He should order 10 sandwiches of 6 foot long so, as to make sure that everyone will eat 2 pieces.
What is Conversion ?We need to convert between the units in order to ensure the accuracy and to prevent measurement misinterpretation. For example, we do not measure the pencil's length in kilometres. In this situation, one must convert from kilometres (km) to centimetres (cm) (cm). In most cases, multiplicative conversion factors are used to convert one unit to another of the same quantity. Let's see how to change the length and mass units.
1 Feet = 12 Inches
So, 6 Foot = 72 inches
The Length of sandwich- piece is 4 inch
So, when we convert 6 foot long sandwich into 4 inch,
Then we get number of piece is = 72/4 = 18
From 6 foot long sandwich we get 18 pieces of 4 inch long sub.
Now, Total people who will attend picnic is 40
and each people will eat 2 pieces.
It means total number of piece required = 2 (90) = 180
Mr. eaton required 180 pieces of sandwiches.
Number of sandwiches = 180 / 1.8 = 10
He should order 10 sandwiches of 6 foot long.
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the probability that a new microwave oven is damaged during delivery is 0.10. given that a new microwave oven is damaged during delivery, what is the probability that it stops working in less than 2 years?
The probability that it stops working in less than 2 years is 0.40.
Given:
the probability that a new microwave oven will stop working in less than 2 years is 0.05. the probability that a new microwave oven is damaged during delivery and stops working in less than 2 years is 0.04. the probability that a new microwave oven is damaged during delivery is 0.10.
here
P ( A ∩ B ) = 0.04
P ( A ) = 0.10
we know that,
According to conditional probability:
P ( B / A ) = P ( A ∩ B ) / P ( A )
substitute values
= 0.04 / 0.10
= 004 / 100 / 010/100
= 4 / 100 * 100 / 10
= 4 * 100 / 100 * 10
= 4 * 1 / 10 * 1
= 4 / 10
= 0.40
Therefore the probability that it stops working in less than 2 years is 0.40.
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A die is rolled. Find the probability of the given event. Write your answers as whole numbers or reduced fractions.
(a) The number showing is a 4
P(4) = (b) The number showing is an even number
P(even) =
(c) The number showing is greater than 3
P(greater than 3) =
The probability for given conditions are a) p(4)=0.166, b) p(even)=0.5 and c) p(greater than 3)=0.5
A die is rolled, then the sample space for outcomes is {1,2,3,4,5,6}
Total number of outcomes =6
Probability of showing number 4. number of favourable outcomes is 1 because there is only one 4 in the sample space of outcomes , [tex]P(4)=\frac{number\ of\ favourable\ outcomes}{total\ number\ of\ outcomes}\\\\P(4)=\frac{1}{6}=0.166[/tex]Probability of showing an even number, even numbers in sample space are {2,4,6} number of favourable outcomes =3 [tex]P(even)=\frac{3}{6}=\frac{1}{2}=0.5[/tex]Probability of showing a number greater than 3, numbers greater then three is sample space are {4,5,6} number of favourable outcomes =3 [tex]P(greater\ than\ 3)=\frac{3}{6}=\frac{1}{2}=0.5[/tex]Thus, the probability for given conditions are a)p(4)=0.166, b)p(even)=0.5 and c)p(greater than 3)=0.5
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Help..NEOW PLSSSSSSSSSSSSSSSS
Answer: Yes, they are proportional
Answer:
No.
Step-by-step explanation:
A proportional relationship shows that each time the amount of money would have increased/decreased in the same amount if she had payed it off constantly and it did not therfore your answer is no.
A disk D, a hemisphere H, and a portion P of a paraboloid are shown. Suppose F is a vector field on R3 whose components have continuous partial derivatives. Explain why this statement is true: curl F. ds = -|| = / curt 1 SS curl F. ds = curl F. ds D H P 4 4 4 P H D 2 x2
Yes, this statement is true. Because flux integral of curl vector does not depend on surface, it depends only on the boundary of the surfaces. Till we are integrating in the same boundary limits.
Given:
The image displays a paraboloid's part P, its hemisphere H, and its disk D. Assume F is a vector field on R3 with continuous partial derivatives in each of its components.
we are asked why the statement is true = ?
Yes, this claim is accurate. Because the flux integral of the curl vector is surface-independent, it only depends on the boundaries of the surfaces. till our integration is within the same boundary limitations.
Hence above given expression will hold true.
