Answer: –55x + 570
Step-by-step explanation:
The person above me completely missed the question so this is the right one
From a sample with nequals24, the mean number of televisions per household is 4 with a standard deviation of 1 television. Using Chebychev's Theorem, determine at least how many of the households have between 2 and 6 televisions. At least nothing of the households have between 2 and 6 televisions.
Answer:
At least 18 of the households have between 2 and 6 televisions.
Step-by-step explanation:
Chebyshev Theorem
The Chebyshev Theorem can also be applied to non-normal distribution. It states that:
At least 75% of the measures are within 2 standard deviations of the mean.
At least 89% of the measures are within 3 standard deviations of the mean.
An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100(1 - \frac{1}{k^{2}})[/tex].
In this question:
Mean = 4
Standard deviation = 1
Percentage of households that have between 2 and 6 televisions.
2 = 4 - 2*1
So 2 is two standard deviations below the mean
6 = 4 + 2*1
So 6 is two standard deviations above the mean
By Chebyshev's Theorem, at least 75% of the measures are within 2 standard deviations of the mean.
Out of 24
0.75*24 = 18
At least 18 of the households have between 2 and 6 televisions.
The purchase price of a home is $159,000.00 and the 30-year mortgage has a 20% down payment and an annual interest rate of 4.4%. What is the monthly mortgage payment? Enter your answer as a dollar value, such as 3456.78
Answer: The monthly mortgage payment is $640
Step-by-step explanation:
The cost of the house is $159,000
The down payment made is 20%. This means that the amount paid as down payment is
20/100 × 159000 = 31800
The balance to be paid would be
159000 - 31800 = $127200
We would apply the periodic interest rate formula which is expressed as
P = a/[{(1+r)^n]-1}/{r(1+r)^n}]
Where
P represents the monthly payments.
a represents the amount of the loan
r represents the annual rate.
n represents number of monthly payments. Therefore
a = $127200
r = 0.044/12 = 0.0037
n = 12 × 30 = 360
Therefore,
P = 127200/[{(1+0.0037)^360]-1}/{0.0037(1+0.0037)^360}]
P = 127200/[{(1.0037)^360]-1}/{0.0037(1.0037)^360}]
P = 127200/{3.779 -1}/[0.0037(3.779)]
P = 127200/(2.779/0.0139823)
P = 127200/198.75127840198
P = $640
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
You are given the equation [tex]f(x)=x+6[/tex] and [tex]g(x)=x^4[/tex]. When you combine G(F(x)) your equation would come out as [tex]g(f(x))=x^4(x+6)[/tex]. Once you distribute the equation you will get [tex]g(f(x))=(x+6)^4[/tex]
Therefore you answer choice would be B. [tex](x+6)^4[/tex]
Choose the equation for the graph
below.
a. y =
1
X-2
2
b.y =
x²–4
3
c. y =
x+2
-3
d.y=
e. y =
2x+4
1
x2+2x+1
Answer:
C
Step-by-step explanation:
Plugged into calculator
Vertical asymptotes: x=-2
Horizontal asymptotes: y=0
No oblique asymptotes
During the worst periods of inflation in America, the price of food increased at a rate of 12 % per month. If your food bill was $300 one month during this period, what was it two months later?
Exponential; $337.08
Linear; $672.00
Exponential; $376.32
Linear; $372.00
Answer:
Exponential; $376.32
Step-by-step explanation:
Generally, an increase of 12% in a month means the prices are 12% more than they were in the previous month. That is, the value has been multiplied by 1.12.
The same would be true for the second month, so the overall multiplier for the two months is ...
(1.12)(1.12) = 1.12^2 = 1.2544
This makes the food bill for the second month amount to ...
1.2544 × $300 = $376.32
_____
As with all percentages, you need to be clear about what base is being used. Here, we have assumed the base for a monthly increase is the value at the beginning of the month.
If, instead, it is the value at the beginning of the year, then the increase is linear, not exponential. 12% of the value at the beginning of the year is the same throughout the year.
