a) A large hotel in Miami has 900 rooms (all rooms are equivalent). During Christmas, the hotel is usually fully booked. However, as it is possible for a customer to cancel their reservation, the hotel overbooks its rooms. 1000 people were given assurance of a room. Let us assume that each customer cancels their reservation with a probability of 0.1. If the total number of customers who still keep their booking is more than 900, the hotel has to unfortunately send some customers to other accommodation. What is the probability that this happens, as per the Central Limit Theorem
Answers
Answer:
14.69% probability that this happens
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)
1000 people were given assurance of a room.
This means that \(n = 1000\)
Let us assume that each customer cancels their reservation with a probability of 0.1.
So 0.9 probability that they still keep their booking, which means that \(p = 0.9\)
Probability more than 900 still keeps their booking:
\(n = 1000, p = 0.9\)
So
\(\mu = 0.9, s = \sqrt{\frac{0.9*0.1}{1000}} = 0.0095\)
901/1000 = 0.91
So this is 1 subtracted by the pvalue of Z when X = 0.91.
\(Z = \frac{X - \mu}{\sigma}\)
By the Central Limit Theorem
\(Z = \frac{0.91 - 0.9}{0.0095}\)
\(Z = 1.05\)
\(Z = 1.05\) has a pvalue of 0.8531
1 - 0.8531 = 0.1469
14.69% probability that this happens
Related Questions
Please help before 7 min
Answers
Answer:
The Value of x = 23.1 unit
Step-by-step explanation:
Given:
Parallel line intersect
Find:
The value of "X"
Computation:
We know that given lines are parallels
So, by using Ratio theorem we can find the value of "x"
Ratio theorem of parallel lines say
AB / BC = AD / DE
So,
14 / 20 = x / 33
x = [14 x 33] / 20
The Value of x = 23.1 unit
PLEASE I NEED THE ANSWER TO 1 + 1
Answers
Answer:
uhhhhh 3
Step-by-step explanation:
Step-by-step explanation: I know, hardest question known to man.
Match the prompts together.
Answers
When matched, the prompts on asymptotes would be:
Vertical asymptote at x=0: The cost of producing pills can never reach 0.Decreasing on (0,∞): As the number of pills produced gets smaller, the average cost of production greatly increases.Horizontal asymptote at y=0: The cost of producing pills cannot be negative.Positive on (0,∞): As more pills are produced, the average cost per pill decreases.How to match the asymptote statements ?The presence of a vertical asymptote at x=0 signifies that the cost of producing pills can never reach a value of 0, remaining persistently positive. Simultaneously, the horizontal asymptote at y=0 serves as a reassuring indication that the cost of producing pills cannot be negative, as it steadfastly remains at or above zero.
This crucial constraint ensures that the cost incurred in the pill production process is always a non-negative quantity. Consequently, the prompt related to the impossibility of negative costs aligns with this notion.
Find out more on horizontal asymptote at https://brainly.com/question/1851758
#SPJ9
help please quickly and give explanation
Answers
Answer:
Because y is a common variable, we can assume that they are equal to each other.
Mr. Nelson is checking some of the school's sport balls to make sure they are in good shape and
properly inflated. Use the table of recommended air pressures to define the ranges for properly inflated
balls.
Ball
Average recommended psi Tolerance
(pounds per square inch)
Soccer ball 12.05
+3.55
Basketball 8.00
+0.5
I
Volleyball
4.44
+0.18
Part I: Write an absolute value inequality for the recommended air pressure range for each type of ball.
Use the variable x for the ball's actual air pressure. (3 points)
Answers
Answer:
Step-by-step explanation:
Hello!
The variable of interest is
X: air pressures of properly inflated sports balls.