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if the populations are normally distributed but the population variances are unknown the z-statistic can be used as the basis for statistical inferences about the difference in two population means using two independent random samples. true false
The given statement is false.
Given that,
The z-statistic can be used as the foundation for statistical inferences about the difference in two population means using two independent random samples if the populations are normally distributed but the population variances are unknown.
If the sample sizes are small, the populations are normally distributed, and the population variances are known, the z statistic can be used as the foundation for statistical inferences about the difference between two population means using two independent random samples.
Therefore, the above given statement can be concluded as false.
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N is an integer with -5 < 2n <6
write down all the values of n?
The value of n should be greater than -5/2 and less than 3. So the value of n under the interval (-5/2, 3).
In the given question, n is an integer with -5<2n<6.
We have to write the value of integer.
As we know;
Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. A common way to represent the set of integers in mathematical terms is z with bold.
To find the value of integer n we firstly divide the whole inequality by 2.
The given inequality is -5<2n<6.
Divide by 2, we get
-5/2<n<3
Now we can say that the value of n should be greater than -5/2 and less than 3. So the value of n under the interval (-5/2, 3).
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Jack bought 3 pencils and 4 notebooks and paid a total of $10.93. Sara bought 5 pencils and *
2 notebooks and paid a total of $7.53. What is the cost of a notebook?
$2.19
$2.24
$2.29
$2.35
Answer:
the correct answer is B
Step-by-step explanation:
$2.29 is the cost of a notebook.
Here, we have,
given that,
Jack bought 3 pencils and 4 notebooks and paid a total of $10.93. Sara bought 5 pencils and 2 notebooks and paid a total of $7.53.
let, the cost of a notebook = n
the cost of a pencil = p
we would solve this with simultaneous equations,
so if we write it as:
4n + 3p = 10.93
2n + 5p = 7.53
=> we get,
multiplying the equations by 5 and 3, we get,
20n + 15p = 54.65
6n + 15p = 22.59
(subtract)
14n = 32.06
divide both sides by 14,
14n ÷ 14 = 32.06÷ 14
n = 2.29
notebooks = 2.29
So the final answer is notebooks are $2.29.
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Question 3(Multiple Choice Worth 2 points)
(Theoretical Probability MC)
The probability P(DD) of the letters D and D is 4/9
How to determine the probability?The letters of the alphabets used to generate the word ADD are given as
Sample space (letters) = {A, D, D}
It is assumed that when a card (i.e. letter) is selected, the card is returned to the set
This means that the selection is with replacement
These letters mean that
P(Letter D) = Count of letter D/Number of letters
So, we have the following representation
P(Letter D) = 2/3
Now, the sample space is
Sample space (letters) = {A, D, D}
These letters mean that
P(Letter D2) = 2/3
So, we have the probability equation
P(DD) = P(D) * P(D2)
This gives
P(DD) = 2/3 * 2/3
Evaluate
P(DD) = 4/9
So, the probability is 4/9
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you want to estimate the mean sat score of all georgia students. you know the mean score for a random sample of georgia students is 1050. what number is your best guess as to the mean score for all georgia students?
The best guess for the mean score for all the Georgia students would be 1050 number here.
Given that:
The mean score for a random sample of Georgia students is 1050.
Assuming,
1) X-bar = 42; µ = 44; standard deviation (sigma) = 10; N = 64. Calculate the standard error.
1) The standard error is computed as:
[tex]\sigma_{\bar X} = \frac{\sigma}{\sqrt{n}} = \frac{10}{\sqrt{64}} = 1.25[/tex]
2) You know that X-bar = 42, mu = 44, sigma-sub-X = 10, and N = 64, Calculate z-obtained.
2) The Z-value is computed as:
[tex]Z = \frac{\bar X - \mu}{\frac{\sigma}{\sqrt{N}}} = \frac{42- 44}{\frac{10}{\sqrt{64}}} = -1.6[/tex]
3) The mean score on most IQ tests is 100 with a standard deviation of 15. If Sally has a score of 110 on an IQ test, what is her z-score.
3) The Z -score here is computed as:
[tex]Z = \frac{X -\mu}{\sigma} = \frac{110-100}{15} = 0.6667[/tex]
The best point estimate for the population mean score is equal to the sample mean which is 1050 in this case. Therefore the best guess for the mean score for all the Georgia students would be 1050 here.