Able, ben and cal each played a game.
able scored six times bens score.
cal scored a third of able's score. write down the ratio of able's score to ben;s score to cal's score
Answer:
Ratio of Able's score to Ben=6:1
Ratio of Ben's score to Cal's=1:2
Ratio of able's score to ben;s score to cal's score=6:1:2
Step-by-step explanation:
Let Ben's score =x
Able scored six times Ben's score
Able=6*x
=6x
Cal scored a third of Able's score
Cal=1/3 of 6x
=1/3(6x)
Ratio of Able's score to Ben
6x:x
=6:1
Ratio of Ben's score to Cal's score
x:1/3(6x)
=x:6x/3
=x:2x
=1:2
Ratio of able's score to ben;s score to cal's score=6:1:2
PLEASE ANSWER THIS , I WILL MAKE U BRAINLIEST IF RIGHT
Answer:
hope this helps you
Solve: x - 1 < 3 help me plssss
Answer:
x =2
Step-by-step explanation:
becaue 2-1 is smaller than 3
Answer:
Hello!
I believe your answer is:
x=2
If this is not correct, please let me know and I will try again!
Step-by-step explanation:
help!! Algebra 1!!
sorry if the picture is bad
Answer:
The first one matches with f(x)√x because a square root cannot be negative
The second one matches with f(x)=√(x-5) because the square root would be negative if it were less than five.
The third one matches with f(x)=8x because there is nothing that makes it a not possible answer
The last one matches with 7/(x-8) because there cannot be a denominator of zero.
A $210 suit is marked down by 10%. Find the sale price.
Answer:
sale prices = $252
Step-by-step explanation: 280 - (280 x 10%) = 280 - 28 = $252
Answer:
$189
Step-by-step explanation:
10% of 210 = 21
210 - 21 = 189
Please answer this correctly
Answer:
Look at the money bags below!!! (but I'll give you the answer)
Step-by-step explanation:
John F: 7 full bags - 1 half
Juan A: 9 full bags
Jason A: 3 full bags
Nick J: 3 full bags- 1 half
Alfonso S: 8 full bags
Hope this helped and wasn't confusing!!! xx - Asia
1/x=1/2 / 4/5
Solve for x.
X =
Answer:
1/x = 1/2÷4/5
1/x=1/2 x 5/4
1/x=5/8
5x=8
x=1.6
What is the value of the trig ratio cos x ? Help ASAP
Answer:
14/50 or 7/25
Step-by-step explanation:
cos x = adj/hyp
adj = 14
hyp = 50
---------
you ca learn more about trig
sin x = opp/hyp
tan x = opp/adj
The value of the trigonometric ratio, cos x in a right angle triangle XYZ is [tex]\dfrac{14}{50}[/tex].
Trigonometric ratios – The relation between the angles and the sides of a right-angle triangle is called Trigonometric ratios.
The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
In the given figure a right-angle triangle XYZ we know that
ZY is the length of the perpendicular. XY is the base of the triangle and ZX is the hypotenuse.
By trigonometric ratio, we know that
[tex]Cos \Theta = \dfrac{adjacent}{hypotenuse}[/tex]
Where [tex]\Theta[/tex] is the acute angle between the base and the Hypotenuse
On substituting value,
[tex]Cos \Theta = \dfrac{14}{50}[/tex]
The value of the trigonometric ratio, cos x in a right angle triangle XYZ [tex]\dfrac{14}{50}[/tex].
Learn more about Trigonometric ratios here:
https://brainly.com/question/25122825
#SPJ2
The Employment and Training Administration reported that the U.S. mean unemployment
insurance benefit was $238 per week (The World Almanac, 2003). Aresearcher in the state
of Virginia anticipated that sample data would show evidence that the mean weekly unemployment
insurance benefit in Virginia was below the national average.
a. Develop appropriate hypotheses such that rejection of H0 will support the researcher’s
contention.
b. For a sample of 100 individuals, the sample mean weekly unemployment insurance
benefit was $231 with a sample standard deviation of $80. What is the p-value?
c. At αα = .05, what is your conclusion?
d. Repeat the preceding hypothesis test using the critical value approach.
Answer:
Step-by-step explanation:
a) We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
H0: µ = 238
For the alternative hypothesis,
H1: µ < 238
This is a left tailed test
b) Since the population standard deviation is not given, the distribution is a student's t.
