find the standard deviation of binomial random variable. A die is rolled 18 times and the number of fours that comes up is tallied
Answers
Complete Question
The complete question is shown on the first uploaded image
Answer:
The standard deviation is [tex]\sigma =1.5811[/tex]
Step-by-step explanation:
The sample size is n = 18
Generally the probability of getting a four in the toss of the fair die is mathematically represented as
[tex]p = \frac{1}{6 }[/tex]
While the probability of not getting a four is
[tex]q = 1 - p[/tex]
[tex]q = 1 - \frac{1}{6}[/tex]
[tex]q = \frac{5}{6}[/tex]
Now the standard deviation for the binomial random number is mathematically represented as
[tex]\sigma = \sqrt{n * pq }[/tex]
substituting values
[tex]\sigma = \sqrt{18 * \frac{1}{6}* \frac{5}{6} }[/tex]
[tex]\sigma =1.5811[/tex]
Related Questions
Calculate
(14x5x4) / (28 x 2)
Answers
Answer:
5
Step-by-step explanation:
(14 × 5 × 4) ÷ (28 × 2)
Solve brackets.
280 ÷ 56
Divide.
= 5
PLEASE HELP!!! You want to distribute 7 candies to 4 kids. If every kid must receive at least one candy, in how many ways can you do this?
Answers
Answer:
1140 ways.
Step-by-step explanation:
The applicable formula is: (n +r - 1)C(r-1), where n is the number of identical items (the candies), and r is the possible number of recipients (the kids).
The 17 identical candies, can be distributed among the 4 children in :
=(17 + 4 - 1)C(4–1) = 20C3 ways.
= 20!/((20–3)!*3!) ways.
= 20*19*18*17!/(17!*(3*2*1)) = 20*19*18/6 ways
= 20*19*3 ways.
=1140 ways.
Solve the equation by completing the square. Round to the nearest hundredth if necessary. x2 – x = 25
Answers
Answer:5.52 or -4. 52
Step-by-step explanation:
Q‒1. [5×4 marks] a) How many three-digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, and 6? (150) b) How many three-digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 if each digit can be used only once? c) How many odd numbers can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 if each digit can be used only once? d) How many three-digit numbers greater than 330 can be formed from the digits 0, 1, 2, 3, 4, 5, and 6? e) How many three-digit numbers greater than 330 can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 if each digit can be used only once?
Answers
Answer:
a) 294
b) 180
c) 75
d) 174
e) 105
Step-by-step explanation:
I assume that for each problem, the first digit can't be 0.
a) There are 6 digits that can be first, 7 digits that can be second, and 7 digits that can be third.
6×7×7 = 294
b) This time, no digit can be used twice, so there are 6 digits that can be first, 6 digits that can be second, and 5 digits that can be third.
6×6×5 = 180
c) Again, each digit can only be used once, but this time, the last digit must be odd.
If only the last digit is odd, there are 3×3×3 = 27 possible numbers.
If the first and last digits are odd, there are 3×4×2 = 24 possible numbers.
If the second and last digits are odd, there are 3×3×2 = 18 possible numbers.
If all three digits are odd, there are 3×2×1 = 6 possible numbers.
The total is 27 + 24 + 18 + 6 = 75.
d) If the first digit is 3, and the second digit is 3, there are 1×1×6 = 6 possible numbers.
If the first digit is 3, and the second digit is greater than 3, there are 1×3×7 = 21 possible numbers.
If the first digit is greater than 3, there are 3×7×7 = 147 numbers.
The total is 6 + 21 + 147 = 174.
e) If the first digit is 3, and the second digit is greater than 3, then there are 1×3×5 = 15 possible numbers.
If the second digit is greater than 3, there are 3×6×5 = 90 possible numbers.
The total is 15 + 90 = 105.
Please answer this correctly
Answers
Answer:
1/9
Step-by-step explanation:
first, u need 9 ---> 1/3
then u need 8 ---> 1/3 also
Multiply them and get...1/9
Hope this helped
5(2x - 3) = 5
What does x equal?