Average recommended psi Tolerance
(pounds per square inch)
Soccer ball 12.05 ±3.55
Basketball 8.00 ±0.5
Volleyball 4.44 ±0.18
Each recommendation is expressed like the "average air pressure" ± "standard deviation of the recommended air pressure" so if you express it in inequality it will be:
X[bar]-S ≤ X ≤ X[bar]+S
So for each ball type, you can write it as:
Soccer ball
12.05-3.55 ≤ X ≤ 12.05+3.55
8.5 ≤ X ≤ 15.6
Basketball
8.00-0.5 ≤ X ≤ 8.00+0.5
7.5 ≤ X ≤ 8.5
Volleyball
4.44-0.18 ≤ X ≤ 4.44+0.18
4.26 ≤ X ≤ 4.62
I hope this helps!
Answer:
Step-by-step explanation:
This is what I got!
Part I:
Soccer ball: | x – 12.05 | ≤ 3.55
Basketball: | x – 8 | ≤ 0.5
Volleyball: | x – 4.44 | ≤ 0.18
Part II:
Basketball: | x – 8 | > 0.5
Part III:
Basketball:
| x – 8 | ≤ 0.5
x – 8 ≤ 0.5
x ≤ 8.5
x – 8 ≥ 0.5
x ≥ 7.5
7.5 ≤ x ≤ 8.5
The triangle above has the following measures.
m
a=7.5 y
Use the 45-45-90 Triangle Theorem to find the length of the hypotenuse. Include correct units.
Show all your work.
Answers
The length of the hypotenuse is 10.61 yd.
We have,
The sum of the angles in a triangle = 180
Now,
Two angles are 45.
This means,
The side opposite to angle 45 are equal.
So,
a = c
And,
a = 7.5 yd
Now,
Applying the Pythagorean theorem.
b² = a² + c²
b² = 7.5² + 7.5²
b² = 112.5
b = √112.5
b = 10.61
Thus,
The length of the hypotenuse is 10.61 yd.
Learn more about triangles here:
https://brainly.com/question/25950519
#SPJ1
Find the segment length indicated. Assume the lines which appear to be
tangent are tangent. The center is marked.
6.6
6.6
O 16.9
O 8.9
O 10.2
O 11.2
Answers
The whole number m is a term in an arithmetic sequence with common difference 2. Show that the sum of the term m and the next two terms is a multiple of 3, no matter what the value of m.
Answers
Answer:
S
ThenSn=n(a1+an)2Sn=n(a1 + an)2 , where nn is the number of terms, a1a1 is the first term and anan is the last term. The sum of the first nn terms of an arithmetic sequence is called an arithmetic series .
Step-by-step explanation:
A tank is full of water. Find the work (in ft-lb) required to pump the water out of the spout. Use the fact that water weighs 62.5 lb/ft3. (Round your answer to the nearest whole number.) 3 ft6 ft12 ft A frustum of a cone with a spout is given. The smaller radius is 3 ft, the larger radius is 6 ft, and the height is 12 ft.
Answers
The work required to pump the water out of the spout is approximately 64,307,077 ft-lb
To find the work required to pump the water out of the spout, we need to calculate the weight of the water in the tank and then convert it to work using the formula: work = force × distance.
First, let's calculate the volume of water in the tank. The frustum of a cone can be represented by the formula: V = (1/3)πh(r1² + r2² + r1r2), where r1 and r2 are the radii of the two bases and h is the height.
Given r1 = 3 ft, r2 = 6 ft, and h = 12 ft, we can calculate the volume:
V = (1/3)π(12)(9 + 36 + 18) = 270π ft³
Now, we can calculate the weight of the water using the density of water:
Weight = density × volume = 62.5 lb/ft³ × 270π ft³ ≈ 53125π lb
Next, we convert the weight to force by multiplying it by the acceleration due to gravity (32.2 ft/s²):
Force = Weight × acceleration due to gravity = 53125π lb × 32.2 ft/s² ≈ 1709125π lb·ft/s²
Finally, we can calculate the work by multiplying the force by the distance. Since the water is being pumped out of the spout, the distance is equal to the height of the frustum, which is 12 ft:
Work = Force × distance = 1709125π lb·ft/s² × 12 ft ≈ 20509500π lb·ft ≈ 64307077 lb·ft
for more search question water
https://brainly.com/question/17120212
#SPJ8
QUESTION 1
Use the sine rule to find x. Rationalise and leave your answer in surd form; a+b√c
Use special angles where Sine 30 = and sine 45 = 2x-1 45 2x + 2 30
Answers
It can be seen that x = (3 ± √(9 + 32√3)) / 8, which can be expressed in surd form as (3 + √(9 + 32√3)) / 8 or (3 - √(9 + 32√3)) / 8.