Since n = 100
Degrees of freedom, df = n - 1 = 100 - 1 = 99
t = (x - µ)/(s/√n)
Where
x = sample mean = 231
µ = population mean = 238
s = samples standard deviation = 80
t = (231 - 238)/(80/√100) = - 0.88
We would determine the p value using the t test calculator. It becomes
p = 0.19
c) Since alpha, 0.05 < than the p value, 0.19, then we would fail to reject the null hypothesis. Therefore, At a 5% level of significance, the sample data showed insignificant evidence that the mean weekly unemployment insurance benefit in Virginia was below the national average.
d) Since α = 0.05, the critical value is determined from the t distribution table. Recall that this is a left tailed test. Therefore, we would find the critical value corresponding to 1 - α and reject the null hypothesis if the test statistic is less than the negative of the table value.
1 - α = 1 - 0.05 = 0.95
The negative critical value is - 1.66
Since - 0.88 is greater than - 1.66, then we would fail to reject the null hypothesis.
Consider the function y=f(x)=3x. The values of f(1/2) and f(1/4), rounded to the nearest hundredth, are_______ and__________ , respectively.
Answer:
f(1/2)=1.5
f(1/4)=0.75
Please help me with this problem I am lost
Answer:
[tex]\frac{49}{15}[/tex]
Step-by-step explanation:
[tex]\frac{2}{5} \times \frac{7}{-6} \times -7[/tex]
[tex]\frac{2}{5} \times \frac{7}{-6} \times \frac{-7}{1}[/tex]
[tex]\frac{2 \times 7 \times -7}{5 \times -6 \times 1}[/tex]
[tex]\frac{-98}{-30}=\frac{98}{30}=\frac{49}{15}[/tex]
Answer:
-3.26 repeating
Step-by-step explanation:
2×7=14
5×(-6) = -30
14/30×(-7)= -3.26 repeating
Assume a simple random sample of 10 BMIs with a standard deviation of 1.186 is selected from a normally distributed population of recent Miss America winners. Use 0.01 significance level to test the claim that the BMI for recent Miss America winners are from a population with standard deviation of 1.34.
A. Identify the null hypothesis and the alternative hypothesis.
B. Find the critical value or values.
C. Find the test statistic.
D. State the conclusion that addresses the original claim.
Answer:
a) H0: [tex]\sigma = 1.34[/tex]
H1: [tex]\sigma \neq 1.34[/tex]
b) [tex] df = n-1= 10-1=9[/tex]
And the critical values with [tex]\alpha/2=0.005[/tex] on each tail are:
[tex] \chi_{\alpha/2}= 1.735, \chi_{1-\alpha/2}= 23.589[/tex]
c) [tex] t=(10-1) [\frac{1.186}{1.34}]^2 =7.05[/tex]
d) For this case since the critical value is not higher or lower than the critical values we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true deviation is not significantly different from 1.34
Step-by-step explanation:
Information provided
n = 10 sample size
s= 1.186 the sample deviation
[tex]\sigma_o =1.34[/tex] the value that we want to test
[tex]p_v [/tex] represent the p value for the test
t represent the statistic (chi square test)
[tex]\alpha=0.01[/tex] significance level
Part a
On this case we want to test if the true deviation is 1,34 or no, so the system of hypothesis are:
H0: [tex]\sigma = 1.34[/tex]
H1: [tex]\sigma \neq 1.34[/tex]
The statistic is given by:
[tex] t=(n-1) [\frac{s}{\sigma_o}]^2 [/tex]
Part b
The degrees of freedom are given by:
[tex] df = n-1= 10-1=9[/tex]
And the critical values with [tex]\alpha/2=0.005[/tex] on each tail are:
[tex] \chi_{\alpha/2}= 1.735, \chi_{1-\alpha/2}= 23.589[/tex]
Part c
Replacing the info we got:
[tex] t=(10-1) [\frac{1.186}{1.34}]^2 =7.05[/tex]
Part d
For this case since the critical value is not higher or lower than the critical values we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true deviation is not significantly different from 1.34
3. Write 52/6
as a mixed number.
Give your answer in its simplest form.
Answer:
26/3 as an improper fraction in simplest form. :)
Step-by-step explanation:
What’s the correct answer for this question?
Answer:
C.
