A research firm conducted a survey to determine the mean amount of money smokers spend on cigarettes during a day. A sample of 100 smokers revealed that the sample mean is N$ 5.24 and sample standard deviation is N$ 2.18 Assume that the sample was drawn from a normal population.
2.1) Find the point estimate of the population mean
2.2) Determine the lower limit of the 95% confidence interval for estimating the unknown population mean.
2.3) Determine the upper limit of the 95% confidence interval for estimating the unknown population mean.
Answers
Answer:
2.1
the point estimate of the population mean is
\(\mu = \= x = \$ 5.24\)
2.2
The lower limit \(k= 4.8127 \)
2.3
The upper limit \(u= 5.6673 \)
Step-by-step explanation:
From the question we are told that
The sample size is n = 100
The sample mean is \(\= x = \$ 5.24\)
The standard deviation is \(\sigma = \$ 2.18\)
Generally given that the sample size is large enough n > 30 and that the sample was drawn from a normal population, then the point estimate of the population mean is
\(\mu = \= x = \$ 5.24\)
From the question we are told the confidence level is 95% , hence the level of significance is
\(\alpha = (100 - 95 ) \%\)
=> \(\alpha = 0.05\)
Generally from the normal distribution table the critical value of \(\frac{\alpha }{2}\) is
\(Z_{\frac{\alpha }{2} } = 1.96\)
Generally the margin of error is mathematically represented as
\(E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }\)
=> \(E = 1.96 * \frac{2.18 }{\sqrt{100} }\)
=> \(E =0.4273 \)
Generally the lower limit of the 95% confidence interval for estimating the unknown population mean is mathematically represented as
\(k = \= x -E \)
=> \(k= 5.24 -0.4273 \)
=> \(k= 4.8127 \)
Generally the upper limit of the 95% confidence interval for estimating the unknown population mean is mathematically represented as
\(u= \= x + E \)
=> \(u= 5.24 + 0.4273 \)
=> \(u= 5.6673 \)
Related Questions
\(\frac{6-\sqrt{8} }{\sqrt{2}-1 }\)
Answers
Answer:
2 +4√2
Step-by-step explanation:
Perhaps you want the simplified form of (6-√8)/(√2 -1).
ConjugateThe denominator can be rationalized by multiplying numerator and denominator by the conjugate of the denominator:
\(\dfrac{6-\sqrt{8}}{\sqrt{2}-1}=\dfrac{(6-\sqrt{8})(\sqrt{2}+1)}{(\sqrt{2}-1)(\sqrt{2}+1)}=\dfrac{6\sqrt{2}+6-\sqrt{16}-\sqrt{8}}{2-1}=\boxed{2+4\sqrt{2}}\)
__
Additional comment
The conjugate of the denominator is the same pair of terms with the sign between them changed. The product of the binomial and its conjugate is then the difference of squares. Since the square of a square root eliminates the radical, multiplying by the conjugate has the effect of removing the radical from the denominator.
The same "difference of squares" relation can be used to remove a complex number from the denominator.
(a -b)(a +b) = a² -b²
In general, the differences of terms of the same power can be factored. This means that denominators with this form can be "rationalized" by taking advantage of that factoring.
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![[tex]\frac{6-\sqrt{8} }{\sqrt{2}-1 }[/tex]](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/kJ2mrJbUXYxW6DY7zAZy3exel3Aay2TN.png)
Answer:
\(4\sqrt{2}+2\)-----------------------
Simplify the expression in steps:
\(\cfrac{6-\sqrt{8} }{\sqrt{2}-1 } =\)
\(\cfrac{6-2\sqrt{2} }{\sqrt{2}-1 } =\)
\(\cfrac{2(3-\sqrt{2} )(\sqrt{2} +1)}{(\sqrt{2}-1)(\sqrt{2}+1) } =\)
\(\cfrac{2(3\sqrt{2}+3-(\sqrt{2}^2) -\sqrt{2} )}{(\sqrt{2})^2-1 } =\)
\(\cfrac{2(2\sqrt{2}+3-2) }{2-1} =\)
\(\cfrac{2(2\sqrt{2}+1) }{1} =\)
\(4\sqrt{2}+2\)
20 POINTS FOR ANSWERING ALL PARTS
Answers
Answer:
wont let me download
Step-by-step explanation:
The mean absolute deviation of Mr. Zimmerman's class is 0.46. What does this mean?
