Normal Distribution (Standard deviation)
Image attached! Due in 1 hour! please help!
Answers
I don't know what kind of calculator you have at your disposal, so I'll just give one way of computing the sample mean and standard deviation.
• To get the mean, add up all the data points and divide the total by the number of data:
[tex]\bar x = \displaystyle \sum_i \frac{x_i}n = \frac{1243+1264+\cdots+1275}9 \approx 1273.89 \\ \implies \boxed{\bar x \approx 1274}[/tex]
• To get the s.d. s, first compute the variance s² by adding up the squared difference between each of the data points and the sample mean, and divide the total by 1 less than the number of data:
[tex]s^2 = \displaystyle \sum_i \frac{\left(x_i-\bar x\right)^2}{n-1} = \frac{(1243-1274)^2+(1264-1274)^2+\cdots+(1275-1274)^2}8 \approx 1211.61[/tex]
The s.d. is the square root of the variance:
[tex]s^2 \approx 1211.61 \implies s \approx 34.8082 \implies \boxed{s\approx 35}[/tex]
The 90% confidence interval for the sample mean has upper and lower limits, respectively, of
[tex]\bar x \pm \dfrac{\left|Z_{\alpha/2}\right| s}{\sqrt n}[/tex]
(positive root for upper limit, negative root for lower limit)
where [tex]Z_{\alpha/2}[/tex] is the critical value for a (1 - α)×100% confidence level. By critical value, I mean
[tex]\mathrm{Pr}\left[ Z \le Z_c \right] = c[/tex]
where Z is a random variable following the standard normal distribution.
In this case, we have a 90% confidence level, so α = 0.1, and the critical value is [tex]Z_{0.05} \approx -1.64[/tex]. Then the confidence interval has upper limit
[tex]\bar x + \dfrac{\left|Z_{0.05}\right|s}{\sqrt n} = 1274 + \dfrac{1.64 \times 35}{\sqrt9} \approx 1292.97 \approx \boxed{1293}[/tex]
and lower limit
[tex]\bar x - \dfrac{\left|Z_{0.05}\right|s}{\sqrt n} = 1274 - \dfrac{1.64 \times 35}{\sqrt9} \approx 1254.8 \approx \boxed{1255}[/tex]
Related Questions
When a number is decreased by 30 % of itself, the result is 14. What is the number?
Answers
Answer: 20
Step-by-step explanation:
We set up the equation.
Let the number = x
x-0.3*x = 14
0.7x = 14
x = 20
Part A: If (26)X = 1, what is the value of x? Explain your answer. (5 points)
Part B: If (59x = 1, what are the possible values of x? Explain your answer. (5 points)
Answers
Answer: Part A: 1/26 or 0.38
Part B: 1/59 or 0.017
Step-by-step explanation:
how to spell spell spell
Answers
Answer:
Spell spell?
Step-by-step explanation:
Answer:
Reading, using a dictionary and playing online word games are all helpful.
Step-by-step explanation:
read.
Communicate.
Learn.
What is 9 ounces equal to in pounds?
Answers
(i hope this helps!)
9 / 16 = 0.5625
50 PTS!! WILL MARK BRAINLY
Explain why the equation (x-4)^2-28=8 has two solutions. 50 pt
heres what to fill out:
There are 2 solutions because the square root of any ______ number will give us both a ____ and _____ number as a solution .
fill in the blanks
Answers
Answer:
There are 2 solutions because the square root of any positive real number will give us both a positive and negative number as a solution .
Answer:
There are 2 solutions because the square root of any positive real number will give us both a positive and negative number as a solution.
Step-by-step explanation:
[tex](x-4)^2-28=8[/tex]
Add 28 to both sides:
[tex]\implies (x-4)^2=36[/tex]
Square root both sides:
[tex]\implies x-4=\pm 6[/tex]
[tex]\implies x=10, x=-2[/tex]
David has 400 yards of fencing and wishes to enclose a rectangular area against a pre-existing fence. What is the maximum area that David can have?
