Answer:
0.9173 = 91.73% probability that the average duration of unemployment was between 30 and 37 weeks.
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 estabilishes 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.
Mean of 34.6, standard deviation of 10.2
This means that [tex]\mu = 34.6, \sigma = 10.2[/tex]
Sample of 36
This means that [tex]n = 36, s = \frac{10.2}{\sqrt{36}} = 1.7[/tex]
What is the probability that the average duration of unemployment was between 30 and 37 weeks?
This is the pvalue of Z when X = 37 subtracted by the pvalue of Z when X = 30.
X = 37
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{37 - 34.6}{1.7}[/tex]
[tex]Z = 1.41[/tex]
[tex]Z = 1.41[/tex] has a pvalue of 0.9207
X = 30
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{30 - 34.6}{1.7}[/tex]
[tex]Z = -2.71[/tex]
[tex]Z = -2.71[/tex] has a pvalue of 0.0034
0.9207 - 0.0034 = 0.9173
0.9173 = 91.73% probability that the average duration of unemployment was between 30 and 37 weeks.
Donna, Austin, and goran have a total of $84 in their wallets. Donna had $6 less than goran. Austin has 3 times what goran has. How much does each have?
Answer: Goran = 18, Donna = 12, Austin = 54
Step-by-step explanation:
x + x - 6 + 3x = 84
5x - 6 = 84
5x = 90
x = 18
Hope this helps!
Of interest is to determine the mean age of students at the time they take the comprehensive exam for all students enrolled in graduate programs that require students to take comprehensive exams. A simple random sample of 31 students enrolled in graduate programs was selected, and the age of each student when they took the comprehensive exam was recorded. The mean age at the time of taking the comprehensive exam for this sample of 31 students was 27.5 years with a standard deviation of 2.9 years; there were no outliers in the sample that would lead one to suspect heavy skewness in the distribution. If appropriate, use this information to calculate and interpret a 98% confidence interval for the mean age of students at the time they take the comprehensive exam for all students enrolled in graduate programs that require students to take comprehensive exams. Use this information to answer questions 3-5
Answer:
The 98% confidence interval for the mean age of students at the time they take the comprehensive exam for all students enrolled in graduate programs that require students to take comprehensive exams is between 26.2 and 28.8 years. This means that we are 98% sure that the mean age of all students taking the exam is between 26.2 and 28.8 years.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 31 - 1 = 30
98% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 30 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.98}{2} = 0.99[/tex]. So we have T = 2.457
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.457\frac{2.9}{\sqrt{31}} = 1.3[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 27.5 - 1.3 = 26.2 years
The upper end of the interval is the sample mean added to M. So it is 27.5 + 1.3 = 28.8 years
The 98% confidence interval for the mean age of students at the time they take the comprehensive exam for all students enrolled in graduate programs that require students to take comprehensive exams is between 26.2 and 28.8 years. This means that we are 98% sure that the mean age of all students taking the exam is between 26.2 and 28.8 years.
What is the mean absolute deviation of 35 38 41 35 36 55
Answer:
7.8333
Step-by-step explanation:
x=?.........................
Answer:
x = 58°
Step-by-step explanation:
Length of tangents drawn to a circle from a point outside the circle, are equal in measure.
By using this property,
Two tangents PQ and PR will be equal.
And angles opposite to these sides will be equal.
Therefore, ∠PQR ≅ ∠PRQ
By triangle sum theorem,
m∠PQR + m∠PRQ + m∠QPR = 180°
x° + x° + 64° = 180°
2x = 180 - 64
2x = 116
x = 58°
Two high schools have a similar number of students and parking lots of similar size. The safety officers at both schools want to investigate whether there is an average difference in the number of cars parked per day in the student parking lots for the school year. A random sample of 15 school days will be selected. For each selected day, the number of cars parked in the student parking lots will be counted at both schools and the difference will be recorded. Assuming all conditions for inference are met, which of the following is the appropriate test for the investigation?
a. A two-sample 2-test for a difference between proportions
b. A two-sample t-test for a difference between means
c. A matched-pairs t-test for a mean difference
d. A chi-square test of homogeneity
e. A chi-square test of independence
Answer: c. . A matched-pairs t-test for a mean difference
Step-by-step explanation:
Based on the information given in the question and assuming all conditions for inference are met, the appropriate test for the investigation will be a matched-pairs t-test for a mean difference.
