
Answer:
\(2p^2\)
Step-by-step explanation:
Step 1: Apply the exponentiation property:
\((8p^6)^\frac{1}{3} = 8^\frac{1}{3} * (p^6)^\frac{1}{3}\)
Step 2: Simplify the cube root of 8:
The cube root of 8 is 2:
\(8^\frac{1}{3} =2\)
Step 3: Simplify the cube root of \((p^6)\):
The cube root of \((p^6)\) is \(p^\frac{6}{3} =p^2\)
Step 4: Combine the simplified terms:
\(2 * p^2\)
So, the simplified expression is \(2p^2\).
what is the product of 3 square root 7 and 17 square root 14 in simplest radical form
Answers
\(3 \sqrt{7} \times 17 \sqrt{14} \)
This is the problem that we need to solve. The best way to get about it is to first:
Multiply the constant numbers (3 and 17). 3×17 is 51. Next multiply the radicals. \( \sqrt{7} \times \sqrt{14} = \sqrt{7 \times 14} = \sqrt{108} \)Simplify the squareroot of 108 since it is 49 times 2. It would be equal to 7 squareroots of 2. Our final answer would be:\(51 \times 7\sqrt{2} = 357 \sqrt{2} \)51 x 7 is 357, so the answer above is right.The skills needed are multiplication, mulitplication of radicals, and simplifying radicals, so if you want to review anything use these as reference.
Hope you understood and have a nice day!!
the least common multiple of a positive integer n and 18 is 180, and the greatest common divisor of n and 45 is 15. what is the sum of the digits of n?
Answers
The sum of the digits of n is 12.
Given data;
The greatest common divisor of n and 45 is 15, whereas the least common multiple of n and 18 is 180.
To get the sum of the digits of n;
Let,
LCM (n, 18) = 180
GCD (n, 45) = 15
(I) LCM (n, 18) = 180 = n must be the divisor of 180
Divisors of 180 ⇒ 1, 2, 3, 6, 9, 10, 18, 180
As 1, 2, 3, 6, 9, and 18 are divisors of 18.
The smallest n is 9.
(II) GCD (n, 45) = 15 = n has a factor of 3 and 5
So, n = 3
Therefore, the sum of the digits of n is 12.
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The distribution is uniform. B. The distribution is skewed to the left. C. The distribution is bell shaped. D. The distribution is skewed to the right.
Answers
The shape of a uniform distribution is rectangular. (option d)
A uniform distribution is characterized by a constant probability for each value within a given range. This means that all values within that range have an equal likelihood of occurring. Visually, a uniform distribution appears as a rectangle on a graph, hence the name "rectangular distribution."
To understand the shape of a uniform distribution in mathematical terms, let's consider a continuous uniform distribution over an interval [a, b]. The probability density function (PDF) for a continuous uniform distribution is defined as:
f(x) = 1 / (b - a) for a ≤ x ≤ b
= 0 otherwise
Since the probability density is constant within the defined range and zero outside it, the resulting shape is rectangular. Each value within the interval has an equal probability of occurring, resulting in a uniform distribution.
Hence the correct option is (d)
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Complete Question:
A uniform distribution's shape is:
A. Bell-shaped.
B. Positively skewed.
C. Negatively skewed.
D. Rectangular.
E. Skewed either positively or negatively depending upon the dataset.
what is the answer to −9 ×(−8)
Answers
Answer:
-9x(-8)
9x8
=72
Step-by-step explanation:
one third of a land is on maize, a fifth of the remainder is on potatoes and the rest which is 0.5 ha is on beans. how much of the land is on potatoes?
Answers
Answer: \(1250\ m^2\)
Step-by-step explanation:
Let x= Total land.