A. 5000 yd^2
B. 10000 yd^2
C. 15000 yd^2
D. 20000 yd^2
Answer: D
Answers
The maximum area that David can have is 10,000 yd^2
Area of a rectangleThe formula for calculating the area of a rectangle is expressed as:
A = lw
l is the lengthw is the widthIf David has 400 yards of fencing, then;
P = 2(l +w)
400 = 2( l+ w)
200 = l + w
l = 200 - w
Substitute into the area
A = (200-w)w
A = 200w - w^2
If the area is maximized, then;
dA/dw = 0
dA/dw = 200 - 2w
2w =200
w = 100 yards
Recall that;
200 = l + w
l = 200 - 100
l = 100
The maximum area = 100 * 100
The maximum area = 10,000 yd^2
The maximum area that David can have is 10,000 yd^2
Learn more on area of rectangle here: https://brainly.com/question/2607596
concept of pattern in mathematics.
Answers
Step-by-step explanation:
A pattern is a series or sequence that repeats.
Math pattern are sequences to calculate or
solve a problem.
If each car is 16 centimeters long, what is the length of a 15-car train?
Answers
Answer:
yes, 240 cm is equal to 2.4 meters
Step-by-step explanation:
16cm times 15 cars is 240 cm. convert 240 cm to meters equals 2.4, so yes he has enough track for 15 cars on the train.
Answer:
240 cm
Step-by-step explanation:
multiply 16cm by 15 train cars to get 240 cm.
hope this helps and pls mark brainliest
Which number line shows the solution to
11x + 14 < –8?
Answers
Answer:
D
Step-by-step explanation:
11x + 14 < -8
Cancel the addition by subtracting
11x + 14 - 14 < -8 - 14
11x < -22
11x / 11 < -22/11
x < -2
Therefore, the answer is D
Brainliest if correct
Answers
Answer:
w = 9
Step-by-step explanation:
18 + 4w = 6w
6w - 4w = 2w
2w = 18
18/2 = 9
2w/2 = w
w = 9
[tex]\large\textbf{Hey there!}[/tex]
[tex]\large\textbf{18 + 4w = 6w}\\\large\textbf{4w + 18 = 6w}\\\large\text{SUBTRACT 62to BOTH SIDES}\\\large\textbf{4w + 18 - 6w = 6w - 6w}\\\large\text{SIMPLIFY IT!}\\\large\textbf{-2w + 18 = 0}\\\large\text{SUBTRACT 18 to BOTH SIDES}\\\large\textbf{-2w + 18 - 18 = 0 - 18}\\\large\text{CANCEL out: 18 - 18 because it give you 0}\\\large\text{KEEP: 0 - 18 because it help solve for the w-value}\\\large\text{NEW EQUATION: \bf -2w = 0 - 18}\\\large\text{SIMPLIFY IT!}\\\large\textbf{-2w = -18}[/tex]
[tex]\large\text{DIVIDE -2 to BOTH SIDES}\\\mathbf{\dfrac{2w}{-2}= \dfrac{-18}{-2}}\\\large\text{CANCEL out:} \rm\dfrac{-2}{-2}}\large\text{ because it give you 1}\\\large\text{KEEP: }\rm{\dfrac{-18}{-2}}\large\text{ because it gives you the w-value}\\\large\text{NEW EQUATION: \bf w = }\rm{\bf \dfrac{-18}{-2}}\\\large\text{SIMPLIFY IT!}\\\large\textbf{w = 9}\\\\\huge\textbf{Therefore, your answer is: \boxed{\mathsf{w = 9}}}\huge\checkmark[/tex]
[tex]\large\textbf{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Match the base to the corresponding height,
Answers
Step-by-step explanation:
hint base x height
or length x width
Skye's Ice Cream Shoppe is Mario's favorite place to get ice cream. Unfortunately, because he was late arriving there, his friends had already ordered. He did not know what they ordered for him. They told him that it was either a waffle cone or a sundae and that the ice cream flavor was apricot, chocolate, or blackberry .
a. Make a list of all of the possible ice cream orders.
b. What is the probability that Mario will get something with apricot ice cream?
C. What is the probability that he will get a sundae?
d. What is the probability that he will get either something with chocolate or a waffle cone with blackberry?
e. What is the probability that he will get orange sherbet?
