Therefore , the solution of the given problem of probability comes out to be there is a 0.0084 percent chance that a raw number chosen at random will be higher than 96.
What is probability exactly?The primary goal of the designs inside a practice known as criteria is the evaluation of the likelihood that a claim is accurate or that a specific event will occur. Any number between 0 and 1 can be used to represent chance, with 1 usually representing a range level of certainty and 0 typically representing possibility. A probability diagram shows the chance that a specific event will occur. Just the digits 0% and approximately 100% make up the decimal 1, 0, and 0.
Here,
To resolve this issue, we can use the conventional normal distribution. First, we must standardise the 96 number using the following equation:
=> z = (x - μ) / σ
where the mean is, the standard deviation is, and x is the number we're interested in. When we enter the numbers, we obtain:
=> z = (96 - 85) / 4.6 = 2.3913
The area to the right of z = 2.3913 can then be determined using a calculator or a conventional normal distribution table.
The area to the right of 2.39, according to a standard normal distribution chart, is 0.0084. (rounded to four decimal places).
As a result, there is a 0.0084 percent chance that a raw number chosen at random will be higher than 96.
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19 to the -3rd power times 19×19 to the -4th power times nine to the third power using only positive exponents
The simplified expression with only positive exponents is 729 / 19^7.
We can simplify the expression as follows, using the exponent rules:
19 to the -3rd power = 1 / (19^3)
19×19 to the -4th power = (19^2)^-2 = 1 / (19^2)^2 = 1 / (19^4)
nine to the third power = 9^3
Therefore, the expression can be written as:
(1 / (19^3)) × (1 / (19^4)) × (9^3)
To simplify further, we can combine the two terms with powers of 19 into a single term:
(1 / (19^3 × 19^4)) × (9^3) = (1 / 19^7) × (9^3)
Finally, we can evaluate 9^3 to get the final answer:
(1 / 19^7) × (9^3) = (1 / 19^7) × 729 = 729 / 19^7
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The given question is incomplete, the complete question is:
19 to the -3rd power times 19×19 to the -4th power times nine to the third power. Simplify the expression using only positive exponents
Which drawing shows two rays whit the same endpoint?
Two rays with the same endpoint would form an angle, where the common endpoint is the vertex of the angle.
A ray is a part of a line that has a fixed starting point, called the endpoint, and extends infinitely in one direction. Thus, a ray can be thought of as a half-line. If two rays have the same endpoint, they will form an angle. The common endpoint is the vertex of the angle, and the two rays extend outward from the vertex in opposite directions, forming a straight line on one side of the vertex. In mathematical notation, the angle formed by two rays with the same endpoint A can be denoted as ∠BAC, where B and C are the points where the rays extend outwards. Note that the order in which the rays are written matters; ∠BAC and ∠CAB represent different angles.
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What is the volume of a cone the a radius of 5 in. and a height of 7 in. to the nearest tenth of a cubic inch?
How many polygons are in the sixth iteration of this particular fractal expansion? Which formula did you use to determine
this, and why?
In general, you would need to know the number of polygons in the original shape and the rule for how the shape is expanded or repeated in each iteration to calculate the number of polygons in a fractal expansion.
What is fractal expansion ?A fractal is a geometric shape that has intricate detail at arbitrarily small scales and typically has fractal dimensions that rigorously surpass topological dimensions. Several fractals resemble one another at different scales, as shown in the Mandelbrot set's sequential magnifications. Self-similarity, also known as expanding symmetry or unfolding symmetry, is the display of similar patterns at progressively smaller scales; if this replication is precisely the same at every scale, as in the Menger sponge, the shape is referred to as affine self-similar. The academic field of measure theory includes fractal geometry.
Depending on the particular kind of fractal under consideration, a polygon's fractal expansion can be calculated using a specific algorithm. However, the formula will typically entail iteratively transforming the original polygon with geometric operations.