Answers
Answer:
x=2
Step-by-step explanation:
5(2x - 3) = 5
Divide by 5
5/5(2x - 3) = 5/5
2x-3 = 1
Add 3 to each side
2x-3 +3 = 1+3
2x = 4
Divide by 2
2x/2 = 4/2
x =2
Answer:
x = 2
Step-by-step explain:
5(2x-3) = 5
Divide both sides by 5
2x-3 = 1
Add 3 to both sides
2x = 4
Divide both sides by 2
x = 2
How many different simple random samples of size 5 cab be obtained from a population whose size is 46
Answers
Answer:
1370754
Step-by-step explanation:
From what I can see, you are probably studying combinations and permutations at the moment. Since this is a question about how many groups of five can be produced from a sample size of 46, the groups are random and not in order, which may rule for us to use the combination formula.
Once you compute this, this answer is basically saying that 1370754 groups of 5 can be created from a sample size of 46
In this activity, you will use equations to represent this proportional relationship: Olivia is making bead bracelets for her friends. She can make 3 bracelets in 15 minutes.
Part A
Find the constant of proportionality in terms of minutes per bracelet.
Part B
What does the proportionality constant represent in this situation?
Part C
Write an equation to represent the proportional relationship. Use the constant of proportionality you found in part A. Be sure to assign a variable for each quantity.
Part D
Now find the constant of proportionality in terms of number of bracelets per minute.
Part E
What does the proportionality constant represent in this situation?
Part F
Write an equation to represent the proportional relationship. Use the constant of proportionality you found in part D. Be sure to assign a variable for each quantity.
Part G
How are the constants of proportionality you found in parts A and D related?
Part H
Are the two equations you developed in parts C and F equivalent? Explain.
Answers
Answer:
Step-by-step explanation:
A) The constant of proportionality in terms of minutes per bracelet is
15/3 = 5 minutes per bracelet
B) The constant of proportionality represents man hour rate
C) let k = constant of proportionality, t = time in minutes and b = number of bracelets produced. Therefore,
t = kb
D) the constant of proportionality in terms of number of bracelets per minute is
3/15 = 1/5
E) The constant of proportionality represents production rate
F) let k = constant of proportionality, t = time in minutes and b = number of bracelets produced. Therefore,
b = kt
G) The constants of proportionality are reciprocals
H) Two equations are equivalent if they have the same solution. They are not equivalent. By inputting the different values of k, the solutions will always be the same. Therefore, they are equivalent.
Answer:the sample answers, change them up so you dont get in trouble
A To find the constant of proportionality in minutes per bracelet, divide the total time by the number of bracelets:
constant of proportionality=15 MINUTES/3 BRACELETS=5 minutes per bracelet.
B The proportionality constant of 5 minutes per bracelet means it takes Olivia 5 minutes to make 1 bracelet.
C Here’s one way to set up the equation:
time = constant of proportionality × number of bracelets
Let m be time in minutes and let b be the number of bracelets. Substitute the variables (m and b) and the value of the proportionality constant (5 minutes per bracelet) into the equation: m = 5b.
thats all ik srry
Step-by-step explanation:
what does r equal? 1/13r=-8/15
Answers
Answer:
[tex]\boxed{\sf \ \ \ -\dfrac{15}{104} \ \ \ }[/tex]
Step-by-step explanation:
hello,
first of all let's assume that r is different from 0 as this is not allowed to divide by 0
[tex]\dfrac{1}{13r}=\dfrac{-8}{15}[/tex]
multiply by 13r it comes
[tex]\dfrac{13r}{13r}=1=\dfrac{-8*13r}{15}[/tex]
now multiply by 15
[tex]-8*13r=15\\<=> r = \dfrac{-15}{8*13}=-\dfrac{15}{104}[/tex]
hope this helps
Answer:[tex]r=-\frac{104}{15}[/tex] or -6.93333....
Step-by-step explanation:
[tex]\mathrm{Multiply\:both\:sides\:by\:}13[/tex]
[tex]13\cdot \frac{1}{13}r=13\left(-\frac{8}{15}\right)[/tex] =-104/15
simplify
[tex]r=-\frac{104}{15}[/tex]
MARK BRAINLIEST PLEASE
Julie has three boxes of pens. The diagram shows expressions for the number of pens in each box. Look at these equations.
Equals B +12
B equals C +4
Write an equation to show the relationship between a + c
Answers
Answer:
a=c+16here,
a=b+12
b=a-12----> equation (i)
b= c+4
putting the value of b from the equation (I)
a-12=c+4
a=c+4+12
a=c+16
hope this helps...
Good luck on your assignment...
The value of a + c is 16.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
a=b+12
So, b=a-12 ---- equation (i)
and, b= c+4
Substitute the value of b from the equation (I)
a-12=c+4
a=c+4+12
a=c+16
Hence, the value of a+ c is 16.
