Answer:
0.9719
Step-by-step explanation:
Find the mean and standard deviation of the sampling distribution.
μ = 5.1
σ = 1.1 / √49 = 0.157
Find the z score.
z = (x − μ) / σ
z = (4.8 − 5.1) / 0.157
z = -1.909
Use a calculator to find the probability.
P(Z > -1.909)
= 1 − P(Z < -1.909)
= 1 − 0.0281
= 0.9719
The probability of the randomly used item mean length is greater than 4.8 inches is 0.9719
What is Probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
What is Standard deviation?In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values.
What is Mean?The arithmetic mean is found by adding the numbers and dividing the sum by the number of numbers in the list.
Given,
Mean = 5.1 inches
Standard deviation = 1.1 inches
Sample size = 49
New mean = 4.8
Z score = Difference in mean /(standard deviation / [tex]\sqrt{sample size}[/tex])
Z score = [tex]\frac{4.8-5.1}{1.1/\sqrt{49} }=-1.909[/tex]
Z score = -1.909
Then the probability
P(Z>-1.909)
=1-P(Z>-1.909)
=1-0.0281
=0.9719
Hence, The probability of the randomly used item mean length is greater than 4.8 inches is 0.9719
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Assist Please
show work
Answer:
the profit is $8
Step-by-step explanation:
so Susan started with 0, lost 11, equals -11
earned 18, =7
lost 7, =0
earned 8, =$8 for the final answer
These box plots show daily low temperatures for a sample of days in two different towns.
A
---------------------------------------------------------
Answer: I just took the test and it is D
Mario invested $5100 at 13%
to be compounded daily. What will be the value of Mario's investment in 2 years? Round your answer to the nearest cent, if necessary. Note: 365 days in a year and 30 days in a month.
Answer:
Amount = $6614 and 19 cent
Step-by-step explanation:
Formula for compound interest is
A= p(1+r/n)^(nt)
Compounded daily
So n= 365*2= 730
T= 2
r= 0.13
P= 5100
A= p(1+r/n)^(nt)
A= 5100(1+0.13/730)^(730*2)
A= 5100(1+1.78082*10^-4)^(1460)
A= 5100(1.000178082)^1460
A= 5100(1.2969)
A= 6614.19
Amount = $6614 and 19 cent
For a free lunch giveaway, a restaurant draws 1 card from a bowl of business cards. Val puts in 5 cards. The bowl has 50 cards. What is the probability that Val will win?
Answer:The probability Val will win is 1/5 or 10/50 or 2/10
Step-by-step explanation:
i will give brainliest and 5 stars if you help ASAP
Answer:
[tex] Area = 240 m^2 [/tex]
Step-by-step explanation:
The area of the right triangle above = [tex] \frac{1}{2}*base*height [/tex].
Where,
base = 16 m
height = 30 m
Plug in the above values into the area formula:
[tex] Area = \frac{1}{2}*16*30 [/tex]
[tex] Area = 8*30 [/tex]
[tex] Area = 240 m^2 [/tex]
Refer to the attachment for solution.
p(a) = 0.60, p(b) = 0.20, and p(a and b) = 0.15 what is p(a or b) choices: A. 0.12, B. 0.65, C. 0.40, or D. 0.80 (Note- This is on AP3X)
Answer:
[tex]p(a\ or\ b) = 0.65[/tex]
Step-by-step explanation:
Given
[tex]p(a) = 0.60[/tex]
[tex]p(b) = 0.20[/tex]
[tex]p(a\ and\ b) = 0.15[/tex]
Required
[tex]p(a\ or\ b)[/tex]
The relationship between the given parameters and the required parameters is as follows;
[tex]p(a\ and\ b) = p(a) + p(b) - p(a\ or\ b)[/tex]
Substitute values for the known parameters
[tex]0.15 = 0.60 + 0.20 - p(a\ or\ b)[/tex]
[tex]0.15 = 0.80 - p(a\ or\ b)[/tex]
Collect Like Terms
[tex]p(a\ or\ b) = 0.80 - 0.15[/tex]
[tex]p(a\ or\ b) = 0.65[/tex]
Hence;
[tex]p(a\ or\ b) = 0.65[/tex]
A couple has a total household income of $84,000. The husband earns $18,000 less than twice what the wife earns. How much does the wife earn? Select the correct answer below:
Answer:
$34000
Step-by-step explanation:
We can set up a systems of equations, assuming [tex]h[/tex] is the husbands income and [tex]w[/tex] is the wife's income.