For instance, by continually removing the central triangle from a larger equilateral triangle, the Sierpinski triangle—a well-known fractal—can be created. The remaining triangle is divided into three smaller replicas, which are then put together to make an equilateral triangle at the end of each iteration. The formula below can be used to determine the amount of triangles in each iteration:
the number of triangles in the nth repetition is represented by
Another illustration is the Koch snowflake, which is created by repeatedly dividing each of an equilateral triangle's three sides into two segments and swapping out the middle segment for two segments that also make an equilateral triangle. The following algorithm can be used to determine how many line segments are used in each iteration:
the number of line segments in the nth cycle is represented by L(n).
Generally speaking, the expansion formula for a fractal will rely on the particular rule or algorithm that was used to create the fractal.
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Gracie is rewriting the expression (24 + 40) as an integer times the sum of two integers. By factoring out a 2, she knows she can rewrite the expression as 2 times the sum of two integers. What are all the other numbers greater than 2 that Gracie can factor out of (24 + 40) to rewrite the expression as an integer times the sum of two integers?
Step-by-step explanation:
To rewrite (24 + 40) as an integer times the sum of two integers, Gracie first factored out 2, obtaining:
(24 + 40) = 2 × (12 + 20)
We can check that this is true by distributing the 2:
2 × (12 + 20) = 2 × 12 + 2 × 20 = 24 + 40
Now, Gracie is looking for other numbers greater than 2 that she can factor out of (24 + 40) to rewrite the expression as an integer times the sum of two integers.
One way to approach this is to look for other common factors between 24 and 40. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40. The common factors of 24 and 40 are 1, 2, 4, 8, and the largest factor is 8.
Therefore, Gracie can factor out 4 or 8 to rewrite the expression as an integer times the sum of two integers. For example:
(24 + 40) = 4 × (6 + 10)
(24 + 40) = 8 × (3 + 5)
Note that we can also factor out 1 or 2, but that would not change the expression in any meaningful way.
Noah and his children went into a grocery store and where they sell apples for $1 each and mangos for $2 each. Noah has $20 to spend and must buy at least 9 apples and mangos altogether. If Noah decided to buy 4 apples, determine the maximum number of mangos that he could buy. If there are no possible solutions, submit an empty answer.
Answer:
8 Mangoes
Step-by-step explanation:
Since he decides to buy 4 apples, that would cost him: 4 × $1 = $4
That leaves him: $20 - $4 = $16.
So, how many mangoes can Noah possibly buy with $16?
That is: $16/$2 = 8(We divide by $2 because it is the cost of one mango)
A cylinder and a cone are stacked on top of each other. They both have 2-foot diameters and heights of 9 feet. What is the combined volume, in cubic feet? Ue 3. 14 for
bAnswer:
Step-by-step explanation:
The combined volume of the cylinder and cone with diameters of 2 feet and heights of 9 feet is 42.39 ft3.
The volume of the cylinder and cone can be calculated using the formula V=πr2h. The radius of both is 1 foot and the height of both is 9 feet. Therefore, the volume of the cylinder is Vcylinder = π(1)2(9) = 28.26 ft3. The volume of the cone can be calculated using Vcone = π(1)2(4.5) = 14.13 ft3, where 4.5 is the height of the cone. To calculate the combined volume, add the volumes of the cylinder and the cone: Vtotal = 28.26 + 14.13 = 42.39 ft3.
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Please HELP ASAP Quick
Which are strategies to manage risk that comes with investing?
Spread investments over time
Invest in British pound
Hold your investments for a long time
Diversify your investments
Therefore , the solution of the given problem of unitary comes out to be each asset class as part of the diversification plan.
What is an unitary method?By combining the information obtained using this nanosection technique with all variable additional data from two individuals who used a specific strategy, the task can be completed. Simply put, this mean that, if the desired outcome materialises, either the specified entity will be known or, actually, the colour from both enormous processes will be skipped. For forty pens, a refundable charge of Rupees ($1.01) might be required.
Here,
The next two are methods for reducing the danger associated with investing out of the four you offered:
Dollar-cost averaging is the term used to describe this method of spreading investments out over time. Regardless of the investment's price, it entails making a set amount of investments at regular intervals over a length of time.
Spread your investments across various asset classes (such as stocks, bonds, real estate, etc.) and/or various companies within each asset class as part of the diversification plan.