Learn more about Algebra here:
https://brainly.com/question/24875240
#SPJ2
The slope of a line is 1, and the y-intercept is -1. What is the equation of the line written in slope-intercept form?
Answers
Answer:
y=x-1
Step-by-step explanation:
since the slope is just one up and one over and it's positive it would just be x
and since the intercept is just -1 it would be y=x-1
How fast was the battery charged? _______ percent per minute. How long did it take the battery to be fully charged? ________ minutes.
Answers
Answer:
Q1 is: 2.2 percent per minute
Q2 is: 35 minutes
Step-by-step explanation:
For the first question, take 89 percent, and subtract 23 from it, then divide by 30 minutes for the rate per minute.
For the second question take 23 percent, find out how much is left until 100 percent (77 percent) and use the rate from the last question (2.2 percent per minute), to find out how much time charging 77 percent takes. (You get 35 by using: 77 divided by 2.2)
Diane's bank is offering 5% interest, compounded monthly. If Diane invests $10,500 and wants $20,000 when she withdrawals, how long should she keep her money in for? Round to the nearest tenth of a year.
Answers
Answer:
The time period is 13 years.
Step-by-step explanation:
Interest rate (r )= 5% or 5%/12 = 0.42% per months
The investment amount (Present value) = $10500
Final expected amount (future value) = $20000
Since we have given the initial amount and final amount. Therefore we have to calculate the time period for which the initial amount is kept in the bank.
Use the below formula to find the time period.
Future value = present value (1 + r )^n
20000 = 10500(1+0.0042)^n
1.9047619 = (1+0.0042)^n
1.9047619 = 1.0042^n
n = 153.74 months.
Time in years = 153.74 / 12 = 12.8 years or 13 years (round off)
To pass a certain marksmanship test, an individual is required to shoot at a target until he hits it six times. He is judged on the number of trials that are necessary to achieve this. If the probability of his hitting a target on any trial is 0.25, what is the probability that he requires 18 shots?
Answers
Answer:
The probability that he requires 18 shots is 0.04785
Step-by-step explanation:
To answer this, we shall be using the negative binomial distribution
From the question;
P = 0.25 , r = 6
q will be 1-p = 1-0.25 = 0.75 Which is the probability of missing a target on any trial
P(X = 18) = (18-1)C(6-1) (0.25)^6 (0.75)^(18-6)
P(X = 28) = 17C5 (0.25)^6 (0.75)^12) = 0.04785
I NEED HELP PLEASE, THANKS! :)
Answers
Answer:
Option B
Step-by-step explanation:
Again, another great question! Here we are given the following system of equations, bound by quadrant 1 -
[tex]\begin{bmatrix}2x+7y\le \:70\\ 8x+4y\le \:136\end{bmatrix}[/tex]
Convert this to slope - intercept form -
[tex]\begin{bmatrix}y\le \frac{70-2x}{7}\\ y\le \:2\left(-x+17\right)\end{bmatrix}[/tex]
Now the graphed solution of this intersects at a shaded region with which there are 3 important point that lie on the border. They are the following -
( 0, 10 ),
( 15, 9 ),
( 17, 0 )
When these point are plugged into the main function f ( x, y ) = 2x + 6y, the point ( 15, 9 ) results in the greatest solution of 84. Thus, it is our maximum point -
Option B
The y-intercept of a parabola is 1, and its vertex is at (1,0). What function does the graph represent?
OA. Rx) = (x - 1)2
OB. Rx) = (x + 1)2
OC. Rx) = -1(x - 1)
OD. Rx) = -1(x + 1)2
Reset
Next
Answers
Answer:
A
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (1, 0) , thus
y = a(x - 1)² + 0
To find a substitute the coordinates of the y- intercept (0, 1) into the equation
1 = a(- 1)² = a , thus
a = 1
y = (x - 1)² → A
Considering it's y-intercept and vertex, the equation of the parabola is given by:
[tex]y = (x - 1)^2[/tex]
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
[tex]y = a(x - h)^2 + k[/tex]
In which a is the leading coefficient.