Answers
Answer:
a)
apricot waffle conechocolate waffle coneblackberry waffle coneapricot sundaechocolate sundaeblackberry sundaeb) 1/3
c) 1/2
d) 1/2
e) 0
Step-by-step explanation:
a) There are 2 different types of dessert and 3 different ice cream flavors.
Therefore, there are 6 possible ice cream orders:
apricot waffle conechocolate waffle coneblackberry waffle coneapricot sundaechocolate sundaeblackberry sundaeb) There are 2 different desserts with apricot ice cream.
⇒ P(apricot ice cream) = 2/6 = 1/3
c) There are 3 combinations of sundae.
⇒ P(sundae) = 3/6 = 1/2
d) P(chocolate) = 2/6 = 1/3
P(blackberry waffle cone) = 1/6
⇒ P(choc) OR P(BWC) = 1/3 + 1/6 = 1/2
e) P(orange sherbet) = 0
as orange sherbet was not an option!
A bank account earns 2% interest each year. Giselle uses the expression p +0.02p
to find how much money will be in the account after one year if she deposits p dollars.
Answers
Answer:
1.02 is the simplified answer and 102% is the answer to the next one
Step-by-step explanation:
The expression p+0.02p can also be written as 1p+0.02p.
To combine like terms, add the coefficients.
1+0.02=1.02, so 1p+0.02p=1.02p.
I need help solving this problem.
Answers
Answer:
30
Step-by-step explanation:
Let d represent the number of dozens of golf balls ordered. Then 12d is the number of balls.
The cost of the Light Hit balls will be (2.00)(12d). The cost of the Pro Sport balls will be (0.90)(12d). The difference in cost is ...
(2.00)(12d) -(0.90)(12d) = 396.00
1.10d = 33 . . . . . divide by 12, combine terms
d = 30 . . . . . . . divide by 1.10
30 dozen balls of each brand were ordered.
For the following two numbers, find two factors of the first number such that their product is the first number and their sum is the second number.
65,18
Answers
Product of 5 and 13 is 65 and sum of 5 and 13 is 18
Find the volume of a sphere with a diameter of 10 yards
Answers
Answer:
Step-by-step explanation:
diameter = 2 * radius Divide by 2
radius = diameter /2
Formula
Volume_sphere = 4/3 pi r^3
Givens
r = 10 yards
Solution
Volume = 4/3 * 3.14 * 10^3
Volume = 4.1867*10^3
Volume = 4186.7 yards^3
select the correct location on the table. Consider the following equations.f(x)=x^3+3x^2-x-6. g(x)= x^2-3x-2. Approximate the solution to the equation f(x)=g(x) using 3 iterations of successive approximation. Use the graph as a starting point. NO LINKS!!
Answers
Answer:
15/16
Step-by-step explanation:
For the purpose here, we define a starting value as the midpoint of the interval between the integers on either side of the solution. Those integers are 0 and 1, so our starting value for an approximation of x is 1/2.
Each iteration will evaluate the difference f(x)-g(x) at this approximation. If the difference has the sign that matches the difference at the left end of the interval, then the approximation replaces the left end. If the sign matches the difference at the right end, then the approximation replaces the right end. The iteration ends with an approximation that is the midpoint of the new interval.
The attachment shows that our intervals start at [0, 1] and proceed through [1/2, 1], [3/4, 1] to [7/8, 1]. The approximation at the end of the 3rd iteration is x ≈ 15/16.
__
Additional comment
The way this iterative process is defined, the denominator of the n-th approximation will be 2^(n+1). That is, the third iteration will result in a fraction with a denominator of 2^(3+1) = 2^4 = 16, as in 15/16.
As always with repetitive calculations, a graphing calculator or spreadsheet can reduce the work.
OS
Question 2
A circle has a centre C (1,3)The end points of a diameter of the circle are A (-3,2k) and B (5,k)
Find the value of k, k
Answers
Answer:
k = 2
Step-by-step explanation:
We'll need the Midpoint Formula: the midpoint of a segment joining points [tex](x_1, y_1) \text{ and }(x_2, y_2) \text{ is } \left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)[/tex]. In other words, average the x's, then average the y's.