Step-by-step explanation:
First finding height using Pythagoras theorem
(H)²=(B)²+(P)²
8.2²=5.4²+P²
P² = 67.24 - 29.16
P² = 38.08
P = 6.2
Now
Volume of cone = (1/3)πr²h
= (1/3)(3.14)(5.4)²(6.2)
= (1/3)(567.9)
= 189.2 cm³
At Ajax Spring Water, a half-liter bottle of soft drink is supposed to contain a mean of 519 ml. The filling process follows a normal distribution with a known process standard deviation of 6 ml.
1) The normal distribution should be used for the sample mean because:_____.
a) the sample population has a large mean.
b) the population distribution is known to be normal.
c) the population standard deviation is known.
d) the standard deviation is very small.
2) Set up hypotheses and a two-tailed decision rule for the correct mean using the 5 percent level of significance. The hypothesis for a two-tailed decision is:_______.
A. H0: mu not equal to 519, H1: mu = 519, reject if z < -1.96 or z > 1.96.
B. H0: mu not equal to 519, H1: mu = 519, reject if z > 1.96 or z < -1.96.
C. H0: mu = 519, mu not equal to 519, reject if z> 1.96 or z< -1.96.
D. H0: mu = 519, H_1: mu not equal to 519, reject if z > -1.96 or z< 1.96.
a. a.
b. b.
c. c.
d. d.
3) If a sample of 16 bottles shows a mean fill of 522 ml, does this contradict the hypothesis that the true mean is 519 ml?
A) Yes.
B) No
Answer:
1) The normal distribution should be used for the sample mean because the population distribution is known to be normal (answer b).
2) C. H0: mu = 519, H_1: mu not equal to 519, reject if z> 1.96 or z< -1.96.
3) Yes. There is enough evidence to support the claim that the true mean is not 519 ml.
Step-by-step explanation:
1) When the population follows a normal distribution, it is correct to assume a normal distribution for the sample mean.
2) As it is a two-tailed decision rule, we are interested in detecting a significant difference below and above the mean. This is why we use the unequal sign in the alternative hypothesis.
The null hypothesis state that there is not significant difference from 519.
The critical value for a significance level of 5% is z=1.96.
[tex]H_0: \mu=519\\\\H_a:\mu\neq 519[/tex]
3) The claim is that the true mean is not 519 ml.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=519\\\\H_a:\mu\neq 519[/tex]
The significance level is 0.05.
The sample has a size n=16.
The sample mean is M=522.
The standard deviation of the population is known and has a value of σ=6.
We can calculate the standard error as:
[tex]\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{6}{\sqrt{16}}=1.5[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{M-\mu}{\sigma_M}=\dfrac{522-519}{1.5}=\dfrac{3}{1.5}=2[/tex]
This test is a two-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=2\cdot P(z>2)=0.046[/tex]
As the P-value (0.046) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the true mean is not 519 ml.
Composition of the function is commuatative
Answer:
The functions g and f are said to commute with each other if g ∘ f = f ∘ g. Commutativity is a special property, attained only by particular functions, and often in special circumstances. For example, |x| + 3 = |x + 3| only when x ≥ 0. ... The composition of one-to-one functions is always one-to-one.
\
Mr. Azu invested an amount at rate of 12% per annum and invested another amount, GH¢ 580.00 more than the first at 14%. If Mr. Azu had total accumulated amount of GH¢2,358.60, how much was his total investment?
Answer:
GH¢2082.12
Step-by-step explanation:
Let "a" represent the amount invested at 12%. Then (a+580) is the amount invested at 14%. The total amount invested (t) is ...
t = (a) +(a +580) = 2a+580
Solving for a, we get
a = (t -580)/2
__
The accumulated amount from the investment at 12% is 1.12a. And the accumulated amount from the investment at 14% is 1.14(a+580). Together, these accumulated amounts total GH¢2358.60.
1.12(t -580)/2 +1.14((t -580/2 +580) = 2358.60
0.56t -0.56(580) +0.57t -0.57(580) +1.14(580) = 2358.60 . . . remove parens
1.13t + 5.8 = 2358.60 . . . . . . . . . simplify
1.13t = 2352.80 . . . . . . . . . . . . . . subtract 5.8
t = 2352.80/1.13 = 2082.12 . . . . divide by the coefficient of t
Mr. Azu's total investment was GH¢2082.12.