h + w = 84000
h = 2w - 18000
We can substitute h into the equation as 2w - 18000:
(2w - 18000) + w = 84000
Combine like terms:
3w - 18000 = 84000
Add 18000 to both sides
3w = 102000
And divide both sides by 3
w = 34000
Now that we know how much the wife earns, we can also find out how much the husband earns by substituting into the equation.
h + 34000 = 84000
h = 50000
Hope this helped!
a kicker starts a football game by "kicking off". The quadratic function y = -10x^2 + 25x models football's height after x seconds. How long, in seconds, is the football in the air?
Answer: 2.5 seconds
Step-by-step explanation:
x refers to time. Since we want to know how long it is in the air, we need to find the time (x) for the ball to land on the ground (y = 0)
0 = -10x² + 25x
0 = -5x(2x - 5)
0 = -5x 0 = 2x - 5
[tex]0 = x\qquad \dfrac{5}{2}=x[/tex]
x = 0 seconds is when the ball was kicked
x = 5/2 --> 2.5 seconds is when the ball landed on the ground
In 2018, the population of a district was 25,000. With a continuous annual growth rate of approximately 4%, what will the
population be in 2033 according to the exponential growth function?
Round the answer to the nearest whole number.
Answer:
40,000 populationsStep-by-step explanation:
Initial population in 2018 = 25,000
Annual growth rate (in %) = 4%
Yearly Increment in population = 4% of 25000
= 4/100 * 25000
= 250*4
= 1000
This means that the population increases by 1000 on yearly basis.
To determine what the population will be in 2033, we need to first know the amount of years we have between 2018 and 2033.
Amount of years we have between 2018 and 2033 = 2033-2018
= 15 years
After 15 years, the population will have increased by 15*1000 i.e 15,000 more than the initial population.
Hence the population in 2033 will be Initial population + Increment after 15years = 25,000+15000 = 40,000 population.
Many stores run "secret sales": Shoppers receive cards that determine how large a discount they get, but the percentage is revealed by scratching off that black stuff only after the purchase has been totaled at the cash register. The store is required to reveal (in the fine print) the distribution of discounts available. Determine whether the following probability assignment is legitimate?
10% off 20% off 30% off 50% off
a. 0.2 0.2 0.2 0.2
b. 0.5 0.3 0.2 0.1
c. 0.8 0.1 0.05 0.05
d. 0.75 0.25 0.25 -0.25
e. 1 0 0 0
Answer:
b
Step-by-step explanation:
it makes the most senses the lower the discount the higher the chance
) If the half-life of 238Pu is 87.7 yr, write a function of the form =QtQ0e−kt to model the quantity Qt of 238Pu left after t years. Round the value of k to five decimal places. Do not round intermediate calculations.
Answer:
0.079
Step-by-step explanation:
According to the given situation, the calculation of the value of k is presented as follows:
[tex]Q(t)= Q_0e^{-kt}\\\\ 0.5Q_0 = Q_0e^{-k(97.7)}\\\\ 0.5 = e^{-k(87.7)}[/tex]
now,
[tex]k = \frac{In0.5}{-87.7}[/tex]
After solving the above equation we will get the value of k.
= 0.079
Therefore for determining the value of k we simply solve the above equation i.e. by considering all the information mentioned in the question
Answer:
3.5e^-0.0079t
Step-by-step explanation:
None, Good luck mate
A roll of steel is manufactured on a processing line. The anticipated number of defects in a 10-foot segment of this roll is two. What is the probability of no defects in 10 feet of steel
Answer:
the probability of no defects in 10 feet of steel = 0.1353
Step-by-step explanation:
GIven that:
A roll of steel is manufactured on a processing line. The anticipated number of defects in a 10-foot segment of this roll is two.
Let consider β to be the average value for defecting
So;
β = 2
Assuming Y to be the random variable which signifies the anticipated number of defects in a 10-foot segment of this roll.
Thus, y follows a poisson distribution as number of defect is infinite with the average value of β = 2
i.e
[tex]Y \sim P( \beta = 2)[/tex]
the probability mass function can be represented as follows:
[tex]\mathtt{P(y) = \dfrac{e^{- \beta} \ \beta^ \ y}{y!}}[/tex]
where;
y = 0,1,2,3 ...