Then for Maize = \(\dfrac{x}{3}\)
For Potatoes = \(\dfrac15(x-\dfrac {x}{3})=\dfrac15(\dfrac{2x}{3})=\dfrac{2}{15}x\)
For beans = \(x- (\dfrac{x}{3}+\dfrac{2}{15}x)=0.5 \ ha\)
\(\Rightarrow\ x- (\dfrac{5x+2x}{15})=0.5 \ ha\\\\\Rightarrow\ x- (\dfrac{7x}{15})=0.5 \ ha\\\\\Rightarrow\ \dfrac{15x-7x}{15}=0.5 \ ha\\\\\Rightarrow\ \dfrac{8x}{15}=0.5 \ ha\\\\\Rightarrow\ x=0.5\times\dfrac{15}{8} \ ha\\\\\Rightarrow\ x=0.9375 \ ha\)
1 ha = 10000.00 m²
0.9375 ha = 9375 m²
Land for potatoes = \(\dfrac{2}{15}(9375) =1250\ m^2\)
Hence, \(1250\ m^2\) of the land is on potatoes.
State whether each of the following statement is true or false. Justify your answer.
(i) {2,3,4,5} and {3,6} are disjoint sets.
(ii) {a,e,i,o,u} and {a,b,c,d} are disjoint sets
(iii) {2,6,10,14} and {3,7,11,15} are disjoint sets
(iv) {2,6,10} and {3,7,11} are disjoint sets
Answers
The answer is (i) The statement is False, (ii) The statement is false, (iii) The statement is true, (iv) The statement is true.
(i) Let A = {2, 3, 4, 5} and B = {3, 6}
Now A∩B
= {2, 3, 4, 5} ∩ {3, 6} = {3}
Hence, A and B are not disjoint. So the statement is false.
(ii) Let A = {a, e, i, o, u} and B = {a, b, c, d}
Now A∩B
= {a, e, i, o, u} ∩ {a, b, c, d}= {a}
Hence, A and B are not disjoint. So the statement is false.
(iii) Let A = {2, 6, 10, 14} and B = {3, 7, 11, 15}
Now, A∩B
= {2, 6, 10, 14} ∩ {3, 7, 11, 15} = Φ
Hence, A and B are disjoint sets. So the statement is true.
(iv) Let A = {2, 6, 10} and B = {3, 7, 11}
Now A∩B
= {2, 6, 10} ∩ {3, 7, 11} = Φ
Hence, A and B are disjoint sets. So the statement is true.
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what is the volume of this square based pyramid?
Answers
Hey There! I can help you by explaining how to solve it but not answering sorry! Anyhow, To find the volume of a square based pyramid I suggest you start with the square and do L x W. Than Solve the triangles by using formula 0.5 * b * h. Hint: On the bottom triangle use 8cm from the square with the 3.8cm. Hope you now understand and can find the answer!
Which of the following is NOT one of the main components of the cell theory?
1.Cells must contain DNA
2.All living things are made of cells
3.cells can only come from other cells
4.Cells are the basic unit of life
Answers
Answer:
number 1 so a (=
Step-by-step explanation:
Let f be the function given by f(x) 9x. If four subintervals of equal length are used, what is the value of the right Riemann sum approximation for (x) dx?
Answers
The value of the right Riemann sum approximation for integral ∫₀² f(x) dx is (c) 60.
The right Riemann sum approximation is obtained by dividing the interval [0, 2] into four subintervals of equal length and evaluating the function at the right endpoints of each subinterval. In this case, each subinterval has a length of (2-0)/4 = 0.5. The right endpoints of the subintervals are 0.5, 1.0, 1.5, and 2.0.
To calculate the right Riemann sum, we evaluate the function at these right endpoints and sum up the values multiplied by the subinterval length.
f(0.5) = \(9^{0.5\) = 3
f(1) = 9¹ = 9
f(1.5) = \(9^{1.5\) = 27
f(2) = 9² = 27
The right Riemann sum is then
= (0.5 * f(0.5)) + (0.5 * f(1.0)) + (0.5 * f(1.5)) + (0.5 * f(2.0))
= 0.5 * (3 + 9 + 27 + 81)
= 60.
Therefore, the value of the right Riemann sum approximation for ∫2 to 0 f(x) dx is 60, which corresponds to option (c).
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Given question is incomplete, the complete question is below
let f be the function given by f(x)= 9ˣ, if four subintervals of equal length are used, what is the value of the right riemann sum approximation for∫₀² f(x) dx. 20b. 40c. 60d. 80
please explain how to do this one as well ...