Answers
Answer:
is a measure of the average absolute distance between each data value and the mean of a data set.
Given ΔMNO, find the measure of ∠MNO.
Triangle MNO with segment LM forming a straight angle with segment MO and segment OP forming a straight angle with segment MO, the measure of angle NOP is 104 degrees, and segment MN and NO are marked congruent.
28 degrees
38 degrees
52 degrees
76 degrees
I know the answer is 28 degrees , I just am not sure how to work out this problem .
Answers
Answer:10907
Step-by-step explanation 10907
Answer:
The answer is 28
Step-by-step explanation:
Hope this helps,
have a great day
These points are linear. Find the slope.
Answers
to get the slope of any straight line, we simply need two points off of it, let's use those in the picture below.
\((\stackrel{x_1}{-4}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{2}-\underset{x_1}{(-4)}}} \implies \cfrac{8 }{2 +4} \implies \cfrac{ 8 }{ 6 } \implies \cfrac{4 }{ 3 }\)
The 4th grade class experienced a 15% decrease in enrollment. Last year, the 4th grade class had 280 students. How many students are enrolled in the 4th grade class this year?
Answers
Answer: 238
Step-by-step explanation: 15% of 280 is 42 so subtract 42 from the number and it equals 238
39. From the top of a vertical cliff 50 meters high, the angles of depression of an object that is levelled with
the base of the cliff is 30°. How far is the object from the base of the cliff?
A. 50 meters
B. 50-√3 meters
C. 100 meters
D. 100-√3 meters
40. What expression is used to answer: "A 4-m tall man stands on horizontal ground 43 m from a tree.
The angle of depression from the top of the tree to his eyes is 22°. Estimate the height of the tree."
A. sin 22
B. cos 22
C. tan 22
D. cot 22
41. From the top of the building of a food chain, the angle of depression from where Miguel stands is
45°. If the building is 12 meters high, how far is he from it?
A. 11 meters
B. 12 meters
C. 13 meters
D. 14 meters
42. A plane, at an altitude of 3,000 feet, observes the airport at an angle of 27°. What is the
horizontal distance between the plane and the airport to the nearest foot?
A. 3,000 feet
B. 4,000 feet
C. 5,000 feet
D. 6,000 feet
43. An escalator has an angle of elevation of 10° and a vertical rise of 6 m. Find the length of the
escalator.
C. 34.55 m
D. 36 m
A. 6,09 m
B. 34,03 m
Answers
Answer: cos4
Step-by-step explanation: 50 meters
B. 50-√3 meters
C. 100 meters
D. 100-√3 meters
40. What expression is used to answer: "A 4-m tall man stands on horizontal ground 43 m from a tree.
The angle of depression from the top of the tree to his eyes is 22°. Estimate the height of the tree."
A. sin 22
B. cos 22
C. tan 22
D. cot 22
Enter the words as an expression.
Subtract 15 from 60, then divide by 9.
Answers
Answer:
60-15/9
Step-by-step explanation:
Subtract (-) 15 from 60: 60-15
Divide (/) by 9: 60-15/9
Answer:
60 - 15 ÷ 9 = x
OR if you want the equation to be solved:
60 - 15 ÷ 9 = 5
Hope this helps and have a nice day!
PS if you could mark brainliest that'd be great! I usually don't ask but I'm very close to "expert" rank.
Evaluate the following expression: (-3)^-2
Answers
Answer:
\(\frac{1}{9}\)
Step-by-step explanation:
Anything to the negative power becomes a fraction
x⁻ⁿ = 1/xⁿSo here we have (-3)⁻² which then becomes \(\frac{1}{(-3)^{2} }\)
This then simplifies to \(\frac{1}{9}\)
Need help answering question 4 please
Answers
The answer is 140 because 14 x 10 is 140
Temperatures in northern Canada ranged as high as 37°F one summer. That same year the lowest temperature was −28°F. What was the range of temperatures for the year?