Since currency values can be influenced by a number of variables and are sometimes unpredictable, investing in a particular currency (such as the British pound) is not always a risk management plan.
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What is the value of the first term in the
sequence below?
Rule:
Start at ?
Add 3 then divide by 2 each time
5
3.5-
4 -3.5
The first term in the given sequence is 5
How to determine the first term in the sequenceFrom the question, we have the following parameters that can be used in our computation:
Rule:
Start at 5Add 3 then divide by 2 each timeThe sequence starting at 5 and following the given rule is:
5(5+3)/2 = 4, (4+3)/2 = 3.5, (3.5+3)/2 = 3.25, (3.25+3)/2 = 3.125, ...The first term in the sequence is simply the starting number, which is 5.
Hence, the value of the first term in the sequence is 5.
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the cube root of 125 is 5. how much larger is the cube root of 126.2? estimate using the linear approximation.
The cube root of 126.2 is approximately 0.016 larger than the cube root of 125.
Linear approximation is a strategy for approximating the values of complicated functions. When a graph is relatively straight, this approximation is quite effective. A linear approximation for a function is a straight line that represents a close approximation of the original function.
The formula to be used is given by
df/dx = (f(x+dx)-f(x))/dx
The first derivative of the cube root of x can be computed as follows:
f(x) = x^(1/3)
df/dx = (1/3)*x^(-2/3)
Using this formula, we can calculate the linear approximation of the cube root of 126.2. This can be done as follows:
f(x + dx) ≈ f(x) + df/dx * dx
In the given case, the f(x) = ∛125 ⇒ 5
Let dx = 126.2 - 125 ⇒ 1.2
Then the linear approximation of the cube root of 126.2 is given by
f(126.2) ≈ f(125) + df/dx * dx
⇒ f(126.2) ≈ 5 + (1/3)*125^(-2/3) * 1.2
⇒ f(126.2) ≈ 5 + 0.016
⇒ f(126.2) ≈ 5.016
Therefore, the cube root of 126.2 is roughly 0.016 greater than the cube root of 125.
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There are 5 cities in a country and any 2 are connected with 1 road that goes straight between them
Using functions we can find that there would be nine roadways for six cities. This is due to the fact that each city must be connected to every other city, and since there are 5 pairs of connected cities, there must be 5 highways.
What is a function?A function is a statement, concept, or rule that establishes an association between two variables.
Functions in mathematics are required for the development of meaningful relationships. If there are more than one dependent values for a particular independent value, then we are aware of this.
In that situation, the relation is not a function. Nevertheless, if there are multiple dependent values for a given independent value.
The relationship is then a function.
Now as per the question,
The remaining 4 cities must then be connected, which requires building an additional 4 roads, for a total of 9.
There would be 12 roadways for 7 cities.
This is due to the fact that each city must be connected to every other city, and since there are 6 pairs of connected cities, there must be 6 highways.
Then, the final five cities must be connected, which requires five more roads, for a total of twelve.
The number of highways for N cities would be N(N-1)/2.
This is because there are N(N-1)/2 pairs of cities that need to be connected, and each city must be connected to every other city.
For instance, if N = 10, 90 highways or 10× 9 = 90 pairs of cities must be connected.
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The complete question is:
There are five cities in a country, and two are connected with one road that goes straight between them. How many roads would be in this country if there were 6 cities? 7 cities? And N cities?
solve x+8=3x wefsdf eferc4frtvtgervgbeg4t
Answer:
x = 4
Step-by-step explanation:
x + 8 = 3x
8 = 2x
x = 4
So, the answer is x = 4
Which expression does not have the same value as −2+3×6/5
a (2 * 9 + 14) / 10
b (5 * 8 - 8) / 10
c (5 * 4 + 12) / 10
d is 5 * 8 / 10 - 8
What’s the lateral and the surface
so let's put the prism upright, Check the picture below.
keeping in mind that for a triangular prism the bases are the triangular parts, so le'ts find the area of those guys
[tex]\stackrel{ \textit{\LARGE Lateral} }{\stackrel{ \textit{Area of the three rectangles} }{(7)(5)~~ + ~~(3)(7)~~ + ~~(4)(7)}}\implies \text{\LARGE 84} \\\\\\ \stackrel{ \textit{\LARGE Total} }{\stackrel{ \textit{Area of the bases} }{2\left[\cfrac{1}{2}(\underset{b}{4})(\underset{h}{3}) \right]}~~ + ~~84}\implies \text{\LARGE 96}[/tex]
Find the area of this triangle
7cm and 3cm as the base,5cm as the side. No height
The area of the triangle is approximately 6.4936 square centimeters.