Since a matched-pairs t-test can be used to determine if a significant mean difference exist between two paired data, then this will be appropriate in this case since the safety officers at both schools want to know if there's an average difference in the number of cars parked per day in the student parking lots for the school year.
The appropriate test for the investigation of the given case is done by: Option C: A matched-pairs t-test for a mean difference
When to use the matched pair t test and when to use the t test?When there has to be done comparison between means of two sets of paired data, then we use matched pair t test.
For the given case the investigation is to know whether there is an average difference in the number of cars parked per day in the student parking lots for the school year for both the schools in consideration.
So there are two data sets and comparison of their mean is to be done.
Thus, the appropriate test for the investigation of the given case is done by: Option C: A matched pairs t-test for a mean difference.
Learn more about matched pair t-test here:
https://brainly.com/question/14690592
Find the measure of the missing angle
The angle is 90 because that' s a right angle.
Answer:
50
Step-by-step explanation:
that is a right angle so 90 degrees
so you could do
90-40=50
hope this helps:)
NCERT SOLUTIONS FOR CLASS 7
MATHS
ALL CHAPTERS
Answer:
https://www.learncbse.in/ncert-solutions-for-class-7-maths/
Write the equation in standard form for the circle with center (0,
–
8) and radius 2
19.
Use this link to find your answer
https://lalinks.org/linksweb
A bookstore keeps track of books sold in one day? Approximately how many books sold were hardcover nonfiction?
Answer:
27%
Step-by-step explanation:
The total books sold were 182 and the amount of books sold that were nonfiction hardcover were 49 as represented in the frequency table.
To find the percentage we must divide the nonfiction hardcover by the total books.
49/182≈0.269 or 0.27
Multiply the decimal by a 100 to change it into a percentage, so our answer is 27%.
Answer:a 27%
Step-by-step explanation:
An athletic coach conducted an experiment to test whether a four-week stretching and flexibility program reduces the number of muscular injuries that occur during athletic events. The coach randomly selected 30 athletes from several sports and randomly assigned 15 athletes to the four-week program. The remaining 15 athletes did not participate in any type of flexibility program during the four weeks.
Which statements about this study are true?
This study uses random sampling.
This study uses a control group.
This study uses a repeated measures design.
This study uses blocking.
This study uses blinding.
The TRUE statements about the study described above are :
• USE OF RANDOM SAMPLING
• USE OF A CONTROL GROUP
When selection from a population is performed such that all subjects in the population have equal chance of being selected, then we have a random process, the 30 selected athletes we're chosen without bias.
Also, when a certain group used in a research aren't subjected to the treatment process if the research, but are only used to compare the behavior of the TREATMENT group, then such group are called the CONTROL group. Hence, the 15 athletes who did not participate in any of the flexibility program are the control group.
The research doesn't exhibit any blinding or blocking procedure as it does not hide any information or contain an undesired variable.
Therefore, the TRUE statements are the study makes use of RANDOM SAMPLING AND A CONTROL GROUP.
Learn more : https://brainly.com/question/14735769
Answer:
This study uses random sampling.
Step-by-step explanation:
i got it wrong
How would i be able to prove that LMNQ is a square
Answer:
B
Step-by-step explanation:
Why correlation does not prove causation ?
Answer:
here you go
Step-by-step explanation:
"Correlation is not causation" means that just because two things correlate does not necessarily mean that one causes the other. ... Correlations between two things can be caused by a third factor that affects both of them. This sneaky, hidden third wheel is called a confounder
Why does correlation not equal causation example?
It does not tell us why and how behind the relationship but it just says the relationship exists. Example: Correlation between Ice cream sales and sunglasses sold. As the sales of ice creams is increasing so do the sales of sunglasses. Causation takes a step further than correlation.
17. Oranges cost 25 cents for 1/2 kilogram. How much would 8 kilograms of ornages cost? Show all of your work. Make sure to include your answer, proof, and evidence. PLZ NEED ASAP
9514 1404 393
Answer:
$4.00
Step-by-step explanation:
We assume the price is proportional to the quantity of oranges. If p is the desired price in dollars, we want ...
p/8 = 0.25/(1/2)
p = 8(0.50) = 4.00 . . . . multiply by 8, simplify
8 kg of oranges would cost $4.00.