Answers
Answer:
65 degrees
Step-by-step explanation:
Find the range of temperatures by finding the difference between the lowest and highest temperatures:
37 - (-28)
37 + 28
= 65
So, the range of temperatures was 65 degrees
The length of a shadow and the height of the object casting the shadow are proportional. If a 16 foot giraffe cast a 20 foot shadow, how tall is a tree that casts a 30 foot shadow.
Answers
Answer:
26 feet
Step-by-step explanation:
In ΔTUV, u = 3.4 inches, m∠U=144° and m∠V=35°. Find the length of v, to the nearest 10th of an inch.
Answers
The length of v to the nearest 10th of an inch is 2.0 inches.
What is a triangle?A triangle is a 2-D figure with three sides and three angles.
The sum of the angles is 180 degrees.
We can have an obtuse triangle, an acute triangle, or a right triangle.
We have,
We can use the Law of Sines,
Which states that for any triangle ABC:
a/sin(A) = b/sin(B) = c/sin(C)
where a, b, and c are the lengths of the sides of the triangle opposite the angles A, B, and C.
Now,
a = UV = u = 3.4 inches
A = ∠TUV
= 180° - m∠U - m∠V
= 180° - 144° - 35°
= 1°
B = ∠UTV
= m∠U
= 144°
C = ∠TVU
= m∠V
= 35°
Using the Law of Sines,
v/sin(C) = u/sin(B)
Substituting in the values.
v/sin(35°) = 3.4/sin(144°)
Solving for v.
v = (3.4 × sin(35°)) / sin(144°)
v = 1.97 inches
Therefore,
The length of v to the nearest 10th of an inch is 2.0 inches.
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50 points
Solve for x. Round to the nearest tenth of a degree, if necessary.
Answers
The value of angle x = 56.63 degree.
In the Given figure
EF = 4.4
FD = 8
∠F = x degree
Since we know that
CosΘ = (adjacent of a)/hypotenuse
Therefore,
Cosx = 4.4/8
= 0.55
Take inverse of cos both sides,
x = 56.63 degree
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Find the distance between the points (6,5) and (4,-2). use of the graph is optional
Answer ? Anyone
Answers
Answer:
√53
Step-by-step explanation:
Distance between two points =
√(4−6)^2+(−2−5)^2
√(−2)^2+(−7)^2
= √4+49
=√53
= 7.2801
Hope this helps uwu
9514 1404 393
Answer:
option 2: √53
Step-by-step explanation:
The distance formula is useful for this:
d = √((x2 -x1)² +(y2 -y1)²)
d = √((4-6)² +(-2-5)²) = √((-2)² +(-7)²) = √(4+49)
d = √53
The distance between the given points is √53.
Suppose a charity event serves a prix fixe dinner that consists of one from each category: (1) soup or salad (not both), (2) appetizer, (3) entree, (4) dessert, and (5) beverage. The restaurant is offering five kinds of soup, three kinds of salad, four kinds of appetizers, six entrees, five desserts, and four beverages. How many different prix fixe dinners are possible
Answers
Answer:
3840
Step-by-step explanation:
Using the fundamental counting principle
The restaurant is offering five kinds of soup, three kinds of salad, four kinds of appetizers, six entrees, five desserts, and four beverages.
There are 5 independent events happening (5 prixe dinners)
(1) soup or salad (not both)
We have five kinds of soup, three kinds of salad
soup or salad (not both), = 5 + 3
= 8
(2) appetizer = 4
(3) entrees = 6
(4) dessert = 5
(5) Beverage = 4
Hence,
8 × 4 × 6 × 5 × 4
= 3840
The number of different prix fixe dinners are possible is 3840
A 30−60−90 triangle has a longer leg with length 53√4 and a hypotenuse with length 5/2 . What is the length of the shorter leg?