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An airline finds that 5% of the persons making reservations on a certain flight will not show up for the flight. if the airline sells 155 tickets for a flight that has only 150 seats, what is the probability that a seat will be available for every pe?
The probability that a seat will be available for every person holding a reservation and planning to fly is 0.8980.
What is probability?
Probability is a branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely a proposition is to be true. The probability of an event is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty.
Given:
The probability that a person who makes reservations on a certain flight and does not show up for the flight is p=0.05.
The probability that a person who makes reservations on a certain flight and does show up for the flight is 1-p=1-0.05=0.95.
The airlines sell 160 tickets for a flight with only 155 seats.
Let X be a random variable that denotes the number of persons who show up for the flight and it follows a binomial distribution with parameters n = 160 and p = 0.95.
Hence, X~ Binom (n = 160, p = 0.95).
Here,
np=160×0.95=152>5
n(1-p)=160×0.05 = 8.1>5
Hence, both np and n(1-p) are greater than 5, the binomial distribution can be approximated to normal distribution.
The probability that a seat will be available for every person holding a reservation and planning to fly is calculated as follows:
P(X ≤ 155) = (P < 155 + 0.5)
[tex]=P(x < 155.5)\\\\=P(\frac{X-np}{\sqrt{np(1-p)}} < \frac{155.5 - (160 \times 0.95}{\sqrt{160\times 0.95 \times 0.05}})\\\\=P(Z < \frac{155.5-152}{2.7568})\\\\=P(Z < 1.27)\\\\=0.8980[/tex]
Hence the probability that a seat will be available for every person holding a reservation and planning to fly is 0.8980.
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A spherical snowball is melting. Find the approximate change in volume if the radius decreases from 7 cm to 6.8 cm. .. If the radius decreases from 7 cm to 6.8 cm, the change in volume will be 119.6654 cm3. (Round to the nearest tenth as needed.)
A spherical snowball is melting and its radius decreases from 7 cm to 6.8 cm. Its approximate change in volume is 123.2 cm³.
The approximated value can be obtained using derivative approach.
The volume of the sphere is given by:
V = 4/3 πr³
dV/dr = 4 . πr²
Suppose the change of the radius is Δr, using the above derivative, the change of volume can be approximated as:
ΔV = 4 . πr² Δr
Parameters given:
r = 7 cm
Δr = 7 - 6.8 = 0.2 cm
Hence,
ΔV = 4 . π7² (0.2)
ΔV = 4 . π7² (0.2)
ΔV = 123.2 cm³
Therefore, the approximate change in volume is 123.2 cm³
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Suppose that insurance companies did a survey. They randomly surveyed 430 drivers and found that 330 claimed they always buckle up. We are interested in the population proportion of drivers who claim they always buckle up.
a) x = ? b) n = ? c) p' = ? d)
Which distribution should you use for this problem? (Round your answer to four decimal places.)
P- (_) (_,_)
e) Construct a 95% confidence interval for the population proportion who claim they always buckle up.
i. state the confidence interval
ii. sketch graph
iii. calculate error bound
The 95% confidence interval for the population proportion who claim they always buckle up is 0.0204.
a) x: 330
b) n: Number of drivers who are surveyed = 430
c) p': proportion of drivers in a sample who claimed to always buckle up = 0.7674
d) normal distribution should be used for this problem.
e) 95% confidence interval for the population proportion who claim they always buckle up.
The error margin is:
1.96 × sqrt(p(1-p) ÷ n)
1.96 × sqrt(0.7674 × 0.2326 ÷ 430) = 0.0204
(0.7674 - 0.0204,0.7674 + 0.0204) = (0.747, 0.7878)
The confidence interval is (0.747, 0.7878).
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3 times x plus 4 is no less than 4 times the sum of x and 1
There isn't a ton of information regarding exactly what you are looking for to answer this question. However, if you are trying to simply convert the following word phrase to an expression, here you go:
3 Times x - Since there is an unknown variable (x), we can simply write the multiplication as 3x. "Plus 4" is also mentioned, so we write the first part as (3x + 4).No Less Than - This simply means "<". 4 Times the Sum of X and 1 - We can write this as 4(x + 1), considering we are adding an x variable to 1, however also multiplying. To organize this, we add parenthesis.
Hence, the final expression would be written as:
[tex](3x+4) < 4(x+1)[/tex]
Hope this helps!