We can use Heron's formula to find the area of a triangle given the lengths of its sides. Heron's formula states that the area (A) of a triangle with sides a, b, and c is:
A = √[s(s-a)(s-b)(s-c)]
where s is the semi-perimeter of the triangle, defined as:
s = (a + b + c) / 2
Using the values given in the problem, we have:
a = 7 cm, b = 3 cm, c = 5 cm
The semi-perimeter is:
s = (a + b + c) / 2 = (7 + 3 + 5) / 2 = 7.5 cm
Substituting these values into Heron's formula, we get:
A = √[s(s-a)(s-b)(s-c)]
= √[7.5(7.5-7)(7.5-3)(7.5-5)]
= √[7.5(0.5)(4.5)(2.5)]
= √[42.1875]
= 6.4936 cm² (rounded to 4 decimal places)
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Find the value of x.
Answer:
116
Step-by-step explanation:
We can see that the two lines in between the triangle are the same size. This must mean that if we were to move the inner triangle and line it up to the triangle on the edge it must be the same size. We are also told that one of the angles on the side is 116. This means that the value of x must also be 116!
Hope this helps, have a lovely day! :)
7 i - 15= 16 with the way
Answer:
31/7
Step-by-step explanation:
7 i - 15 = 16
1. add 15 to both sides you will get
7i = 31
2. dividing both sides gives us 31/7
3. i = 31/7
what is the maximum value of the probability of a event
The maximum value οf the prοbability οf any event cannοt exceed 1.
What is the maximum value οf the prοbability?The maximum value οf the prοbability οf an event is 1. The prοbability οf an event represents the likelihοοd οr chance that the event will οccur, and it is always expressed as a number between 0 and 1. A prοbability οf 0 means the event is impοssible, while a prοbability οf 1 means the event is certain tο οccur.
Prοbabilities between 0 and 1 represent the degree οf uncertainty οr likelihοοd οf the event. Since the sum οf prοbabilities οf all pοssible οutcοmes is always 1, the maximum value οf the prοbability οf any event cannοt exceed 1.
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a geology class is studying a sample of rock and a sample of dry sponge the rock sample has a mass of 1 x 10¹ kg. The dry sponge sample has a mass of 2x 10⁻³ kg. Which sample has a greater mass? How many times greater?
The sample that has a greater mass is given as follows:
The sample of rock.
The sample of rock has a mass that is 5000 times the mass of the sample of dry sponge.
What is scientific notation?A number in scientific notation is given by the notation presented as follows:
[tex]a \times 10^b[/tex]
With the base being [tex]a \in [1, 10)[/tex], meaning that it can assume values from 1 to 10, with an open interval at 10 meaning that for 10 the number is written as 10 = 1 x 10¹, meaning that the base is 1, justifying the open interval at 10.
To obtain which amount is greater, we must verify the bases when the exponent is the same, hence:
Rock: 1 x 10¹ kg = 10 kg.Sponge: 2 x 10^-3 kg = 0.2 x 10^-2 kg = 0.02 x 10^-1 kg = 0.002 kg.Hence the rock has the greater mass, and the ratio is given as follows:
10/0.002 = 5000.
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help please I really appreciate it
Answer:
Quadratic Function, Second Difference
rohan had 36 pens . he gave 15 of them to mike and 11 of them to karan . what fraction of his original 36 pens does rohan have left ? write two equivalent fractions for that amount ?
Answer: 10/36 or 5/8
Step-by-step explanation:
Let’s start by solving how many pens Rohan has left. 36-11-15=36-26=10. Rohan has 10 pens left. Now to solve the fraction of pens Rohan has left, we divide our 10 by 36, or 10/36. Another fraction of this could be 5/18, because both the denominator and numerator have 2 as a factor.