Which number line is the correct solution to y z l?
-5
43 -2 -1 0
1
2
3
4
5
B
-5
4 -3 -2
-
0
2
3
5
4
-5
-3
-2 -1
o
2
3
D
-5 4 3 2 1
2
9514 1404 393
Answer:
A C D AStep-by-step explanation:
These state exam questions are checking that you know certain things about linear equations and inequalities, and how to solve and graph them. It is also checking that you now the meanings of certain math terms and can translate those meanings to relationships between numbers.
__
1. The "slope-intercept form" of a linear equation is ...
y = mx + b . . . . . . where m is the slope and b is the y-intercept
Note that the left side is "y =", eliminating the last two answer choices.
The problem tells you the slope is m = 2, and the y-intercept is b = 5. Then the equation is ...
y = 2x + 5 . . . . matches A
__
2. The picture is fuzzy, but we think it says y ≥ 1. The little bar in the comparison symbol means "or equal to", so you're looking for a graph that shows numbers greater than or equal to 1. The "or equal to" means the end dot on the graph will not be an open circle, but will be a solid dot. The "greater than" means the shaded part of the line is to the right of that dot.
graph C is the appropriate representation
__
3. The picture is fuzzy, but we think it says 126 < -7x. For this sort of inequality, you are expected to know that multiplying or dividing by a negative number will reverse the inequality symbol.
126 < -7x . . . . given
126/-7 > x . . . . divide both sides by the coefficient of x, -7
-18 > x . . . . . matches D
__
4. This is a vocabulary question. Angles are "complementary" when their sum is 90°. The sums of the given angle pairs are ...
A: 90° . . . . the correct answer choice
B: 100°
C: 180°
D: 185°
Completed Attempt 1
2
x
4
6
9
10
This net will be folded to form a prism.
C.
A
B.
С
D
E
F
Which pairs of faces will be opposite one another when the prism is created? Check all that apply.
D and F
A and C
A and B
Answer:
A & C
B & E
D & F
Step-by-step explanation:
Leave a like if this helped
Determine which of the two acute angles has a sine of 5/11 (click photo)
Answer:
A
Step-by-step explanation:
sin: [tex]\frac{opposite}{hypotenuse}[/tex]
sin: [tex]\frac{CB}{AC}[/tex] = [tex]\frac{5}{11}[/tex]
For triangle ABC, sin(A) = 5/11
What is acute angle?"If the angle measure less than 90° then it is an acute angle."
What is sine theta?For a right triangle,
sin(theta) = opposite side/hypotenuse
where theta is an acute angle.
For given example,
we have been given a right triangle ΔABC
Since ∠B = 90°, ∠A and ∠C must be an acute angles.
⇒ sin(A) = BC/AC
⇒ sin(A) = 5/11
and sin (C) = AB/AC
⇒ sin(C) = (4√6)/11
Therefore, sin(A) = 5/11
Learn more about sine of angle here:
https://brainly.com/question/15141309
#SPJ2
Solve the proportion.
4
y
=
7
?
y =
Answer:
y=28/5
Step-by-step explanation:
Okay so for this we can use cross- multiplication. Basically, the product of the numerator of the first number and the denominator of the second is equal to the product of the denominator of the first and the numerator of the second.
What I mean is: 4*7=5*y
so,
28=5y
y=28/5
Which value is NOT equivalent to the others
PLS HELP :(
Answer:
Its 3 on top of 4
Answer:
The top right one
Step-by-step explanation:
4x4(2)
1. At a clothing store, Zoey bought 2 shirts for $7.25 each and 2
pairs of jeans for $24 each. She used a coupon for $10 off the
total price of the clothes. The discounted price of the clothes Zoey
bought can be found using this expression.
[2(7.25) + 2(24)] - 10
What is the discounted price in dollars and cents of the clothes
Zoey bought?
In order to receive full credit on this question you must show your
calculations. You may NOT use a calculator. Show EACH step.
Answer:
52.5 is the discounted price.
