Consider the set {1, 2, 3, 4}.
a. Make a list of all samples of size 2 that can be drawn from this set of integers.
b. Construct the sampling distribution of sample means for samples of size 2 selected from this set.
c. Provide the distribution both in the form of a table and histogram.
Answers
Answer:
(a)
[tex]List = \{(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(2,4),(3,1),(3,2),(3,3),(3,4),\\(4,1),(4,2),(4,3).(4,4)\}[/tex]
(b) Sampling Distribution (Table)
[tex]\begin{array}{cccccccc}{\bar x} & {1} & {1.5} & {2} & {2.5} & {3} & {3.5} & {4} & {Pr}& {\frac{1}{16}} & {\frac{1}{8}} & {\frac{3}{16}} & {\frac{1}{4}} & {\frac{3}{16}} & {\frac{1}{8}} & {\frac{1}{16}} \ \end{array}[/tex]
(b) Sampling Distribution (Histogram)
See attachment
Step-by-step explanation:
Given
[tex]Set = \{1,2,3,4\}[/tex]
[tex]n =4[/tex]
Solving (a): A list of sample size 2
We have:
[tex]n =4[/tex]
[tex]r = 2[/tex] --- the sample size
First, we calculate the number of list using permutation (orders matter)
[tex]n(List) = n^r[/tex]
So, we have:
[tex]n(List) = 4^2[/tex]
[tex]n(List) = 16[/tex]
And the list is:
[tex]List = \{(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(2,4),(3,1),(3,2),(3,3),(3,4),\\(4,1),(4,2),(4,3).(4,4)\}[/tex]
Solving (b): Sample distribution of sample means of (a)
First, calculate the mean of each set using:
[tex]Mean = \frac{Sum}{2}[/tex]
So, we have:
[tex](1,1) \to \frac{1+1}{2} \to 1[/tex] [tex](1,2) \to \frac{1+2}{2} \to 1.5[/tex] [tex](1,3) \to \frac{1+3}{2} \to 2[/tex] [tex](1,4) \to \frac{1+4}{2} \to 2.5[/tex]
[tex](2,1) \to \frac{2+1}{2} \to 1.5[/tex] [tex](2,2) \to \frac{2+2}{2} \to 2[/tex] [tex](2,3) \to \frac{2+3}{2} \to 2.5[/tex] [tex](2,4) \to \frac{2+4}{2} \to 3[/tex]
[tex](3,1) \to \frac{3+1}{2} \to 2[/tex] [tex](3,2) \to \frac{3+2}{2} \to 2.5[/tex] [tex](3,3) \to \frac{3+3}{2} \to 3[/tex] [tex](3,4) \to \frac{3+4}{2} \to 3.5[/tex]
[tex](4,1) \to \frac{4+1}{2} \to 2.5[/tex] [tex](4,2) \to \frac{4+2}{2} \to 3[/tex] [tex](4,3) \to \frac{4+3}{2} \to 3.5[/tex] [tex](4,4) \to \frac{4+4}{2} \to 4[/tex]
Write out the sample means (sorted)
[tex]\bar x =\{1,1.5,1.5,2,2,2,2.5,2.5,2.5,2.5,3,3,3,3.5,3.5,4\}[/tex]
Construct a frequency table
[tex]\begin{array}{cc}{\bar x} & {f} & {1} & {1} & {1.5} & {2} & {2} & {3} & {2.5} & {4} & {3} & {3} & {3.5} &{2} & {4} & {1} & Total & 16\ \end{array}[/tex]
Construct the sampling distribution where the probability is calculated using: [tex]\frac{f}{Total}[/tex]
So, we have:
[tex]\begin{array}{cccccccc}{\bar x} & {1} & {1.5} & {2} & {2.5} & {3} & {3.5} & {4} & {Pr}& {\frac{1}{16}} & {\frac{1}{8}} & {\frac{3}{16}} & {\frac{1}{4}} & {\frac{3}{16}} & {\frac{1}{8}} & {\frac{1}{16}} \ \end{array}[/tex]
Related Questions
Help please! I’ll give brainliest!
Answers
Answer:
B
Step-by-step explanation:
solution to the system is where they intercept
Which object has the largest resultant force?
10N-
10N-
30 N-
A
C
30 N
5N
-5N
10N-
5N-
5N-
5N-
B
D
10N
10 N
Answers
Answer:
To find the resultant force of an object, we need to add up all the forces acting on it. The resultant force is the overall force that the object experiences, taking into account all the individual forces.