Rani and her friends are raking leaves as a part of a school service project. The regular price
of the supplies they need is $60, but the store manager is giving them a 20% discount. Rani
wants to know the sale price of the supplies.
What percent represents the regular price of
the supplies
Answer:
Sale Price-$48 What Percent Represents the reg. Price?-%100
Step-by-step explanation:
20% of 60 is 12, so if supplies are 20% off, they are $12 off, so 60 - 12 =48.
And if the regular price is $60, then $60 is the whole price, a.k.a. 100% of the price. So, the percent that represents the regular price of supplies is 100%.
Please Help me
QUESTION 9
x
0246
8
10
12
24
14
*****
y
9
9
10
11
11
12
13
13
I
[1.5 darks] Given the (x, y)-data as shown in Table below
Find the best line model for the data
and find the correlation coefficient r.
Solution. Please write your
detailed solution here, You can
also put some needed information
in the Table above:
Answer:
To find the best line model for the data, we will use linear regression analysis.
First, we need to calculate the mean of x and y:
mean of x = (0 + 2 + 4 + 6 + 8 + 10 + 12 + 24 + 14) / 9 = 8
mean of y = (9 + 9 + 10 + 11 + 11 + 12 + 13 + 13 + 14) / 9 = 11
Next, we need to calculate the deviations of x and y from their respective means:
deviation of x = x - mean of x
deviation of y = y - mean of y
x y deviation of x deviation of y (deviation of x)^2 deviation of x * deviation of y
0 9 -8 -2 64 16
2 9 -6 -2 36 12
4 10 -4 -1 16 4
6 11 -2 0 4 0
8 11 0 0 0 0
10 12 2 1 4 2
12 13 4 2 16 8
24 13 16 2 256 32
14 14 6 3 36 18
Then, we can calculate the slope (b) of the best-fit line using the formula:
b = sum of (deviation of x * deviation of y) / sum of (deviation of x)^2
b = (16 + 12 + 4 + 0 + 0 + 2 + 8 + 32 + 18) / (64 + 36 + 16 + 4 + 0 + 4 + 16 + 256 + 36) = 0.190
Next, we can calculate the y-intercept (a) of the best-fit line using the formula:
a = mean of y - b * mean of x
a = 11 - 0.190 * 8 = 7.48
Therefore, the equation of the best-fit line is:
y = 0.190x + 7.48
Finally, we can calculate the correlation coefficient (r) using the formula:
r = sum of (deviation of x * deviation of y) / (sqrt(sum of (deviation of x)^2) * sqrt(sum of (deviation of y)^2))
r = (16 + 12 + 4 + 0 + 0 + 2 + 8 + 32 + 18) / (sqrt(64 + 36 + 16 + 4 + 0 + 4 + 16 + 256 + 36) * sqrt(16 + 16 + 1 + 0 + 0 + 1 + 4 + 4 + 1)) = 0.905
Therefore, the best-fit line for the given data is y = 0.190x + 7.48, and the correlation coefficient is r = 0.905.
Step-by-step explanation:
14) The Sum of Two number is 18. The sum of the squaries of numbers is 194. find the numbers
Answer:
5 and 13
Step-by-step explanation:
given the first number is x and the second number is y
then x + y = 18 => y = 18 - x
also
x^2 + y^2 = 194
substitute
x^2 + (18 - x)^2 = 194
x^2 + x^2 - 36x + 324 = 194
2x^2 - 36x + 130 = 0
2(x^2 - 18x + 65) = 0
x^2 - 18x + 65 = 0/2
x^2 - 13x - 5x + 65 = 0
x(x - 13) - 5(x - 13) = 0
(x - 13)(x - 5) = 0
=> x - 13 = 0 => x = 13
=> x - 5 = 0 => x = 5
if x = 13, y = 18 - 13 = 5
if x = 5, y = 18 - 5 = 13
so x and y can be either 5 and 13
Find the distance between the points (-3, -6) and (1, -2).