Convert 4,300 kilometers into miles round your answer to the nearest whole number
4300 km to miles:
[tex]{ \red{ \tt{2671.896}}}[/tex]
2671.896 in nearest whole number :
[tex]{ \blue{\boxed{ \tt{2672}}}}[/tex]
the summary of the percent of times each and every category appears for the entire sample is called the:
The summary of the percent of times each and every category appears for the entire sample is called the frequency distribution , the correct option is (d) .
In the question ,
it is asked about what is The summary of the percent of times each and every category appears for the entire sample is called ,
it is called frequency distribution ,
Frequency distribution : it lists all categories of data and number of occurrences for each data category and
it is also the summary of percent of times each and every category appears for entire sample .
Therefore , the correct option is (d) .
The given question is incomplete , the complete question is
The summary of the percent of times each and every category appears for the entire sample is called the ,
(a) mode
(b) categorical percentage rate
(c) percentage distribution
(d) frequency distribution
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a ferris wheel is 16 meters in diameter and makes one revolution every 7 minutes. for how many minutes of any revolution will your seat be above 12 meters?
After 1.67 minutes, the Ferris wheel will be higher than 12 meters.
Given,
The Ferris wheel has a 16-meter diameter.
The circumference of a circle with a diameter of 16 meters, which is calculated as follows, is the distance travelled by the Ferris wheel in one rotation; 16π meter
The Ferris wheel makes one revolution in 7 minutes, hence the following is true:
16π meter = 7 minutes
1 meter = (7/16π) minutes
12 meters = (7 ×12)/16π minutes
12 meters = 1.67 minutes
Therefore,
The Ferris wheel will be above 12 meters after 1.67 minutes.
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forty teams play a tournament in which every team plays every other team exactly once. no ties occur, and each team has a 50% chance of winning any game it plays. the probability that no two teams win the same number of games is m/n, where m and n are relatively prime positive integers. find log2n
The probability that no two teams win the same number of games is 742.
There are (40/2) = 780 total pairings of teams, and thus 2⁷⁸⁰ possible outcomes. In order for no two teams to win the same number of games, they must each win a different number of games. Since the minimum and maximum possible number of games won are 0 and 39 respectively, and there are 40 teams in total, each team corresponds uniquely with some k, with 0 ≤ k ≤ 39, where k represents the number of games the team won. With this in mind, we see that there are a total of 40! outcomes in which no two teams win the same number of games. Further, note that these are all the valid combinations, as the team with 1 win must beat the team with 0 wins, the team with 2 wins must beat the teams with 1 and 0 wins, and so on; thus, this uniquely defines a combination.The desired probability is thus 40!/2⁷⁸⁰ . We wish to simplify this into the form m/n , where m and n are relatively prime. The only necessary step is to factor out all the powers of 2 from 40!, the remaining number is clearly relatively prime to all powers of 2.The number of powers of 2 in 40! is
= (40/2) + (40/4) + (40/8) + (40/16) + (40/32)
= 20 + 10 + 5 + 2 + 1
= 38.
780-38 = 742.
Hence, the probability that no two teams win the same number of games is 742.
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help pls by pst sunday december 4, 2022 12:00 images below
Select the correct answer from each drop-down menu. Consider the following polynomials equations. A = 3 x 2 ( x − 1 ) B = − 3 x 3 + 4 x 2 − 2 x + 1 Perform each operation and determine if the result is a polynomial. Is the result of A + B a polynomial? Is the result of A - B a polynomial? Is the result of A · B a polynomial?
Carrying out the operations on the polynomials shows that
A + B - polynomial
A - B - polynomial
A * B - polynomial
How to determine the result of the operationsThe given polynomials are
A = 3x²( x − 1 )
B = -3x³ + 4x² − 2x + 1
A + B
= 3x²( x − 1 ) + (-3x³ + 4x² − 2x + 1)
= 3x³ - 3x² - 3x³ + 4x² − 2x + 1
= x² − 2x + 1
This is a polynomial
A - B
= 3x²( x − 1 ) - (-3x³ + 4x² − 2x + 1)
= 3x³ - 3x² + 3x³ - 4x² + 2x - 1
= 6x³ - 7x² + 2x - 1
This is a polynomial
A * B
= 3x²( x − 1 ) * (-3x³ + 4x² − 2x + 1)
= (3x³ - 3x²) * (-3x³ + 4x² − 2x + 1)
= -9x^6 + 12x^5 - 6x⁴ + 3x³ + 9x^5 - 12x⁴ + 6x³- 3x²
= -9x^6 + 21x^5 - 18x⁴ + 9x³- 3x²
This is a polynomial
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Dolores is making a music video using a drone. She sets the drone on a
platform 1 meter above the ground. Then she uses the controls to make it
rise at a constant rate. The drone reaches a height of 16 meters in 5 seconds.