Hence, the probability of no defects in 10 feet of steel
y = 0
[tex]\mathtt{P(y =0) = \dfrac{e^{- 2} \ 2^ \ 0}{0!}}[/tex]
[tex]\mathtt{P(y =0) = \dfrac{0.1353 \times 1}{1}}[/tex]
P(y =0) = 0.1353
7. Suppose that y varies inversely with x. Write an equation for the inverse variation,
y = 4 when x = 6
A
у
x =
2
B
х
y =
24
с
24
y =
OD y = 2x
Answer:
The answer is
[tex]y = \frac{24}{x} [/tex]Step-by-step explanation:
The statement
y varies inversely with x is written as
[tex]y = \frac{k}{x} [/tex]
where k is the constant of proportionality
To find k substitute the values of x and y into the equation
From the question
y = 4
x = 6
We have
[tex]4 = \frac{k}{6} [/tex]
Cross multiply
k = 4 × 6
k = 24
So the formula for the variation is
[tex]y = \frac{24}{x} [/tex]Hope this helps you
Answer: 5
Step-by-step explanation:
Match the base to the corresponding height.
Base (b)
Height (h)
b
h
h
b
The base 1 is matched with height 2, base 2 is matched with height 3 and base 3 is matched with height 1. The base to the corresponding height is matched in the attached figure.
What is a triangle?Triangle is the closed shaped polygon which has 3 sides and 3 interior angles. The height of the triangle is the dimension of the elevation from the opposite peak to the length of the base.
Thus, the base 1 is matched with height 2, base 2 is matched with height 3 and base 3 is matched with height 1. The base to the corresponding height is matched in the attached figure.
In the given figure, three triangles is shown with base and height. Here,
The base 1 is matched with height 2, as the height shown in figure 2 is the dimension of the elevation from the opposite peak to the length of the base 1.Similarly, base 2 is matched with height 3.Base 3 is matched with height 1.
Thus, the base 1 is matched with height 2, base 2 is matched with height 3 and base 3 is matched with height 1. The base to the corresponding height is matched in the attached figure.
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Yuko added a 15 percent tip when she paid her cab driver. If the fare was $25.50, what was the total amount she paid? A. $28 B. $30 C. $31
Answer:
B. $30
Step-by-step explanation:
First, find the amount of the tip.
Multiply the tip rate and taxi fare.
tip rate * taxi fare
The tip rate is 15% and the taxi fare is $25.50
15% * 25.50
Convert 15% to a decimal. Divide 15 by 100 or move the decimal place two spots to the left.
15/100=0.15
15.0 ---> 1.5 ---> 0.15
0.15 * 25.50
3.825
The tip amount is $3.825
Next, find the total amount she paid.
Add the taxi fare and the tip amount.
taxi fare + tip amount
The taxi fare is $25.50 and the tip amount is $3.825
$25.50 + $3.825
$29.325
Round to the nearest dollar. Typically, this would round down to $29, but that is not an answer choice. So, if we round up, the next best answer is $30.
Therefore, the best answer choice is B. $30
What is the solution to the linear equation?
2/5 + p = 4/5 + 3/5p
Answer:
p = 1Step-by-step explanation:
[tex] \frac{2}{5} + p = \frac{4}{5} + \frac{3}{5} p[/tex]
Multiply through by the LCM
The LCM for the equation is 5
That's
[tex]5 \times \frac{2}{5} + 5p = 5 \times \frac{4}{5} + \frac{3}{5}p \times 5[/tex]
We have
2 + 5p = 4 + 3p
Group like terms
5p - 3p = 4 - 2
2p = 2
Divide both sides by 2
We have the final answer as
p = 1Hope this helps you
What is lim x → 0 e^2x - 1/ e^x - 1
Hello, please consider the following.
[tex]\displaystyle \forall x \in \mathbb{R}\\\\\dfrac{e^{2x}-1}{e^x-1}\\\\=\dfrac{(e^x)^2-1^2}{e^x-1}\\\\=\dfrac{(e^x-1)(e^x+1)}{e^x-1}\\\\=e^x+1\\\\\text{So, we can find the limit.}\\\\\lim_{x\rightarrow 0} \ {\dfrac{e^{2x}-1}{e^x-1}}\\\\=\lim_{x\rightarrow 0} \ {e^x+1}\\\\=e^0+1\\\\\large \boxed{\sf \bf \ =2 \ }[/tex]
Thank you
Which of the following graphs accurately displays a parabola with its directrix and focus?