Answer:
4*sqrt(2)
Step-by-step explanation:
To find the distance between two points, we use the distance formula, which is the following:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
Plugging in the values for the given points, we get the following:
d = sqrt((1 - (-3))^2 + (-2 - (-6))^2)
= sqrt((1 + 3)^2 + (-2 + 6)^2)
= sqrt(4^2 + 4^2)
= sqrt(32)
= 4*sqrt(2)
Therefore, the distance between the points (-3, -6) and (1, -2) is 4*sqrt(2).
Stats and probability find E
If VAR[-4X+5]=13 and E[X]=2.5, find E[(X-3)^2]
(a) 1.06
(b) -3.00
(c) -1.75
(d) 3.06
If VAR[-4X+5]=13 and E[X]=2.5, so E[(X-3)²] will be 1.06. The correct answer is A
We have VAR[-4X+5] = 13, which means VAR[-4X] = 13 since VAR[c] = 0 for any constant c, and VAR[aX] = a² VAR[X] for any constant a.
So we have:
VAR[-4X] = (-4)² VAR[X] = 16 VAR[X] = 13
Solving for VAR[X], we get:
VAR[X] = 13/16
Now, we want to find E[(X-3)^2]:
E[(X-3)²] = E[X² - 6X + 9]
= E[X²] - 6E[X] + 9 (by linearity of expectation)
We can use the formula VAR[X] = E[X²] - (E[X])² to solve for E[X²]:
VAR[X] = E[X²] - (E[X])²
13/16 = E[X²] - (2.5)²
E[X²] = 13/16 + 6.25
E[X²] = 7.31
Therefore, we have:
E[(X-3)²] = E[X²] - 6E[X] + 9
= 7.31 - 6(2.5) + 9
= 1.06
So the answer is (a) 1.06.
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Two marathon training procedures are tried for comparison purposes. Their efficacy is to be determined in a marathon race. Assume race times are given in minutes. The following results were observed: The data is given below. Procedure-1 Procedure-2
149 166
131 160
159 166
139 181
131 165
160 160
151 149
153 140
157 175
136 167
138 187
152 152
153 188
155 188
145 176
145
174
171
163
189
178
185 157
183
166
178 (a) Do the populations appear to be normal? Hint: use a probability plot to decide and an α
=
0.05
A. Yes, Both procedure A and procedure B appear to be normal
B. Yes, procedure B appears to be normal but procedure A does not appear to be normal
C. No, Both procedure A and procedure B appear to be normal
D. Yes, Both procedure A and procedure B appear to be non-normal
E. No, neither procedure A appears to be normal nor procedure B appears to be normal
F. Yes, procedure A appears to be normal but procedure B does not appear to be normal
(b) Using technology available to you, test to see if the variances are equal or not?
A. There appears to be more variation in the 2nd procedure than in the 1st.
B. They appear to be equal.
C. There appears to be more variation in the 1st procedure than in the 2nd.
D. There appears to be an unequal amount of variation in the 2nd procedure than in the 1st.
(c) Report the p-value of the test you ran in (b)(this is from Levene's te
a) E
b) C
c) p-value 0.03 significant difference in two procedures
A. No, neither procedure A appears to be normal nor procedure B appears to be normal
B. There appears to be more variation in the 1st procedure than in the 2nd.
C. The p-value of the test is 0.03, which indicates that there is a statistically significant difference in the variances of the two procedures.
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What is the measures
Answer:
<COA MESURES = 61
<AOH MESURES = 46
<HOG MESURES = 73
<FOE MESURES = 73
Step-by-step explanation:
i need help solving this
An airline knows that over the long run 90% of passengers who reserve seats show up for their flight. On a particular flight with 300 seats, the airline accepts 324 reservations. Assuming that passengers show up independently, what is the chance that the plane will be overbooked? (hint: think binomial)
Using this formula, we can calculate that the chance that the plane will be overbooked is 35.1%. This means that there is a 35.1% chance that more than 300 passengers will show up for the flight despite the airline only having 300 seats.
The chance that a plane will be overbooked is calculated using a binomial probability formula. The formula is P(x) = nCx * p^x * (1 - p)^(n - x), where n is the number of trials (in this case, 300), x is the number of successes (in this case, 324 reservations), and p is the probability of success (in this case, 90%).
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