What is the equation for the drone's height, y, as a function of time, x?
Jm
Answer: y=3x-1
Step-by-step explanation:
1st subtract 1 from 16 so 15 then do 15/5 to get 3 seconds
Donald bought an old truck for $500
did a full restoration over the course of a
summer. When he had finished the
restoration, he sold it for $2,375. What was
the percent of increase on the truck?
The percent of increase on the truck was 375%.
what is a good half a mile time? today i ran it in 5:43. how can i improve that? i'm a 14 year old girl.
A good half a mile time is totally good, if a half mile is the longest distance you've ever run, try a 3/4 mile run the next time. After a few successful attempts at that distance, increase it to a mile.
In the given question, we have to explain, what is a good half a mile time.
First, some background is required for 5:43 for half a mile. When did you start running? Was that time calculated using a full effort, or was it only the distance covered without walking? Don't worry about if it's good if you're spanking new. Use it as a foundation.
Second, like with most things in life, practise makes perfect, and running performance is no exception. If a half mile is the longest distance you've ever run, try a 3/4 mile run the next time. After a few successful attempts at that distance, increase it to a mile. The goal is to gradually push your boundaries until you consistently cross that threshold and then push your limits even farther.
Your body will be encouraged to adapt to the challenge, grow to it, and become prepared for when the challenge gets harder.
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a spherical snowball is melting in such a way that its diameter is decreasing at rate of 0.2 cm/min. at what rate is the volume of the snowball decreasing when the diameter is 8 cm
20.11 cm3/min is the rate at which the snowball's volume is decreasing.
Given,
The decreasing diameter when the spherical ball is melting = 0.2 cm/min
We have to find the rate in decrease in volume of snowball when diameter is 8 cm.
Here,
Volume of sphere, V = 4/3 π r³ = 4/3 π (D/2)³ = 1/6 π D³
Considering differences according to time,
dV/dt = d/dt (1/6 π D³) = 1/6 π × 3D² dD/dt
dV/dt = 1/2 π D² dD/dt
Substituting
D is 8 cm, and the diameter is changing at a rate of 0.2 cm/min.
dV/dt = 1/2 π D² dD/dt
dV/dt = 1/2 × π × 8² × 0.2 = 20.11 cm³/min
Therefore,
Decreasing snowball volume at a rate of 20.11 cm3/min
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given are five observations collected in a regression study on two variables. xi 2 6 9 13 20 yi 7 18 9 26 23 which of the following scatter diagrams accurately represents the data?
The regression equation is y = 0.9x+ 7.5
given that
xi: 2 6 9 13 20
Yi : 7 18 9 26 23
from the given data we have:
∑x = 2+6+9+13+20 = 50
∑y = 7+18+9+26+23 = 83
Also, we need to calculate:
∑xy = 2 × 7+ 6 × 18+ 9× 9+ 13 × 26+ 20×23 = 1001
∑[tex]x^{2}[/tex] = [tex]2^{2}[/tex] + [tex]6^{2}[/tex] + [tex]9^{2}[/tex] + [tex]13^{2}[/tex] + [tex]20^{2}[/tex] = 690
∑[tex]y^{2}[/tex]= [tex]7^{2}[/tex] + [tex]18^{2}[/tex] + [tex]9^{2}[/tex] + [tex]26^{2}[/tex] + [tex]23^{2}[/tex] = 1659
the slope b is calculated:
b = ∑xy - ∑x × ∑y/n ÷ ∑[tex]x^{2}[/tex] - (∑x)^2 /n
now we need to substitute above values in the equation:
b = 1001 - 50×83 /5 ÷ 690 - (50)^2/5
b= 0.9
the y-intercept (a) is :
a = y - bx
where
y = ∑y/n = 83/5 = 16.6
x = ∑x/n = 50/5 = 10
now substitute these values
a = 16.5 - 0.9 × 10
a = 7.5
the regression equation:
y = bx + a
now ,
y = 0.9x+ 7.5
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Find AD . CD = 5x-1 and AD = 4x+8
The numerical side length of length AD is 44 units
How to determine the length AD?From the question, we have the following lengths that can be used in our computation:
AD= 4x + 8
CD = 5x - 1
Also, from the complete question (added at the end of the solution), we understand that
The lengths AD and CD are congruent
These parameters and statements above mean that
AD = CD
Substitute the known values in the above equation, so, we have the following representation
4x + 8 = 5x - 1
Collect the like terms
5x - 4x = 1 + 8
Evaluate the like terms
x = 9
Substitute x = 9 in AD= 4x + 8
AD= 4 x 9 + 8
Evaluate
AD= 44
Hence, the length is 44 units
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Complete question
Given that lengths AD and CD are congruent.