Answer:
Hey there!
The first graph is the correct answer. A point on the parabola is equally far from the focus as it is to the directrix.
Let me know if this helps :)
The graph that accurately displays a parabola with its directrix and focus is the first graph.
How do we make graph of a function?Suppose the considered function whose graph is to be made is f(x)
The values of 'x' (also called input variable, or independent variable) are usually plotted on horizontal axis, and the output values f(x) are plotted on the vertical axis.
They are together plotted on the point (x,y) = (x, f(x))
This is why we usually write the functions as: y = f(x)
A point shown in the graphs on the parabola is equally far from the focus as it is to the directrix.
Therefore, The first graph is the correct answer.
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A bike wheel. A bike wheel is 26 inches in diameter. What is the bike wheel's diameter in millimeters (1 inch = 25.4 millimeters)?
Answer:
its multiple choice
A. 26inches (1inch/25.4mm)
B. 26inches (25.4mm/1inch)
C. 25.4inches (1mm/26inch)
D. 26inches (1mm/25.4inch)
and its b
On a single toss of a fair coin, the probability of heads is 0.5 and the probability of tails is 0.5. If you toss a coin twice and get heads on the first toss, are you guaranteed to get tails on the second toss? Explain. Yes, since the coin is fair. No, each outcome is equally likely regardless of the previous outcome. Yes, tails will always result on the second toss. No, tails will never occur on the second toss.
Answer:
No, each outcome is equally likely regardless of the previous outcome.
Please answer fast! :)
Answer:
D
Step-by-step explanation:
The fastest way to solve this probelm would be to plug in each x value into these equations untill it outputs the correct two y values.
When you plug 3 into equation D the entire right side it will become.
y-1=0
y=1, which is true.
When you plug 6 into that equation.
y-1=5
y=6 which is also true.
im sorry but the thing is i cant translate these words but the answer is D
Complete each equation with a number that makes it true. 5⋅______=15 4⋅______=32 6⋅______=9 12⋅______=3
Answer: blank 1: 3 Blank 2: 8 blank 3: 1.5 blank 4: 0.25
Step-by-step explanation:
5 times 8=15
4 times 8=32
6 times 1.5=9
12 times 0.25=3
The complete equation is
5⋅____3__=15
4⋅___8___=32
6⋅___1.5___=9
12⋅__0.25____=3
What is Multiplication?Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers. Multiplication is used to simplify the task of repeated addition of the same number.
Multiplication Formula
The multiplication formula is expressed as, Multiplicand × Multiplier = Product; where:
Multiplicand: The first number (factor).Multiplier: The second number (factor).Product: The final result after multiplying the multiplicand and multiplier.Multiplication symbol: '×' (which connects the entire expression)5 * 3=154 * 8=326 * 1.5=912 * 0.25=3Learn more about multiplication here:
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The first step in a mathematical induction proof is to divide by n. (True or False).
Answer:
Step-by-step explanation:
Hello, this is false.
The first step of a mathematical induction proof is to prove the statement for the initial value, which is most of the time for n = 0 or n = 1.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
PLS HELP:Find all the missing elements:
Answer:
b = 9.5 , c = 15Step-by-step explanation:
For b
To find side b we use the sine rule
[tex] \frac{ |a| }{ \sin(A) } = \frac{ |b| }{ \sin(B) } [/tex]a = 7
A = 23°
B = 32°
b = ?