Step-by-step explanation:
(2 · 7.25 + 2 · 24) - 10
(14.5 + 2 · 24) - 10
(14.5 + 48) - 10
62.5 - 10
= 52.5
I had solved the expression you had provided, receving 52.5 as the discounted price in dollars. The work is above. Hope this helped!
middle school math problem
Answer:
part b is 32
Step-by-step explanation:
A credit card advertises an annual interest rate of 23%.
What is the equivalent monthly interest rate?
HELP THIS IS DUE SOON
Solve the linear equation determine whether it’s one solution or infinite or no solution
2(3+2x) = 10
Answer:
One solution, x=1
Step-by-step explanation:
isolate the variable
Answer:
one solution x=1
Step-by-step explanation:
2(3+2x)=10
6+4x=10
4x=4
x=1
<3
i really need help on this please
Answer:
(1,5)
Step-by-step explanation
Subtract one equation to get rid of 5x. You will get -2y-6y=-5-35. y=5. Plug in y and find x. The answer is x=1, y=5.
helppp i’ll give brainlest
Answer:
16square ft
Step-by-step explanation:
2x2+2x3x1/2x4=16 square ft
Area of base: 2x2
Area of one side of the triangular prism: 1/2xbasexheight=1/2 x2x3
Respond Quick PLZ help me out determines if I fail
Answer:
1. infinite many solutions
2. With solution: x+y=7 ,2x+y=6
Without solution: x+y=8 ,x+y=9
Infinite solution: x+y=3, 2x+2y=6
Step-by-step explanation:
By the way, can you follow me?
Thanks!
HEEEEEEEEEEEEEELLLLLLLLLLLLLLLLLLPPPPPPPPPPPPPPPPPP
Answer: 8 inches squared
Step-by-step explanation:
volume formula for cube: side length^3 (in this case it would be 2^3)
2^3 = 2 x 2 x 2 = 8
Your favorite cousin bought a brand new couch during the holidays and decided to finance the purchase $2,800. She signed a contract for a 2 year loan, which compounds daily at 24.9%. What is the monthly payment that she can expect to make? (Select the closest number)
Answer:
56 dollars
Step-by-step explanation:
11. In circle H, if mDHG = (11x - 36)* and mGHF = (x + 12), find mDG.
mˆDG=151∘∘
An arc’s length means the same commonsense thing length always means — you know, like the length of a piece of string
The measure of angle ∠DHG of the circle is = 151°
What is Central Angle?The central angle is an angle with two arms and a vertex in the middle of a circle. The two arms of the circle's two radii intersect the circle's arc at two separate locations. It is an angle whose vertex is the center of a circle with the two radii lines as its arms, that intersect at two different points on the circle.
The central angle of a circle formula is as follows.
Central Angle = ( s x 360° ) / 2πr
where s is the length of the arc
r is the radius of the circle
Central Angle = 2 x Angle in other segment
Given data ,
Let the measure of angle ∠DG of the circle be A
Now , the value of A is
Let the measure of m∠DHG = ( 11x - 36 )°
The measure of m∠GHF = ( x + 12 )°
And , the angles m∠DHG = m∠EHF ( vertically opposite angles )
And , the angles m∠GHF = ∠DHE ( vertically opposite angles )
So , 2 ( ( 11x - 36 )° + ( x + 12 )° ) = 360° ( total angle of a circle = 360° )
On simplifying , we get
2 ( 12x - 24 ) = 360
Divide by 2 on both sides , we get
12x - 24 = 180
Adding 24 on both sides , we get
12x = 204
Divide by 12 on both sides , we get
x = 17
Now , the measure of m∠DHG = ( 11x - 36 ) = 151°
Hence , the measure of m∠DHG of circle is 151°
To learn more about central angle click :
https://brainly.com/question/11877137
#SPJ7
Evaluate 5/8 × 5/9 Give your answer in its simplest form.
Answer:
[tex] \frac{5}{8} \times \frac{5}{9} \\ = \frac{5 \times 5}{8 \times 9} \\ = \frac{25}{72} \\ = 0.3472[/tex]
Answer:
25 / 72
Step-by-step explanation:
5/8 x 5/9 =
5 x 5 / 8 x 9 =
25/72
Which choice is equivalent to the fraction below?
6/17
A. 17 divided 6
B. 6 - 17
C. 6•17
D. 6 divided 17
Answer:
6 divided 17 is equivalent to 6/17