How to solveTo find x using the sine rule, we need to solve the equation:
sine(45) / x = sine(30) / (2x + 2√3)
Simplifying this equation, we have:
(2x - 1) / x = 1 / (2x + 2√3)
Cross-multiplying and simplifying further, we get:
(2x - 1)(2x + 2√3) = x
Expanding the brackets, we have:
\(4x^2 + 4\sqrt3x - 2x - 2\sqrt3 = x\)
Rearranging the terms and simplifying, we get:
\(4x^2 - 3x - 2\sqrt3 = 0\)
Using the quadratic formula, we can solve for x:
x = (-(-3) ± √((-3)^2 - 4(4)(-2√3))) / (2(4))
x = (3 ± √(9 + 32√3)) / 8
Therefore, x = (3 ± √(9 + 32√3)) / 8, which can be expressed in surd form as (3 + √(9 + 32√3)) / 8 or (3 - √(9 + 32√3)) / 8.
Read more about sine rule here:
https://brainly.com/question/20839703
#SPJ1
I need help no one helps me never
Answers
if I choose two cards, one of the time, from a standard deck of cards, what’s my probability that I choose A red card, then without putting it back to a black card
Answers
Answer:
P(Red) = 26/52, P(Black) = 26/51
Step-by-step explanation:
There are 26 red cards and 26 black cards in a standard deck of 52 cards.
This means the probability of picking a red card from the deck is 26/52.
Now, since we are taking out the red card after drawing from the deck, we only have 51 cards. Therefore, the probability of picking a black card from the deck is 26/51.
There are 120 people in a sport centre.
78 people use the gym.
46 people use the swimming pool.
45 people use the track.
21 people use the gym and the pool.
16 people use the pool and the track,
24 people use the gym and the track.
9 people use all three facilities,
Given that a randomly selected person uses at least two facilities, what is the probability they
use all the facilities?
Answers
Answer:
43/120 ≈ 0.3583
Step-by-step explanation:
Adding up the folks who use two facilities counts the folks who use all three 3 times. So, the number who use two or more facilities is ...
21 +16 +24 -2(9) = 43 . . . . people who use 2 or more facilities
The probability that a person chosen randomly from the 120 at the sports center uses at least 2 facilities is ...
43/120 ≈ 0.3583
_____
The given numbers add up as follows:
Gym only: 42
Pool only: 18
Track only: 14
Gym and Pool only: 12
Gym and Track only: 15
Pool and Track only: 7
Gym and Pool and Track: 9
No facilities: 3
To emphasize the slow increase in sales, it would be best for Samantha to use graph B or graph A for her presentation
Answers
Answer:
Graph A
Step-by-step explanation:
As can be seen, the trend in graph A is increasing with each month but not seemingly by as much as graph B;
This is because the scale of the y-axis in graph B has smaller increments;
This creates the impression of a slow increase in sales even though the data in both graphs is actually the same.
Answer: graph A.
appear to increase less.
Step-by-step explanation:
help please due todayyyyy
Time Remaining: 49 minutes
Answers
Answer:
a.
Step-by-step explanation:
Find the value of X for the triangle (Show all work, triangle and equations in picture)
Answers
Answer:
\(x=5\)
Step-by-step explanation:
The perimeter of a figure is the sum of all its sides.