Substitute the values into the above formula
That's
[tex] \frac{7}{ \sin(23) } = \frac{ |b| }{ \sin(32) } [/tex][tex] |b| \sin(23) = 7 \sin(32) [/tex]Divide both sides by sin 23°
[tex] |b| = \frac{7 \sin(32) }{ \sin(23) } [/tex]b = 9.493573
b = 9.5 to the nearest tenthFor cTo find side c we use sine rule
[tex] \frac{ |a| }{ \sin(A) } = \frac{ |c| }{ \sin(C) } [/tex]C = 125°
So we have
[tex] \frac{7}{ \sin(23) } = \frac{ |c| }{ \sin(125) } [/tex][tex] |c| \sin(23) = 7 \sin(125) [/tex]Divide both sides by sin 23°
[tex] |c| = \frac{7 \sin(125) }{ \sin(23) } [/tex]c = 14.67521
c = 15.0 to the nearest tenthHope this helps you
SHALL GIVE BRAINLIEST ANSWER!! A 40% solution of fertilizer is to be mixed with an 80% solution of fertilizer in order to get 80 gallons of a 70% solution. How many gallons of the 40% solution and 80% solution should be mixed? 40% solution =? gallons, 80% solution =? gallons
Answer:
20 gallons of the 40% solution, 60 gallons of the 80% solution
Step-by-step explanation:
Let x = the gallons of the 40% solution, and y = the gallons of a 80% solution. The first thing we want to do here is to convert each percentage into decimal form - including the 70% solution mixture.
40% = 0.40,
80% = 0.80, respectively 70% = 0.70
As you can tell, 0.40 is associated with x gallons, 0.80 is associated with y gallons, and the mixture contains 0.70 [tex]*[/tex] 80 solution, as 0.70 is associated with 80. Therefore we can formulate the following expression,
0.40x + 0.80y = 0.70 [tex]*[/tex] 80
At the same time x + y = 80, as the solution ( mixture ) is present with 80 gallons. Isolating x, x = 80 - y. Let us plug that into our expression, solving for y, following by x gallons.
[tex]0.40\left(\:80\:-\:y\:\right)\:+\:0.80y\:=\:0.70\:\cdot \:80[/tex]
[tex]0.4\left(80-y\right)+0.8y=56[/tex] ( Multiply either side by 10 )
[tex]4\left(80-y\right)+8y=560[/tex] ( Expand )
[tex]320-4y+8y=560[/tex]
[tex]320+4y=560[/tex]
[tex]4y=240[/tex]
[tex]y = \frac{240}{4} = 60[/tex] ( Substitute to solve for x )
[tex]x = 80 - y = 80 - 60 = 20[/tex]
As you can see there are 20 gallons of the 40% solution, and 60 gallons of the 80% solution.
An analyst takes a random sample of 25 firms in the telecommunications industry and constructs a confidence interval for the mean return for the prior year. Holding all else constant, if he increased the sample size to 30 firms, how are the standard error of the mean and the width of the confidence interval affected
Answer:
The standard error decreases and the width of the confidence interval also decreases.
Step-by-step explanation:
The standard error of a distribution (E) is given as:
[tex]E=z_{\frac{\alpha}{2} }*\frac{\sigma}{\sqrt{n} }[/tex]
Where n is the sample size, [tex]z_{\frac{\alpha}{2} }[/tex] is the z score of he confidence and [tex]\sigma[/tex] is the standard deviation.
The sample size is inversely proportional to the standard error. If the sample size is increased and everything else is constant, the standard would decrease since they are inversely proportional to each other. The confidence interval = μ ± E = (μ - E, μ + E). μ is the mean
The width of the confidence interval = μ + E - (μ - E) = μ + E - μ + E = 2E
The width of the confidence interval is 2E, therefore as the sample size increase, the margin of error decrease and since the width of the confidence interval is directly proportional to the margin of error, the width of the confidence interval also decreases.
Let A and B be events. The symmetric difference A?B is defined to be the set of all elements that are in A or B but not both.
In logic and engineering, this event is also called the XOR (exclusive or) of A and B.
Show that P(AUB) = P(A) + P(B)-2P(AnB), directly using the axioms of probability.
Correction:
P(AΔB) = P(A) + P(B) - 2P(AnB)
is what could be proven using the axioms of probability, and considering the case of symmetric difference given.
Answer:
P(AΔB) = P(A) + P(B) - 2P(AnB)
Has been shown.
Step-by-step explanation:
We are required to show that
P(AUB) = P(A) + P(B) - 2P(AnB)
directly using the axioms of probability.
Note the following:
AUB = (AΔB) U (AnB)
Because (AΔB) U (AnB) is disjoint, we have:
P(AUB) = P(AΔB) + P(AnB)..................(1)
But again,
P(AUB) = P(A) + P(B) - P(AnB)...............(2)
Comparing (1) with (2), we have
P(AΔB) + P(AnB) = P(A) + P(B) - P(AnB)
P(AΔB) = P(A) + P(B) - 2P(AnB)
Where AΔB is the symmetric difference of A and B.