In this problem, the vertex is (1,0), hence h = 1, k = 0 and:
[tex]y = a(x - 1)^2[/tex]
The y-intercept is of 1, hence, when x = 0, y = 1, so:
[tex]y = a(x - 1)^2[/tex]
[tex]1 = a(0 - 1)^2[/tex]
[tex]a = 1[/tex]
Hence, the equation is:
[tex]y = (x - 1)^2[/tex]
More can be learned about the equation of a parabola at https://brainly.com/question/24737967
what 4.2 times 0.7 /a is 294 /b is 2.94 /c 29.4
Answers
Answer:
29.4
Step-by-step explanation:
Answer:
2.94
Step-by-step explanation:
4.2 × 0.7 = 2.94
Copy the diagram and oaloulate the sizes of
a bº and cº. What is the sum of the angles of
the triangle?
Answers
Answer:
sum of the angles of the triangle are 180°
Step-by-step explanation:
To find the sum of the interior angles, we use the formula( s-2*180), where s is the number of sides of the shape. If it is a pentagon, 5-2*180= 3*180= 540,
which shows that the sum of the interior angles of a pentagon is 540.
since, it is a triangle in the figure with 3 sides, 3-2*180=1*180=180.
The interior angles are unknown= a, b and c. we know that a+b+c=180 degrees and the exterior angles are mentioned. And we know that, opposite angles are equal. So, a is 40 degrees considering that 40 degrees is the opposite angle of a, b is 95 degrees whereas c is 45 degrees.
now, lets check if the angles indeed have a sum of 180 degrees,
40+95+45= 135+45 which gives 180 degrees.
Answer:
180°
Step-by-step explanation:
→ Angles in a triangles always add up to 180, we can prove this by calculating a, b and c so,
a = 40° (vertical angles are equal)
b = 95° (vertical angles are equal)
c = 45° (vertical angles are equal)
40 + 45 + 95 = 85 + 95 = 180°
Solve the system of linear equations.
Answers
Answer:
dependent systemx = 2 -ay = 1 +az = aStep-by-step explanation:
Let's solve this by eliminating z, then we'll go from there.
Add 6 times the second equation to the first.
(3x -3y +6z) +6(x +2y -z) = (3) +6(4)
9x +9y = 27 . . . simplify
x + y = 3 . . . . . . divide by 9 [eq4]
Add 13 times the second equation to the third.
(5x -8y +13z) +13(x +2y -z) = (2) +13(4)
18x +18y = 54
x + y = 3 . . . . . . divide by 18 [eq5]
Equations [eq4] and [eq5] are identical. This tells us the system is dependent, and has an infinite number of solutions. We can find them in terms of z:
y = 3 -x . . . . solve eq5 for y
x +2(3 -x) -z = 4 . . . . substitute into the second equation
-x +6 -z = 4
x = 2 - z . . . . . . add x-4
y = 3 -(2 -z)
y = z +1
So far, we have written the solutions in terms of z. If we use the parameter "a", we can write the solutions as ...
x = 2 -a
y = 1 +a
z = a
_____
Check
First equation:
3(2-a) -3(a+1) +6a = 3
6 -3a -3a -3 +6a = 3 . . . true
Second equation:
(2-a) +2(a+1) -a = 4
2 -a +2a +2 -a = 4 . . . true
Third equation:
5(2-a) -8(a+1) +13a = 2
10 -5a -8a -8 +13a = 2 . . . true
Our solution checks algebraically.
Two random samples are taken from private and public universities
(out-of-state tuition) around the nation. The yearly tuition is recorded from each sample and the results can be found below. Test to see if the mean out-of-state tuition for private institutions is statistically significantly higher than public institutions. Assume unequal variances. Use a 1% level of significance.
Private Institutions (Group 1 )
43,120
28,190
34,490
20,893
42,984
34,750
44,897
32,198
18,432
33,981
29,498
31,980
22,764
54,190
37,756
30,129
33,980
47,909
32,200
38,120
Public Institutions (Group 2)
25,469
19,450
18,347
28,560
32,592
21,871
24,120
27,450
29,100
21,870
22,650
29,143
25,379
23,450
23,871
28,745
30,120
21,190
21,540
26,346
Hypotheses:
H0: μ1 (?) μ2
H1: μ1 (?) μ2
What are the correct hypotheses for this problem?