The midpoint of a diameter is the centre of the circle!
The midpoint of the segment joining (-3, 2k) and (5, k) is
[tex]\left(\frac{-3+5}{2}, \frac{2k+k}{2} \right)=\left(1,\frac{2k+k}{2}\right)=\left(1,\frac{3k}{2}\right)[/tex]
That last expression is the centre of the circle; it is the same as (1, 3).
[tex]\left(1,\frac{3k}{2}\right)=\left(1,3\right)\\\frac{3k}{2}=3\\3k=6\\k=2[/tex]
please I'm in urgent need of help. what must be added to make (1/4)x^2-(2/3)xy a perfect square?.
Answers
Answer:
[tex]\bigg(\frac{2}{3} {y} \bigg)^{2}[/tex]
STEP BY STEP EXPLANATION
[tex] \frac{1}{4} {x}^{2} - \bigg( \frac{2}{3} \bigg)xy \\ \\ = \bigg(\frac{1}{2} {x} \bigg)^{2} - 2. \bigg(\frac{1}{2} {x} \bigg)\bigg( \frac{2}{3} y \bigg ) + \bigg(\frac{2}{3} {y} \bigg)^{2} \\ \\ = \bigg(\frac{1}{2} {x} - \frac{2}{3} y\bigg)^{2} \\ [/tex]
To make [tex] \red{\bold{\frac{1}{4} {x}^{2} - \bigg( \frac{2}{3} \bigg)xy}} [/tex] a perfect square we should add [tex]\purple{\bold{\bigg(\frac{2}{3} {y} \bigg)^{2}}}[/tex]
Answer:
[tex]4/9y^2[/tex]Step-by-step explanation:
Given:
[tex](1/4)x^2-(2/3)xy[/tex]Consider the identity:
[tex](a - b)^2=a^2-2ab+b^2[/tex]We can see that:
[tex]a^2=(1/2x)^2[/tex][tex]a = (1/2)x[/tex][tex]2ab = (2/3)xy[/tex]We can work out the value of b:
[tex]2ab = (2/3)xy = 2(1/2x)(2/3y)[/tex][tex]b=(2/3)y[/tex]Then we are missing b², what needs to be added:
[tex]b^2=(2/3y)^2=4/9y^2[/tex]What is the slope of the line that contains the points (1,-1) and (-2, 8)?
Answers
Answer:
Slope= 3/-1 or -3
Step-by-step explanation:
-2-1= 3
8- -1= 9
2. Julia purchases a rectangular plot of land with a perimeter of 90 yards. She knows that the length
of the field is twice the width. Find the dimensions (the length and width) of the field.
Answers
Answer:
sorry I don't know.
Step-by-step explanation:
I don't know but I k ow how you feel
Answer:
The length is 30 and the width is 15
Step-by-step explanation:
i dont really know how i got this. T.T sorry i did it in my head but my answer has ro be right hope this helps
Order the angle measures , , and from least to greatest.
(Note that the figure is not drawn to scale.)
Answers
Mark the theorem below
The angle which measures biggest the opposite side of that angle is biggest.Here
8<10<12JH<IH<JINow
<I < <J < <HAnswer:
least to greatest: ∠I < ∠J < ∠H
Explanation:
angle I:
cosI = [tex]\frac{10^2+12^2-8^2}{2*10*12}[/tex]
I = [tex]cos^{-1} (\frac{3}{4} )[/tex]
I = 41.41°
angle H:
cosH = [tex]\frac{10^2+8^2-12^2}{2*10*8}[/tex]
H = [tex]cos^{-1} (\frac{1}{8} )[/tex]
H = 82.82°
angle J:
cosJ = [tex]\frac{8^2+12^2-10^2}{2*8*12}[/tex]
J = [tex]cos^{-1}(\frac{9}{16} )[/tex]
J = 55.77°
They sum up to 180°, so the steps are correct.
One number exceeds another by 5. The sum of the numbers is 25. What are the numbers?
The numbers are?