(2)/(5) and (1)/(x)common denominator =10 find the value of x
Answer:
[tex]x=5/48[/tex]
Step-by-step explanation:
[tex]2/5 + 1/x =10[/tex]
[tex]1/x=10-2/5[/tex]
[tex]1/x=48/5[/tex]
[tex]48x=5[/tex]
[tex]x=5/48[/tex]
Answer:
[tex]x = \frac{5}{48} [/tex]
Step-by-step explanation:
[tex]\frac{2}{5} + \frac{1}{x} = 10 \\ \frac{1}{x} = 10 - \frac{2}{5} \\ \frac{1}{x} = \frac{50 - 2}{5} \\ \frac{1}{ x } = \frac{48}{5} \\
use \: \: \: \: cross \: \: \: multiply
\\ 5 = 48x \\ \frac{5}{48} = \frac{48x}{48} \\ x = \frac{5}{48} \\ [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
WILL GIVE BRAINLIEST! HURRY
Answer:
-1/2 =x
Step-by-step explanation:
4x - 6 = 10x -3
Subtract 4x from each side
4x-4x - 6 = 10x-4x -3
-6 = 6x-3
Add 3 to each side
-6+3 = 6x
-3 = 6x
Divide each side by 6
-3/6 = 6x/6
-1/2 =x
[tex]answer \\ - \frac{1}{2} \\ solution \\ 4x - 6 = 10x - 3 \\ or \: 4x - 10x = - 3 + 6 \\ or \: - 6x = 3 \\ or \: x = \frac{3}{ - 6} \\ x = - \frac{1}{2} \\ hope \: it \: helps[/tex]
Consider the following geometric series.
[infinity]∑n=1 (−8)n−19n
a) Find the common ratio.
b) Determine whether the geometric series is convergent or divergent.
c) If it is convergent, find its sum. (If the quantity diverges, answer diverges.)
Answer:
a) -8/9
b) The series is a convergent series
c) 1/17
Step-by-step explanation:
The series a+ar+ar²+ar³⋯ =∑ar^(n−1) is called a geometric series, and r is called the common ratio.
If −1<r<1, the geometric series is convergent and its sum is expressed as ∑ar^(n−1) = a/1-r
a is the first tern of the series.
a) Rewriting the series ∑(-8)^(n−1)/9^n given in the form ∑ar^(n−1) we have;
∑(-8)^(n−1)/9^n
= ∑(-8)^(n−1)/9•(9)^n-1
= ∑1/9 • (-8/9)^(n−1)
From the series gotten, it can be seen in comparison that a = 1/9 and r = -8/9
The common ratio r = -8/9
b) Remember that for the series to be convergent, -1<r<1 i.e r must be less than 1 and since our common ratio which is -8/9 is less than 1, this implies that the series is convergent.
c) Since the sun of the series tends to infinity, we will use the formula for finding the sum to infinity of a geometric series.
S∞ = a/1-r
Given a = 1/9 and r = -8/9
S∞ = (1/9)/1-(-8/9)
S∞ = (1/9)/1+8/9
S∞ = (1/9)/17/9
S∞ = 1/9×9/17
S∞ = 1/17
The sum of the geometric series is 1/17
What is the image of R for a dilation with center (0,0) and a scale factor of 1 1/2?
Answer: The image is (6,-3)
Step-by-step explanation:
The coordinates of R is ( 4,-2) and to find the image using the scale factor 1.5 you will multiply the x coordinates by 1.5 and the y coordinate also by 1.5 to have the new image of R.
4 * 1.5 = 6
-2 * 1.5 = -3
The new coordinates care (6, -3)
is –68 + 90 positive or negative?
Answer:
22. positive
Step-by-step explanation:
–68 + 90
22
8. Mr. Azu invested an amount at rate of 12% per annum and invested another amount. GHe
580.00 more than the first at 14%. IN Mr. Azu had total accumulated amount of
GH42.358.60. how much was his total investment?
Ans:
Answer:
GH¢.37480.36
Step-by-step explanation:
Let the amount invested at 12% per annum =GH¢.x
He invested 580.00 more than the first at 14%.