In this case, we are given four objects, A, B, C, and D, and the forces acting on them. To find the object with the largest resultant force, we need to calculate the resultant force for each object by adding up all the forces acting on it.
For object A, the forces acting on it are: 10 N, 10 N, and 10 N, for a total of 10 N + 10 N + 10 N = 30 N.
For object B, the forces acting on it are: 5 N, 5 N, 5 N, and 5 N, for a total of 5 N + 5 N + 5 N + 5 N = 20 N.
For object C, the forces acting on it are: 30 N and -5 N, for a total of 30 N + (-5 N) = 25 N.
For object D, the forces acting on it are: 10 N and -5 N, for a total of 10 N + (-5 N) = 5 N.
Therefore, the object with the largest resultant force is object C, with a resultant force of 25 N.
Write an equation of a line in slope-intercept form given the slope (m) and the y-intercept (b).
Answers
Answer: B y = -4/7x + 7
Step-by-step explanation:
The equation in the form y = mx + b
m = -4/7 and b = 7
Equation: y = -4/7x + 7
The table shows a cricket club's income in 2016 from a fete, a quiz and membership fees.
Income
Fete
£250
Quiz
Entry fees
Refreshments
13 at £5 each
£35
25 at £20 each
Membership fees
Express as a ratio
the income from the fete to the income from the quiz to the income from membership
fees.
Give your ratio in its simplest form.
Answers
Answer: 5:2:10
Income from fete = £250
13 x 5 + 35 = 100
25 x 20 = 500
250:100:500
Then simplify ratio -
25:10:50
5:2:10
find the value of r so the line that passes through each pair of points has the given slope (5, 3), (r, -5), m=4
Answers
Answer:
r=3
Step-by-step explanation:
use slope formula : y2-y1 / x2-x1
-5-3 / r-5
the numerator is -8 which means the denominator has to be -2 in order to have the slope be 4
so r-5 = -2
3-5 = -2
odd function f(x) is defined for all real values of x. for the function g(x)=2.3+f(x-9), calculate g(6)+g(8)+g(10)+h(12).
Answers
Answer:
easy theanswer is -14x
Step-by-step explanation:
Use Exponential Functions
From the table below, determine whether the data shows an exponential function. Explain why or why not.
a. No; the domain values are at regular intervals.
b. No; a different value is added to each range value.
c. No; there is no relationship between the x value and its corresponding y value.
d. Yes; the domain values are at regular intervals and the range values have a common factor 2.
Please select the best answer from the choices provided
Answers
Answer:
C. No; there is no relationship between the x value and its corresponding y value.
Step-by-step explanation:
I calculated it logically
Answer:
The correct answer c. No; there is no relationship between the x value and its corresponding y value
How many unique tree graphs (i.e. with different degree patterns) can be made with
4 vertices?
a) 0
b) 1
c) 2
d) 3
Answers
What is 17 divided by 9
Answers
There are 7 women and 9 men with a chance to be on a game show. The producer of the show is going to choose 7 of these people at random to be contestants. What is the probability that the producer chooses 4 women and 3 men? Round your answer to three decimal places.
Answers
Answer:
147/572
Step-by-step explanation:
The number of combinations of n things chosen r at a time is
[tex]\binom{n}{r}=\frac{n!}{r!(n-r)!}[/tex] (Some writers use the symbol [tex]_nC_r[/tex])
Choose 4 women from the 7:
[tex]\binom{7}{4}=\frac{7!}{4!(7-4)!}=35[/tex] ways
Choose 3 men from 9:
[tex]\binom{9}{3}=\frac{9!}{3!(9-3)!}=84[/tex] ways
There are 35 x 84 = 2940 ways to choose both, out of
[tex]\binom{16}{7}=\frac{16!}{7!(16-7)!}=11440[/tex] ways to choose any 7 people from the group of 16.
Probability:
[tex]\frac{2940}{11440}=\frac{147}{572}[/tex]
P.S. As an example of how to calculate combinations, here's the calculation (by hand, a calculator is easier!) of [tex]\binom{9}{3}[/tex].
[tex]\binom{9}{3}=\frac{9!}{3!(9-3)!}=\frac{9!}{3!6!}[/tex]
When you write out the factorials, you can do a bunch of cancellation between the numerator and denominator.
[tex]\frac{9\cdot8\cdot7\cdot\cancel{6\cdot5\cdot4\cdot3\cdot2\cdot1}}{(3\cdot2\cdot1)(\cancel{6\cdot5\cdot4\cdot3\cdot2\cdot1)}}=\frac{9\cdot8\cdot7}{3\cdot2\cdot1}=84[/tex]
Which of the following characteristics are true of all parallelograms? Select all that apply
Answers
Attributes of a parallelogram leads to, Due to the equal length of each side and the 90° angles that they create at their corners, a square is a parallelogram.