Answers
Answer:
x = 13
Step-by-step explanation:
Step 1: Define
f(x) = (x - 1)/2
f(x) = 6
Step 2: Substitute and solve for x
6 = (x - 1)/2
12 = x - 1
x = 13
PLLSS HELP ILL GIVE BRAINLIST PLLLLLSSSS
Identify the multiplication problem that matches the model.
3 x 3
3 x
3
5
2 x
3
5
3 x
Answers
PLEASE HELP ASAP!!
The graph below is the solution for which set of inequalities?
1) x-2y ≤ 4
x+y ≤ 5
x ≥ 0
y ≥ 0
2) 3x-y ≤ 12
2x+y ≤ 10
x ≥ 0
y ≥ 0
3) 2x-y ≤ 8
x+y ≤ 5
x ≥ 0
y ≥ 0
4) x+y ≤ 5
x+y ≤ 4
x ≥ 0
y ≥ 0
Answers
Answer:
Hi,
Step-by-step explanation:
x>=0
y>=0
x+y-5<=0 line passing through (0,5) and (5,0) with (0,0) in minus region
2x-y-8<=0 line passing trough (0,-8) and (4,0) with (0,0) in minus region
Answer C
can yall help me on this i have been stuck on it for a long time
Answers
The least common multiple of two or more numbers is the smallest number that is a multiple of each of the given numbers. For example, the LCM of 2 and 3 is 6, because 6 is the smallest number that is a multiple of both 2 and 3.
For this problem, the number of packs bought is the least common multiple of 10 and 12, which is obtained by factoring them into prime numbers as follows:
10 - 12|2
5 - 6|2
5 - 3|3
5- 1|5
1 - 1
Hence:
lcm(10, 12) = 2² x 3 x 5 = 60.
Hence:
The number of packs of buns is given as follows: 6, as 60/10 = 6.The number of hot dogs is given as follows: 5, as 60/12 = 5.More can be learned about the least common multiple at https://brainly.com/question/10749076
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if the curved surface area of a cylinder is two-third of the total surface area and radius of the base is 6cm,find the height of the cylinder
Answers
Answer:
Height of cylinder = 12 cm
Step-by-step explanation:
Given:
Radius of cylinder = 6 cm
Curved surface area of cylinder = [2/3][Total surface area of cylinder]
Find:
Height of cylinder
Computation:
Curved surface area of cylinder = [2/3][Total surface area of cylinder]
2πrh = [2/3][2πr(h + r)]
h = 2h/3 +[2/3][6]
h - 2h/3 = 4
[3h - 2h] / 3 = 4
h = 12
Height of cylinder = 12 cm
assuming we are testing a hypothesis using the one-way anova test with more than 2 independent normally distributed populations, how can the f-statistic be calculated?
Answers
One measure we use to determine the F-statistics is the ratio of the variability within and across groups when we are doing the one way-ANOVA test.
We are interested in discovering whether there are significant differences between the means of the populations when doing a one-way ANOVA test on more than two independent normally distributed populations. A test statistic used to reach this conclusion is the F-statistic.
The ratio of the variability of the between group and within group is the a tool that we use to find the F-statistics.
F is equal to (SSB/k-1) / (SSW/N-k)
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Solve the equation by factoring. 2x^2 + 6x = -4
Answers
Answer:
x=-2 x=-1
Step-by-step explanation:
2x^2 + 6x = -4
Add 4 to each side
2x^2 + 6x +4= -4+4
2x^2 + 6x +4=0
Factor out 2
2( x^2 +3x+2) = 0
Divide by 2
x^2 +3x +2 =0
( x+2)(x+1) =0
Using the zero product property
x+2 =0 x+1 =0
x=-2 x=-1
Answer:
x = -1, -2
Step-by-step explanation:
Bring the constant term to the left hand side :
2x² + 6x = -42x² + 6x + 4 = 0Divide throughout by 2 :
(2x² + 6x + 4)/2 = 0/2x² + 3x + 2 = 0Splitting the middle term :
x² + x + 2x + 2 = 0x(x + 1) + 2(x + 1) = 0Factors obtained :
(x + 1)(x + 2)Finding the zeros :
x + 1 = 0 ⇒ x = -1x + 2 = 0 ⇒ x = -2What else would need to be congruent to show that ABC= AXYZ by ASA?