Answers
The length of the shorter leg is √2
Pythagoras theroemTo get the length of the shorter leg, we will use the Pythagoras theorem. According to the theorem:
hyp^2 = opp^2 + adj^2
Given the following
Hyp = √4
Opposite = √2
Required
Adjacent side
Substitute into the formula
(√4 )^2 = 2 + adj^2
4 - 2 = adj^2
adj^2 = 2
adj = √2
Hence the length of the shorter leg is √2
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Raphael and his four friends are having lunch. They agree to split the bill evenly at the end after adding a 20% tip. If the total bill is $85.60, how much will each person end up paying? A. $25.68 B. $20.54 C. $18.68 D. $17.12
Answers
The total amount to each person end up paying $20.54.
To find the total amount each person will pay, first calculate the 20% tip on the total bill and then divide the sum by the number of people.
To split the bill evenly among Raphael and his four friends, we first need to find the total cost including the 20% tip.
The tip is 20% of the original bill, which is equivalent to 0.20 x $85.60 = $17.12.
Therefore, the total cost of the bill with the tip is $85.60 + $17.12 = $102.72.
To split this evenly among the five people, we divide by 5:
$102.72 ÷ 5 = $20.54
So each person will end up paying $20.54.
20% of $85.60 is ($85.60 * 0.20) = $17.12
Add the tip to the total bill:
$85.60 + $17.12 = $102.72
Divide the total amount by the number of people (5): $102.72 / 5 = $20.54
Therefore, the answer is B. $20.54.
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So do you have to have a least 2 people answering the question to five them the crowm?
Answers
Answer:
Well... only two people can answer a question. But you must have both two answers for a question to give brainliest to one or another. Got it? :)
Step-by-step explanation:
The coordinates of the vertices of a polygon are shown on the graph below.
On a coordinate plane, point A is at (negative 4, 3), point C is at (0, negative 3), and point B is at (negative 4, negative 3).
What is the name of the polygon?
octagon
pentagon
quadrilateral
triangle
Answers
Answer:
triangle
Step-by-step explanation:
draw the coordinates on a graph
please mark brainliest
Answer:
The person above me is right, To the creator of the question you can give him Brainliest now <3
Step-by-step explanation:
(Triangle)
3
Bane is paid a salary of $400 a week plus 6% commission. How much would he make
in a week if he sold $15,000 worth of materials?
Answers
Answer:
$1300
Step-by-step explanation:
so, he would get the $400 basic salary plus 6% of the $15000.
15000 = 100%
1% = 100%/100 = $150
6% = 1%×6 = 150×6 = $900
so, in total, he would make
$400 + $900 = $1300 in that week.
Need help with this, super confused on the last question. Please anything helps!
Answers
Answer:
On Wednesday they sold 5, over the four days they sold 19, and the third I believe it is 26.32 . Please rate me and mark me brainliest!
Step-by-step explanation:
3. A line segment whose endpoints are (3,9) and (7,k) is perpendicular to a line whose slope is --2. Which
of the following is the value of k?
(1) 1
(3) 11
(2) -7
(4) -5
Answers
Answer:
(3) 11
Step-by-step explanation:
A line perpendicular to one with a slope of -2 will have the opposite reciprocal slope: -1/(-2) = 1/2.
The point-slope equation of the line through (3, 9) with slope 1/2 is ...
y -9 = 1/2(x -3)
Then for point (7, k) on the line we have ...
k -9 = 1/2(7 -3)
k = 9 +2 = 11
The value of k is 11.
Jordan had a bake sale. Muffins cost $3 each and cookies cost $2 each. Jordan earned $24.
(Select all)
- 0 muffins and 8 cookies
- 9 muffins and 2 cookies
- 2 muffins and 9 cookies
- 6 muffins and 4 cookies
- 4 muffins and 6 cookies
Answers
Answer:
0 muffins and 8 cookies
6 muffins and 4 cookies
Explain:
These are the only two combinations of muffins and cookies that Jordan could have sold to earn $24. If Jordan sold 0 muffins and 8 cookies, they would have earned $24 because 0 x $3 + 8 x $2 = $24. If Jordan sold 6 muffins and 4 cookies, they would have earned $24 because 6 x $3 + 4 x $2 = $24.
one card is drawn from a pack of 52cards each of the 52 cards being equally likely to be drawn. what is the probability that the card drawn is a king?