Parallel sides with two opposed pair?Due to the equal length of each side and the 90° angles that they create at their corners, a square is a parallelogram. They are, in this sense, two sets of parallel lines, which provides the framework for the parallelogram, which must have two parallel sides.Attributes of a parallelogram leads to, Due to the equal length of each side and the 90° angles that they create at their corners, a square is a parallelogram. They are, in this sense, two sets of parallel lines, which provides the framework for the parallelogram, which must have two parallel sides.The complete question is,
Which of the following attributes of a parallelogram leads to the conclusion that every square can be categorized as a parallelogram? Choose each option that applies.
four equal sides
two pairs of diametrically opposed equal angles
diagonals are cut in half.
two sets of parallel, opposed sides.
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A squre has 12cm length find it's area and perimeter
Answers
Answer:
a=L² is is the formula for the area of square. where L represent the length.
a=(12cm)²
a=144cm²
p=4(L) is the formula for the perimeter of a square. where L represent the length
p=4(12cm)
p=48cm
Your brother gave you $10 to help with a shoe purchase. This covered 8% of the cost. How much did the shoes cost? Write and solve an equation, let s represent the cost of the shoes.
Answers
The equation to represent the cost of shoes is 0.08s=10 and the cost of shoes is $125.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, your brother gave you $10 to help with a shoe purchase. This covered 8% of the cost.
Let s represent the cost of the shoes.
Now, equation is
8% of s=10
8/100 ×s=10
0.08s=10
s=10/0.08
s=$125
Therefore, the equation to represent the cost of shoes is 0.08s=10 and the cost of shoes is $125.
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Nancy earns Rs. 25,00,000 in 5 months. what is her annual salary
Answers
Explained:
If Nancy earns 25000000 in 5 months you divide it by 5 to find what she earns in 1 month which gets you 5000000, since there is 12 months in an annum(year) you times the 5000000 by 12 getting you 120,000,000
Answer:
You would first divide the amount of months by the total amount of money that she has earned in 5 months.
(You put down 25, 00, 000 so Ima just write it as 2,500,000)
25,000,000/5 = 5,000,000
She earns 5,000,000 a month, and would earn 60,000,000 per year.
Anual salary is how much money you would earn per year, so the answer is 60,000,000. (sixty million).
Step-by-step explanation:
Hope it helps! =D
Which of the following ordered pairs is a solution to y = 2X?
O (3,6)
O (3,9)
O (3.8)
O (3.27)
Answers
Answer:3,9
Step-by-step explanation:
Students at a local university have the option of taking freshman seminars during their first year in college. A survey of the freshmen revealed the following: Among the social science majors, 50% chose to take a freshman seminar; among the humanities majors, 65% chose to take a freshman seminar; and among the physical science majors, it was 30% . Freshmen make up 32% of undergraduates. The probability of taking a freshman seminar, if a student is a science major, is:
Answers
complete question
the probability of taking a freshman seminar, if a student is a science major, is:
a) a total probability.
b) a conditional probability.
c) a complete probability.
d) a joint probability.
Answer:
B. Conditional probability
Step-by-step explanation:
In this given question, what we ant to do is to find the probability thst a student who is a science major is taking a freshman seminar. This clearly a case of conditional probability.
In a conditional probability, we are trying to find out the probability of an event occurring given that another event has already occurred. since the student is a science major, the probability of the student taking a freshman seminar is to be determined.
Please help with this Khan Question :)
Answers
Answer:
the answer is A
Step-by-step explanation:
encircle the number that are divisible by 2 a.4224 b.3012 c.8817 d. 10172
Answers
Answer:
a,b,c are divisible by 2
solve for x
give an exact answer
Answers
Answer:
x = -1
Step-by-step explanation:
0.5(5-7x)=8-(4x+6) note.......0.5 = 1/2
(1/2) ( 5 - 7x) = 8 - 4x - 6
(1/2) (5 - 7x) = 2 - 4x multipy through by 2
5 - 7x = 4 - 8x add 8x to both sides.......subtract 5 from both sides
x = -1
HELP I have been stuck on this problem for a bit now
Answers
Answer:
16
Step-by-step explanation:
72/2 = 36
Square root of 36 is 6; 6 x 2 = 12
square root of 4 is 2 and 2^2 equals 4.