-A. H0: μ1 = μ2 ; H1: μ1 ≠ μ2
-B. H0: μ1 = μ2 ; H1: μ1 > μ2
-C. H0: μ1 ≤ μ2 ; H1: μ1 ≥ μ2
-D. H0: μ1 < μ2 ; H1: μ1 = μ2
-E. H0: μ1 ≠ μ2 ; H1: μ1 = μ2
-F. H0: μ1 ≥ μ2 ; H1: μ1 ≤ μ2
Answers
Answer:
Step-by-step explanation:
For private Institutions,
n = 20
Mean, x1 = (43120 + 28190 + 34490 + 20893 + 42984 + 34750 + 44897 + 32198 + 18432 + 33981 + 29498 + 31980 + 22764 + 54190 + 37756 + 30129 + 33980 + 47909 + 32200 + 38120)/20 = 34623.05
Standard deviation = √(summation(x - mean)²/n
Summation(x - mean)² = (43120 - 34623.05)^2+ (28190 - 34623.05)^2 + (34490 - 34623.05)^2 + (20893 - 34623.05)^2 + (42984 - 34623.05)^2 + (34750 - 34623.05)^2 + (44897 - 34623.05)^2 + (32198 - 34623.05)^2 + (18432 - 34623.05)^2 + (33981 - 34623.05)^2 + (29498 - 34623.05)^2 + (31980 - 34623.05)^2 + (22764 - 34623.05)^2 + (54190 - 34623.05)^2 + (37756 - 34623.05)^2 + (30129 - 34623.05)^2 + (33980 - 34623.05)^2 + (47909 - 34623.05)^2 + (32200 - 34623.05)^2 + (38120 - 34623.05)^2 = 1527829234.95
Standard deviation = √(1527829234.95/20
s1 = 8740.22
For public Institutions,
n = 20
Mean, x2 = (25469 + 19450 + 18347 + 28560 + 32592 + 21871 + 24120 + 27450 + 29100 + 21870 + 22650 + 29143 + 25379 + 23450 + 23871 + 28745 + 30120 + 21190 + 21540 + 26346)/20 = 25063.15
Summation(x - mean)² = (25469 - 25063.15)^2+ (19450 - 25063.15)^2 + (18347 - 25063.15)^2 + (28560 - 25063.15)^2 + (32592 - 25063.15)^2 + (21871 - 25063.15)^2 + (24120 - 25063.15)^2 + (27450 - 25063.15)^2 + (29100 - 25063.15)^2 + (21870 - 25063.15)^2 + (22650 - 25063.15)^2 + (29143 - 25063.15)^2 + (25379 - 25063.15)^2 + (23450 - 25063.15)^2 + (23871 - 25063.15)^2 + (28745 - 25063.15)^2 + (30120 - 25063.15)^2 + (21190 - 25063.15)^2 + (21540 - 25063.15)^2 + (26346 - 25063.15)^2 = 1527829234.95
Standard deviation = √(283738188.55/20
s2 = 3766.55
This is a test of 2 independent groups. Let μ1 be the mean out-of-state tuition for private institutions and μ2 be the mean out-of-state tuition for public institutions.
The random variable is μ1 - μ2 = difference in the mean out-of-state tuition for private institutions and the mean out-of-state tuition for public institutions.
We would set up the hypothesis. The correct option is
-B. H0: μ1 = μ2 ; H1: μ1 > μ2
Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is
(x1 - x2)/√(s1²/n1 + s2²/n2)
t = (34623.05 - 25063.15)/√(8740.22²/20 + 3766.55²/20)
t = 9559.9/2128.12528473889
t = 4.49
The formula for determining the degree of freedom is
df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²
df = [8740.22²/20 + 3766.55²/20]²/[(1/20 - 1)(8740.22²/20)² + (1/20 - 1)(3766.55²/20)²] = 20511091253953.727/794331719568.7114
df = 26
We would determine the probability value from the t test calculator. It becomes
p value = 0.000065
Since alpha, 0.01 > than the p value, 0.000065, then we would reject the null hypothesis. Therefore, at 1% significance level, the mean out-of-state tuition for private institutions is statistically significantly higher than public institutions.
PLEASE HELP! Max has as many sisters as brothers. However, his sister Emily has half as many sisters as brothers. How many girls and boys are in their family?
Answers
Answer:
Four brothers and three sisters.
Step-by-step explanation:
Two identical decks of 52 cards are mixed together, yielding a stack of 104 cards. How many different ways are there to order this stack of 104 cards?
Answers
Answer:
here the order will be 104! =[tex]1.029e^{166}[/tex]
Step-by-step explanation:
since the cards are to arranged in no particular order that is why we used combination to find the result.