Help !!!! Thank you!!!!
Answer:
Option (G)
Step-by-step explanation:
Volume of the real cane = 96 in³
Volume of the model of a can = 12 in³
Volume scale factor = [tex]\frac{\text{Volume of the model}}{\text{Volume of the real can}}[/tex]
= [tex]\frac{12}{96}[/tex]
[tex]=\frac{1}{8}[/tex]
Scale factor of the model = [tex]\sqrt[3]{\text{Volume scale factor}}[/tex]
[tex]=\sqrt[3]{\frac{1}{8}}[/tex]
[tex]=\frac{1}{2}[/tex]
Therefore, scale factor of the model of a can = [tex]\frac{1}{2}[/tex] ≈ 1 : 2
Option (G) will be the correct option.
How many cabinets must he sell to break even?
Answer: He must sell 7 cabinets.
Step-by-step explanation:
So it gives us the equations y= 400x + 1400 and the equations y=600x and to find the break even point we need to set the two equations equal each other to solve for x.
400x + 1400 = 600x
-400x -400x
1400 = 200x
x = 7
Given the set of data: 24, 43, 65, 12, 31, 78, 43, 24, 25, 18, 29, 53, 18, 23, 20, 43, 53, 25 a. Find the mode. b. Find the median. c. Find the mean, to the nearest tenth. d. Find the midrange. e. Find the standard deviation, to the nearest hundredth. f. Determine the quartiles.
Answer: a. 43
b. 27
c. 34.8
d. 45
e. 17.72
f. First quartile = 23
Second quartile = 27
Third quartile =43
Step-by-step explanation:
The given set of data: 24, 43, 65, 12, 31, 78, 43, 24, 25, 18, 29, 53, 18, 23, 20, 43, 53, 25
Arrange in Ascending order:
12 ,18,18 , 20 ,23 ,24 , 24 ,25 , 25 , 29, 31, 43, 43 , 43 , 53 , 53, 65 , 78
Total data points: n= 18 ( even)
a. Mode= Most repeated data value = 43
i.e. mode =43
b. Median = [tex]\dfrac{(\frac{n}{2})^{th}\text{term}+(\frac{n}{2}+1)^{th}\text{term}}{2}[/tex]
[tex]=\dfrac{(\frac{18}{2})^{th}\text{term}+(\frac{18}{2}+1)^{th}\text{term}}{2}\\\\=\dfrac{9^{th}\text{term}+10^{th}\text{term}}{2}\\\\=\dfrac{25+29}{2}\\\\=27[/tex]
i.e. median = 27
c. Mean = (sum of data points)÷n
Sum =12+18+18 + 20 +23 +24 + 24 +25 + 25 + 29+ 31+ 43+ 43 + 43 + 53 + 53+ 65 + 78=627
Mean = 627 ÷ 18 ≈34.8
i.e. Mean = 34.8
d. Mid range = [tex]\dfrac{\text{Maximum value +Minimum value}}{2}[/tex]
[tex]=\dfrac{78+12}{2}\\\\=\dfrac{90}{2}\\\\=45[/tex]
e. Standard deviation =[tex]\sqrt{\dfrac{\sum (x-mean)^2}{n}}[/tex][tex]\sum (x-\mean)^2=(12-34.8)^2+(18-34.8)^2+(18 -34.8)^2+( 20 -34.8)^2+(23 -34.8)^2+(24 -34.8)^2+( 24 -34.8)^2+(25 -34.8)^2+2( 25 -34.8)^2+( 29-34.8)^2+( 31-34.8)^2+( 43-34.8)^2+( 43 -34.8)^2+( 43 -34.8)^2+( 53 -34.8)^2+( 53-34.8)^2+( 65 -34.8)^2+( 78-34.8)^2\\\\=5654.56[/tex]
[tex]\sqrt{\dfrac{5654.56}{18}}=\sqrt{314.1422}\approx17.72[/tex]
f. First quartile = Median of first half (12 ,18,18 , 20 ,23 ,24 , 24 ,25 , 25)
= 23 (middle most value)
Second quartile = Median = 27
Third quartile = Median of second half (29, 31, 43, 43 , 43 , 53 , 53, 65 , 78)
= 43 (middle most value)