Answers
[tex]\bold{\huge{\pink{\underline{ Solution}}}}[/tex]
[tex]\bold{\underline{ Given :- }}[/tex]
The sum of two numbers is 25One number exceeds another by 5[tex]\bold{\underline{ To \: Find :- }}[/tex]
We have to find the two numbers.[tex]\bold{\underline{ Let's \: Begin:- }}[/tex]
Let the number be x
Therefore,
Another number be x + 5
According to the question,
[tex]\sf{ x + ( x + 5 ) = 25}[/tex]
[tex]\sf{ x + x + 5 = 25}[/tex]
[tex]\sf{ 2x + 5 = 25}[/tex]
[tex]\sf{ 2x = 25 - 5}[/tex]
[tex]\sf{ 2x = 20 }[/tex]
[tex]\sf{ x = 20/2}[/tex]
[tex]\sf{ x = 10 }[/tex]
Thus, The first number is 10
Therefore,
Another number will be
[tex]\sf{ = x + 5 }[/tex]
[tex]\sf{ = 10 + 5 }[/tex]
[tex]\sf{ = 15 }[/tex]
[tex]\sf{\red{Hence, \:The \:two \:numbers\: are \:10 \:and\: 15}}[/tex]
"A city official is modeling the demand for bus transportation as a function (,) of two variables:
= price of a daily bus ticket in $, = price of parking per day in a downtown garage in $.
She hypothesizes that demand varies inversely as and directly as 100^2.
Answer the following questions considering that with a daily bus ticket cost of $0.50 and parking price of $6 per day, there are 7,200 bus riders using the bus transportation system.
1. Write the mathematical function describing the demand for bus transportation:
(,) = _"
I'm not sure how to set this up. Also not clear on what "the demand varies inversely as x and directly as 100y^2" means in this context.
Answers
Answer:
Step-by-step explanation:
Your friend is going to buy a used car. The one he is considering costs $4000 and will lose value at a rate of 13% per year. How much less will it be worth in 3 years?
Answers
13% of $4000 is $520
If the $4000 car loses value at a rate of 13% each year for 3 years
$520 x 3 = $1560
Subtract this amount from $4000
$4000 - $1560 = $2440
Answer: In 3 years, the used car will be worth $2440 in 3 years
What is the simplest form of the radical expression?
V2+V5
V2-15
Answers
Sorry,
Neither of these are radical expressions.
Traits of a radical expression:
The radicand is positive. The radical index is as small as possible.The exponent of each factor of the radicand is a natural number less than the radical index.There are no fractions in the radicand.There are no radicals in the denominator of a fraction.
Find the area of the composite figure.
Answers
Answer:
132 square feet
Step-by-step explanation:
The formula for the area of a triangle is 1/2 * b * h. B stands for base and h stands for height. 1/2 multiplied by the base, 10, is 5. We then multiply 5 by 12 which is 60. Let's look at the rectangle now. The area of a rectangle is length by width. The length is 12ft and the width is 6ft. 12 * 6 = 72. 72+60=132 square feet.
pls can u gus tell me the ans and explanation
Answers
Answer:
2325 mL
Step-by-step explanation:
Let x = total volume of the tank. When we fill 4/5 of water into the tank, the amount of water we have can be expressed by 4x/5. Then we only keep 1/3 of that amount (poured away 2/3 of the water), so the amount of water is 4x/15. Thus we set up the equation like this:
4x/15 = 620
4x = 9300
x = 2325
Thus the tank can contain a maximum of 2325 mL.
1)Find the quadratic equation
3(3x [tex] {}^{2} [/tex]+ 1)=12x
2)Find the quadratic equation
[tex]9y {}^{2} - 12y - 14 = 0[/tex]
Answers
Step-by-step explanation:
See picture above for solution.
Find the surface area of the cylinder. Use 3.14 for pi. Do not round the answer.
690.8
224.5
364.8
960.8
Answers
Answer:
690.8
Step-by-step explanation:
I've done this one before
Answer:
690.8 sq units
Step-by-step explanation:
Surface Area(cyl) = 2πrh+2πr²
SA = 2(3.14)(5)(17) + 2(3.14)5²
SA = 6.28(85) + 25(6.28)
= 533.8 + 157
= 690.8