Combination can simply be explained as the method of selecting items from a collection of items where the order of the selections does not matter.
A random sample of 13 items is drawn from a population whose standard deviation is unknown. The sample mean is x¯ = 950 and the sample standard deviation is s = 10. Use Appendix D to find the values of Student’s t.
1. Construct an interval estimate of mu with 99% confidence. (Round your answers to 3 decimal places.)
The 99% confidence interval is from_____ to ______ .
2. Construct an interval estimate of mu with 99% confidence, assuming that s = 20. (Round your answers to 3 decimal places.)
The 99% confidence interval is from_____ to ______ .
3. Construct an interval estimate of mu with 99% confidence, assuming that s = 40. (Round your answers to 3 decimal places.)
The 99% confidence interval is from_____ to ______ .
Answers
Answer:
1. The 99% confidence interval is from 941.527 to 958.473
2. The 99% confidence interval is from 933.054 to 966.946
3. The 99% confidence interval is from 916.108 to 983.892
Step-by-step explanation:
The confidence interval is given by
[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\[/tex]
Where [tex]\bar{x}[/tex] is the sample mean and Margin of error is given by
[tex]$ MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) $ \\\\[/tex]
Where n is the sample size,
s is the sample standard deviation,
[tex]t_{\alpha/2[/tex] is the t-score corresponding to some confidence level
The t-score corresponding to 99% confidence level is
Significance level = α = 1 - 0.99 = 0.01/2 = 0.005
Degree of freedom = n - 1 = 13 - 1 = 12
From the t-table at α = 0.005 and DoF = 12
t-score = 3.055
1. 99% Confidence Interval when s = 10
The margin of error is
[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 3.055\cdot \frac{10}{\sqrt{13} } \\\\MoE = 3.055\cdot 2.7735\\\\MoE = 8.473\\\\[/tex]
So the required 99% confidence interval is
[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 950 \pm 8.473\\\\\text {confidence interval} = 950 - 8.473, \: 950 + 8.473\\\\\text {confidence interval} = (941.527, \: 958.473)\\\\[/tex]
The 99% confidence interval is from 941.527 to 958.473
2. 99% Confidence Interval when s = 20
The margin of error is
[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 3.055\cdot \frac{20}{\sqrt{13} } \\\\MoE = 3.055\cdot 5.547\\\\MoE = 16.946\\\\[/tex]
So the required 99% confidence interval is
[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 950 \pm 16.946\\\\\text {confidence interval} = 950 - 16.946, \: 950 + 16.946\\\\\text {confidence interval} = (933.054, \: 966.946)\\\\[/tex]
The 99% confidence interval is from 933.054 to 966.946
3. 99% Confidence Interval when s = 40
The margin of error is
[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 3.055\cdot \frac{40}{\sqrt{13} } \\\\MoE = 3.055\cdot 11.094\\\\MoE = 33.892\\\\[/tex]
So the required 99% confidence interval is
[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 950 \pm 33.892\\\\\text {confidence interval} = 950 - 33.892, \: 950 + 33.892\\\\\text {confidence interval} = (916.108, \: 983.892)\\\\[/tex]
The 99% confidence interval is from 916.108 to 983.892
As the sample standard deviation increases, the range of confidence interval also increases.
The hourly rate of substitute teachers for 12 local school districts is given below. Assuming that the data are normally distributed, use a TI-83, or TI-84 calculator to find the 90% confidence interval for the mean hourly rate of substitute teachers in the region.20 13 21 18 19 2219 15 12 12 18 21
Answers
Answer:
[tex]17.5-1.796\frac{3.61}{\sqrt{12}}=15.63[/tex]
[tex]17.5+1.796\frac{3.61}{\sqrt{12}}=19.37[/tex]
Step-by-step explanation:
Data given
20 13 21 18 19 22 19 15 12 12 18 21
We can calculate the sample mean and deviation with the following formulas:
[tex]\bar X =\frac{\sum_{i=1}^n X_i}{n}[/tex]
[tex]s= \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]
And we got:
[tex]\bar X = 17.5[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
s=3.61 represent the sample standard deviation
n=12 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom are given by:
[tex]df=n-1=12-1=11[/tex]
Since the Confidence is 0.90 or 90%, the significance is [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], the critical value would be given by [tex]t_{\alpha/2}=[/tex]
Now we have everything in order to replace into formula (1):
[tex]17.5-1.796\frac{3.61}{\sqrt{12}}=15.63[/tex]
[tex]17.5+1.796\frac{3.61}{\sqrt{12}}=19.37[/tex]
What is the measure of angle S?