12 +4 =16
Mark me brainliest please
Answer:
16
Step-by-step explanation:
72/2=36
square root 36=6
6*2=12
root4 squared is 4
12+4=16
Hope that helps :)
can you guys help me!!!! Question 3
Calculate the average reading for all three trials for both the wet bulb and dry bulb
thermometers.
Convert the average temperatures for both thermometers to Celsius using this
formula:
(°F - 32) °C
wet bulb temp: 62.8, 60.0, 61.0
dry bulb temp: 64.5, 64.4, 64.3
Answers
Answer:
F = ( 9/5) X c + 32
Step-by-step explanation:
.......................
Answers
Answer:
Direct variation
Step-by-step explanation:
Given
[tex]\frac{a_1}{b_1} = \frac{a_2}{b_2}[/tex]
Required
The type of variation
The given equation represents a direct variation.
A direct variation is:
[tex]a = kb[/tex]
Where
[tex]k\to[/tex] constant of variation
Make k the subject
[tex]k = \frac{a}{b}[/tex]
For corresponding values of and b, we have:
[tex]k = \frac{a_1}{b_1} = \frac{a_2}{b_2} = \frac{a_3}{b_3} = ............. =\frac{a_n}{b_n}[/tex]
Hence, [tex]\frac{a_1}{b_1} = \frac{a_2}{b_2}[/tex] is a direct variation
Round 0.12406667 to the nearest hundredth
Answers
Answer:
Step-by-step explanation:
0.124
Can someone show the work and answer ASAP
Answers
so 15 miles is the answer❤
Step-by-step explanation:
4²+5²=x²
16+25= 41
x²=41
x= 6.4
5+4+6= 15
How do you do numb 3. please help
Answers
Step-by-step explanation:
first we need to identify the lines themselves.
the line from bottom left to top right is simply
y = x
the line is solid, so the points on the line are included.
the dotted line (the points on the line itself are not included) goes through
(0, 2) and (3, 0)
the y-intercept is therefore 2 (the y value when x = 0).
and for the slope
x changes by +3 (from 0 to 3).
y changes by -2 (from 2 to 0).
the slope is -2/+3 = -2/3
and the line is
y = (-2/3)x + 2
we see that the desired gray area is above both lines (">"), and we need to consider, whether the points in the lines are included or not.
so, the system of inequalities is
y >= x
y > (-2/3)x + 2
need help asappppppp
Answers
Answer:
hypotenuse
Step-by-step explanation:
Answer:
I believe it is D hypotenuse
Step-by-step explanation:
In geometry, a hypotenuse is the longest side of a right-angled triangle.
Find the slope of the line.
Answers
i need help please i dont get this
Answers
Answer:
See attached
Step-by-step explanation:
You want the solution to the inequality -12x < -48 shown on a number line.
SolutionThe solution to the inequality is found by dividing by the x-coefficient
-12x < -48
x > 4 . . . . . . . divide by -12
When working with inequalities, you need to know that multiplying or dividing by a negative number reverses the inequality symbol.
GraphThe value x=4 is not included in the solution set, so an open circle is plotted at that point. All values of x greater than x=4 are included in the solution set, so the number line is shaded to the right of the open circle.
The graph of the solution is shown in the attachment.
__
Additional comment
Often, you can avoid multiplying or dividing an inequality by a negative number by rearranging it. Here, adding 12x+48 to both sides makes it be ...
48 < 12x
Now, you can divide by 12 without worrying about the inequality symbol:
4 < x . . . . . same as above
Ms.Metz had her students estimate the length and width of a math book. Dana's estimate was 40cm by 20cm. The book measured 24cm by 16cm. How far off was her estimate?
Answers
Dana's estimated length was 66.67% far off the actual length and her estimated width was 25% far off the actual width.
What is percent error?Percent error is the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage. In other words, the percent error is the relative error multiplied by 100.
Percent Error Formula
The formula for percent error is:
PE = (|Estimated value-Actual value|/ Actual value) × 100
Given,
Actual length of the book = 24 cm
Actual width of the book = 16 cm
Dana's estimated length of the book = 40 cm
Dana's estimated width of the book = 20 cm
Error in measurement of length of the book =
(Measured Length - Actual Length/Actual length) × 100
= (40 - 24/24) ×100 = 66.67%
Error in measurement of width of the book =
(Measured width - Actual width/Actual width) × 100
= (20 - 16 / 16) × 100 = 25%
Hence, Dana's estimated length and breadth was 66.67% and 25% far off the actual length and width of the book respectively.
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What is a root of a polynomial function?
Answers
Answer:
d. a value of the variable that makes the polynomial equal to zero