В
Given: X=A Z=C
A.BC=YZ
B.AC=XZ
C.Y=C
D.Z=A
Answers
Step-by-step explanation:
ASA stand for "angle-side-angle".
this means 2 angles have to be congruent, and then the side between these 2 angles.
the side(s) between the 2 given angles are AC and XZ.
so, these 2 sides need to be congruent too.
therefore B is the correct answer option.
We would need \(\bar{AC} = \bar{ZC}\) to be congruent to show that ΔABC= ΔXYZ by ASA congruency.
Option B is the correct answer.
What is triangle congruency?There are ways to prove that two triangles are congruent.
- Side-Side-Side (SSS) Congruence.
The three sides of one triangle are equal to the corresponding three sides of another triangle.
- Side-Angle-Side (SAS) Congruence.
The two sides and the included angle of one triangle are equal to the corresponding two sides and included angle of another triangle.
- Angle-Side-Angle (ASA) Congruence.
The two angles and the included side of one triangle are equal to the corresponding two angles and included side of another triangle.
- Angle-Angle-Side (AAS) Congruence.
We have,
ΔABC and ΔXYZ
∠A = ∠X
∠Z = ∠C
This means,
Two corresponding angles are equal.
ASA congruency means we need to have two corresponding angles and one corresponding side.
And the sides must be between the two corresponding congruent angles.
So,
\(\bar{AC} = \bar{ZC}\)
Thus,
We would need \(\bar{AC} = \bar{ZC}\) to be congruent to show that ΔABC= ΔXYZ by ASA congruency.
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Write an equation representing the pound of clay, c, that jamal from the example needs to make b bowls.
explain how to find the amount of clay jamal needs to make 8 bowls.
Answers
Answer:
8=2/3c
Step-by-step explanation:
Each bowl requires 2/3 pounds of clay
To make 8 bowls, Jamal needs 5 1/3 pounds of clay
1. The equation to represent amount is, x= b*c
2. Amount of clay Jamal needs to make 8 bowls is 8c.
What is equation?A mathematical statement that is made up of two expressions connected by an equal sign.
let the amount of clay be x.
The number of bowls be b and c is pounds of clay.
So, Total cost
x= b * c
Now, if number of bowls are 8 then
x= 8*c
x=8c
So, the amount of clay Jamal needs to make 8 bowls is 8c.
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10 points!!! Please answer 8 and 9 and hurry
Answers
Answer:
Step-by-step explanation:
since EG bisects angle DEF
31 = x + 15
31 - 15 = x
x = 16 degree
6x - 4 = 56
6x = 56 + 4
x = 60/6
x = 10
Answer:
8. 16
9. 10
abcdefghijklmnopqrstyvwxyz
Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x - 5)?
-
o
-5
-4
-3
-1
0
1
2
3
4
5
f
.
-5
-4
-3
-2.
-1
o
3
o
1
2
4
5
+
+
-4
-5
-3
-2
-1
+
1
o
+
2.
+
3
+
4
5
Ол
O
3
-5
-4
-3
-2
-1
o
1
2.
3
4
5
Answers
Answer:
3 8-4× less than 6 ×-5 and then you solve the equation
PLEASE HELP
A random sample of 50 purchases from a particular pharmacy was taken. The type of item purchased was recorded, and a table of the data was created.
Item Purchased Health & Medicine Beauty Household Grocery
Number of Purchases 10 18 15 7
Which graphical representation would be best to display the data?
Box plot
Line plot
Histogram
Stem-and-leaf plot
Answers
The graphical representation that would be best to display the data is given as follows:
Histogram.
What is an histogram?An histogram is a graph that shows the number of times each element of x was observed.
The four types of products are given as follows:
Health and Medicine.Beauty.Household.Grocery.Each of these item would represent a bin, and the values of each bin are given as follows:
Health and Medicine: 10.Beauty: 18.Household: 15.Grocery: 7.More can be learned about histograms at brainly.com/question/25983327