Find AD
CD = 5x-1 and AD = 4x+8
on the grid draw the graph of y= 1- 3x for values of x from -2 to 3
Answer:
see solution
Step-by-step explanation:
equation: y = 1 - 3x
when x is -2:
y = 1 -3 * -2 = y = 1+6 = y = 7
coordinates = (x,y) = (-2,7)
when x is -1:
y = 1-3*-1 = y = 1+3 = y = 4
coordinates = (x,y) = (-1,4)
when x is 0:
y = 1 - 3 * 0 = y = 1-0 = y =1
coordinates = (x,y) = (0,1)
when x is 1
y = 1-3*1 = y = 1-3 = y = -2
coordinates = (x,y) = (1,-2)
When x is 2
y = 1-3*2 = y = 1-6 = y = -5
coordinates = (x,y) = (2,-5)
when x is 3
y = 1-3*3 = y = 1-9 = y = -8
coordinates = (x,y) = (3,-8)
Plot these points on the graph and join up the dots to see the line.
bye
-2(12-2(-4))exponent2
Answer:
6400
Step-by-step explanation:
-2(12-2(-4))^2
Simplify:
-2(10(-4))^2
-2(-40))^2
80^2
6400
How do u make 630 into 6.3?
Answer:
by dividing by 100
Step-by-step explanation:
630 ÷ 100 = 6.3
Victoria purchased 0.6 lbs of deli ham for $4.71. What would it cost to purchase 1.4 lbs of the same ham? please and they solve asap and correct answer please
Using proportions and ratios, the cost of 1.4lbs is $10.96
ProportionsProportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.
This is basically the process of comparing two ratios with one another.
In this problem, we will compare the two ratios and solve for the unknown cost of 1.4lbs
0.6 / 4.71 = 1.4 / x
Cross multiply both sides
x = (4.71 * 1.4) / 0.6
x = 10.96
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calculate a 95% confidence interval for the difference in mean revenue at the box office for drama and comedy movies. let dramas be population 1 and comedies be population 2. write your answer using interval notation and round the interval endpoints to two decimal places.
A 95% confidence interval for the difference in mean revenue at the box office for drama and comedy movies is (7.44, 72.56).
We have given that,
Sample mean of peoples who like drama , x₁-bar = 190
Sample mean of peoples who like comedy,x₂-bar = 150
Sample size for darama sample, n₁ = 17
Sample size for comedy sample, n₂ = 14
Standard deviations, s₁ = 60
Standard deviations, s₂ = 30
Confidence level = 0.95 or 95%
Using Z-table , Z-score for 95% confidence level is 1.96..
We have to calculate a 95% confidence interval for the difference in mean revenue at the box office for drama and comedy movies.
It is given by following Confidence interval formula,
x₁-bar - x₂-bar ± Z ( √(s₁²/n₁ + s₂²/n₂))
= 190 - 150 ± 1.96(√(60²/17 + 30²/14))
= 40 ± 1.96(√3600/17 + 900/14))
= 40 ± 32.56
= (7.44, 72.56)
Hence, the required 95% confidence interval is
(7.44, 72.56) .
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Complete question:
A Hollywood studio believes that a movie that is considered a drama will draw a larger crowd on average than a movie that is considered a comedy. To test this theory. the studio randomy selects several movies that are classified as dramas and several movies that are classified as comedies and determines the box office revenue for. each movie. The results of the survey are as follows. Assurne that the population variances are approximately equal, Calculate a
95%
confidence interval for the difference in mean revenue at the box office for drama and comedy movies: Let dramas be Population-1 and comedies be Population 2. Write your answer using interval notation and round the interval endpoints to two decimal places