Answers
The probability of drawing a king from a standard deck of 52 cards is 1/13.
In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.
To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).
The total number of possible outcomes is 52 because there are 52 cards in the deck.
The favorable outcomes, in this case, are the four kings.
Therefore, the probability of drawing a king is given by:
Probability = (Number of favorable outcomes) / (Number of possible outcomes)
= 4 / 52
= 1 / 13
Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.
This means that out of every 13 cards drawn, on average, one of them will be a king.
It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.
Each draw is independent, and the probability of drawing a king is constant.
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Divide 2,756 into 1,375,244
Answers
Step-by-step explanation:
499
im not sure if correct ,
A manager asked her employees how many times they had given blood in the last year. The results of the survey are given below. The random variable x represents the number of times a person gave blood and P(x) represents the probability of selecting an employee who had given blood that percent of the time. What is the mean number of times a person gave blood based on this survey
Answers
Complete Question
The probability distribution table is given below:
\(\left|\begin{array}{c|ccccccc}x&0&1&2&3&4&5&6\\P(x) &0.33 &0.24& 0.16& 0.12 &0.08 &0.05& 0.02\end{array}\right|\)
Answer:
1.61
Step-by-step explanation:
The probability distribution table is given below:
\(\left|\begin{array}{c|ccccccc}x&0&1&2&3&4&5&6\\P(x) &0.33 &0.24& 0.16& 0.12 &0.08 &0.05& 0.02\end{array}\right|\)
We want to determine the mean number of times a person gave blood.
Expected Value, \(E(x)=\sum x_i\cdot P(x_i)\)
\(=(0 \times 0.33)+ (1 \times 0.24)+(2\times0.16)+(3\times0.12)+(4\times0.08)+(5\times0.05)+(6\times0.02)\\=0+0.24+0.32+0.36+0.32+0.25+0.12\\=1.61\\\)
The mean number of times a person gave blood based on this survey is 1.61.
a plane can fly 450 miles in the same time it takes a car to go 150 miles. if the car travels 100 mph slower than the plane, find the speed (in mph) of the plane
Answers
Answer:
The speed of the plane is 150 miles per hour, while the speed of the car is 50 miles per hour.
Step-by-step explanation:
Since a plane can fly 450 miles in the same time it takes a car to go 150 miles, if the car travels 100 mph slower than the plane, to find the speed (in mph) of the plane the following calculation must be performed:
450 to 150 is equal to 3: 1, that is, the plane travels three times the distance of the car.
Therefore, since 100/2 x 3 equals 150, the speed of the plane is 150 miles per hour, while the speed of the car is 50 miles per hour.
Check all of the possible first steps in factoring a polynomial with four terms.factor out a GCFfactor the difference of cubesfactor a sum of cubesfactor a difference of squaresfactor a perfect-square trinomialfactor by grouping
Answers
Answer:4x as much as GCF
Step-by-step explanation:
u need to do 4x
Answer:
Step-by-step explanation:
Polynomials can be solved in several ways.
The possible first steps are: A. Factor out a GCF and F. Factor by grouping
A polynomial with 4 terms is represented as:
Because it has 4 terms, it cannot be solved by sum or difference of cubes or squares.
This mean that: options (b), (c), (d) and (e) are false.
However, the terms of the polynomial can be factored, if they have a common factor, and they can also be grouped.
Hence, the possible first steps are: A. Factor out a GCF and F. Factor by grouping
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help I don't understand
Answers
With the help of proportions in the given similar triangles we know that the value of x is 3.5 units.
What is triangle similarity?Euclidean geometry states that two objects are comparable if they have the same shape or the same shape as each other's mirror image.
One can be created from the other more precisely by evenly scaling, possibly with the inclusion of further translation, rotation, and reflection.
These three theorems—Angle-Angle (AA), Side-Angle-Side (SAS), and Side-Side-Side (SSS)—are reliable techniques for figuring out how similar triangles are to one another.
So, in the given situation:
TR and WY are as follows:
TR/WU
24/2
2/1
Similarly,
TS/WV
2/1
7/x
7/3.5
Therefore, with the help of proportions in the given similar triangles we know that the value of x is 3.5 units.
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