480
56°
930
101°
Answers
Answer:
m∠s = 93°
Step-by-step explanation:
We know that any quadrilateral's sum of angles adds up to 360°. In that case,
360 - (56 + 132 + 79) = m∠s
m∠s = 93°
Answer:
S° = 93 °
Step-by-step explanation:
[tex]The- diagram- is- a- trapezoid (quadrilateral)\\Sum- of- angles-in a- quadrilateral = 360\\ 132\° + 56\° + 79\° + x\° = 360\° \\267\° + x\° = 360\° \\x = 360 \° - 267 \° \\x\° = 93\°[/tex]
simply expression 1+5v+v
Answers
Answer:
1 + 6v
Step-by-step explanation:
1+5v+v
Combine like terms
1 + 6v
Answer:
6v + 1
Step-by-step explanation:
1 + 5v + v
Apply rule : a = 1a
1 + 5v + 1v
Combine like terms.
5v + 1v + 1
(5 + 1)v + 1
(6)v + 1
6v + 1
You are graphing Square ABCDABCDA, B, C, D in the coordinate plane. The following are three of the vertices of the square: A(4, -7), B(8, -7),A(4,−7),B(8,−7),A, left parenthesis, 4, comma, minus, 7, right parenthesis, comma, B, left parenthesis, 8, comma, minus, 7, right parenthesis, comma and C(8, -3)C(8,−3)C, left parenthesis, 8, comma, minus, 3, right parenthesis. What are the coordinates of point DDD? \large((left parenthesis , \large))right parenthesis
Answers
Answer:
D(4,-3)
Step-by-step explanation:
Given three of the vertices of the square: A(4, -7), B(8, -7),C(8, -3)
Let the coordinate of the fourth vertex be D(x,y).
We know that diagonals of a square are perpendicular bisector. So, the midpoint of both diagonals is the same.
The diagonals are BD and AC
Midpoint of BD = Midpoint of AC
[tex]\left(\dfrac{8+x}{2},\dfrac{-7+y}{2}\right) =\left(\dfrac{4+8}{2},\dfrac{-7+(-3)}{2}\right)\\ \left(\dfrac{8+x}{2},\dfrac{y-7}{2}\right) =\left(\dfrac{12}{2},\dfrac{-10}{2}\right)\\ \left(\dfrac{8+x}{2},\dfrac{y-7}{2}\right) =\left(6,-5\right)\\$Therefore$:\\\dfrac{8+x}{2}=6\\8+x=12\\x=12-8\\x=4\\$Similarly$\\\dfrac{y-7}{2}=-5\\y-7=-5*2\\y-7=-10\\y=-10+7=-3[/tex]
The coordinates of the fourth vertex is D(4,-3)
Answer:
(4,-3)
Step-by-step explanation:
Please help I don’t understand And I need an explanation
Answers
Hey there! :)
Answer:
56 m².
Step-by-step explanation:
To find the area, simply split the figure into a triangle and rectangle. Solve for the areas separately:
Solve for the rectangle: (A = l × w)
A = 8 × 5
A = 40 m²
Solve for the triangle: (A = 1/2 (bh))
A = 1/2(4 · 8)
A = 1/2(32)
A = 16 m².
Add up the two areas:
40 + 16 = 56 m².
Answer:
Area of triangle+ the area of rectangle
Step-by-step explanation:
Since, area of triangle is 1/2×base×height in right angled triangle, 1/2×4×8: 1/2×32= 16m²
Area of rectangle is length × breadth= 5×8: 40 m²
Area of the shape is 40m²+16m²= 56m²
How do you solve 36 times [tex]\sqrt{3}[/tex]
Answers
Answer:
62.3538
Step-by-step explanation:
There is nothing to solve. If you need a decimal value, you can use a calculator or table of square roots.
Tammy and Lawrence like to bike competitively. Tammy biked seven less than three times the number of miles that Lawrence biked. If c represents the number of miles Lawrence biked, write an expression for the number of miles Tammy biked.
Answers
Answer:
3c - 7
Step-by-step explanation:
c - the number of miles Lawrence biked
Tammy biked seven less than three times the number of miles that Lawrence biked.
So, 3 x c (the # of miles Lawrence biked) - 7 (she biked seven less)
The answer is 3c - 7.