Therefore:
The amount invested at 14% =GH¢.(x+580)
For each investment option:
Amount Accrued =Principal + Simple Interest
Amount Accrued at 12%
[tex]=x+x*0.12\\=1.12x[/tex]
Amount Accrued at 14%
[tex]=(x+580)+0.14(x+580)\\=x+580+0.14x+81.2\\=1.14x+661.2[/tex]
Mr. Azu had total accumulated amount of GH42,358.60
Therefore:
1.12x+1.14x+661.2=42,358.60
2.26x=42,358.60-661.2
2.26x=41697.4
x=GH¢.18450.18
Therefore:
The amount invested at 12% per annum= GH¢.18450.18
The amount invested at 14% per annum= GH¢.18450.18+580
=GH¢.19030.18
Mr Azu's Total Investment = 18450.18 +19030.18
=GH¢.37480.36
6x – 2y = 10 2x + 3y = 51 Solving the first equation above for y gives: y = x – 5
Answer:
x =6y =13Step-by-step explanation:
This is the method I am familiar with.
I Hope It helps :)
[tex]METHOD- 1 : Elimination\\6x - 2y=10------(1)\\2x+3y =51------(2)\\Multiply -eq-(1)- by -the-coefficient-of-x-in-equation (2)\\Multiply-eq-(2) -by -the-coefficient-of-x-in-equation (1)\\6x - 2y=10------(1) *2\\2x+3y =51------(2)*6\\\\12x-4y=20 ------(3)\\12x+18y=306 ------(4)\\Subtract -eq- (4)- from- eq -(3)\\-22y =-286\\\frac{-22y}{-22} =\frac{-286}{-22} \\y =13\\[/tex]
[tex]Substitute- 13- for y -in-equation -(1)-or-(2)\\6x - 2y=10------(1)\\6x -2(13)=10\\6x -26=10\\6x =10+26\\6x =36\\\frac{6x}{6} =\frac{36}{6} \\x =6[/tex]
Answer:
Correct answers is
Step-by-step explanation:
1. 3
2. B
3. 6
4. (6,13)
Playbill magazine reported that the mean annual household income of its readers is $119,155 (Playbill, January 2006). Assume this estimate of the mean annual household in- come is based on a sample of 80 households, and based on past studies, the population standard deviation is known to be a = $30,000. a. Develop a 90% confidence interval estimate of the population mean. b. Develop a 95% confidence interval estimate of the population mean. c. Develop a 99% confidence interval estimate of the population mean. d. Discuss what happens to the width of the confidence interval as the confidence level is increased. Does this result seem reasonable? Explain.
Answer:
a) CI = (113,637.5 , 124,672.5)
b) CI = (112,581 , 125,729)
c) CI = (110,501.4 , 127,808.6)
Step-by-step explanation:
You have the following information:
[tex]\overline{x}[/tex]: mean annual household income = 119,155
σ: standard deviation = 30,000
n: sample = 80
The interval of confidence is given by the following expression:
[tex]\overline{x}\pm Z_{\alpha/s}(\frac{\sigma}{\sqrt{n}})[/tex]
Z_α/2: distribution density factor
where α and Z_α/2 are given by the range of the confidence interval.
a) For a 90% confidence interval you have:
α = 1 - 0.9 = 0.1
Z_0.1/2 = Z_0.05 = 1.645 (found in a table of normal distribution)
You replace in the equation (1) to obtain the confidence interval:
[tex]119,155\pm (1.645)(\frac{30,000}{\sqrt{80}})\\\\=119,155\pm5,517.5[/tex]
Then, the confidence interval is (119,155 + 5,517.5 , 119,155 - 5,517.5 )
= (113,637.5 , 124,672.5)
b) For a 95% confidence interval you have:
α = 1 - 0.95 = 0.05
Z_0.05/2 = Z_0.025 = 1.96
[tex]119,155\pm (1.96)(\frac{30,000}{\sqrt{80}})\\\\=119,155\pm 6,574.0[/tex]
The confidence interval is (112,581 , 125,729)
c) For a 99% confidence interval:
α = 1 - 0.99 = 0.01
Z_0.01/2 = Z_0.005 = 2.58
[tex]119,155\pm (2.58)(\frac{30,000}{\sqrt{80}})\\\\=119,155\pm 8,653.6[/tex]
The confidence interval is (110,501.4 , 127,808.6)
d) When the confidence level increases the width of the confidence increases too. This can be noticed in the normal distribution, when the confidence level is higher, the area of the tails is reduced, and so, the confidence interval is higher.