The sides are x, (x+3), and (2x). The perimeter is 23, so the sum of the expression equates to 23. Thus:
\(x+(x+3)+(2x)=23\)
Combine like terms:
\(4x+3=23\)
Subtract 3 from both sides:
\(4x=20\)
Divide both sides by 4:"
\(x=5\)
And we're done!
Write the equation in vertex form of the parabola with the vertex (-4,-4) that goes through the point (-2,-16)
Answers
Answer:
\( - 3(x + 4) {}^{2} - 4\)
Step-by-step explanation:
Vertex form is
\(a(x - h) {}^{2} + k = f(x)\)
We know that h and k are both -4. Let x be -2 and y be -16.
\(a( - 2 + 4) {}^{2} - 4 = - 16\)
\(a(2) {}^{2} - 4 = - 16\)
\(4a - 4 = - 16\)
\(4a = - 12\)
\(a = - 3\)
So the equation in vertex form is
\( - 3(x + 4) {}^{2} - 4\)
(88)(√75)
HELP ASAP....
Answers
Answer:
sqr75=sqr25*sqr3=5*sqr3
88(5*sqr3)
decimal = 762.10235533
Answer:
440√3Step-by-step explanation:
Given:
88√75Solution:
88•√(5^2 * 3)Rewrite the expression as:
88•(5√3)Multiply 88 into 5:
440√3762.102 ( 3 decimal place )Point E has the same y-coordinate as point D, but the x-coordinate of point E is the opposite of the x-coordinate of point D.
Answers
The coordinate of point D and point E will be (x, y) and (-x, y), respectively.
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line in the m:n ratio, finding the mid-point of the line, etc.
Let the coordinate of the point D be (x, y).
Point E has a similar y-coordinate as point D. Then the ordinate of the points will be the same.
And the x-direction of point E is something contrary to the x-direction of point D. Then the coordinate of point E will be (-x, y).
The coordinate of point D and point E will be (x, y) and (-x, y), respectively.
More about the coordinate geometry link is given below.
https://brainly.com/question/1601567
#SPJ1
Gameron wants to measure a poster frame, but he only has a sheet of
paper that is 8 1/2 by 11 inches
a.
He lays the long edge of the paper along the long edge of the frame several times
and finds the frame is 4 papers long. How long is this in inches?
In feet?
b.
He lays the short edge of the paper along the short edge of the frame several times
and finds the frame is 3 papers wide. How long is this in inches?
In feet?
plsss help!
Answers
The measure of the frame in feet of the length and width are 3.667 feet and 2.125 feet respectively.
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given here: The measure of the frame is 8.5 inches and 11 inches
a) if the frame is 4 papers long then we have the length of the frame as
11×4=44 inches (since he lays the paper along the edge of frame)
We know 1 inch= 0.0833 foot
Thus 44 inches= 3.66667 foot
b) Again if he lays the paper along the short edge than the width of the frame is 3×8.5=25.5 inches
∴25.5 inches= 2.125 feet
Hence, The measure of the frame in feet of the length and width are 3.667 feet and 2.125 feet respectively.
Learn more about the unitary method here:
https://brainly.com/question/22056199
#SPJ1
A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window. What is the maximum area of a Norman window whose perimeter is 9 feet?
Answers
The maximum area of a Norman window with a perimeter of 9 feet is 81π/4 square feet.
To find the maximum area of a Norman window with a given perimeter, we can use calculus. Let's denote the radius of the semicircle as r and the height of the rectangular window as h.The perimeter of the Norman window consists of the circumference of the semicircle and the sum of all four sides of the rectangular window. Therefore, we have the equation:
πr + 2h = 9We also know that the area of the Norman window is the sum of the area of the semicircle and the area of the rectangle, given by:
A = (πr^2)/2 + rh
To find the maximum area, we need to express the area function A in terms of a single variable. We can do this by substituting r from the perimeter equation:
r = (9 - 2h)/(π)
Now we can rewrite the area function in terms of h only:
A = (π/2) * ((9 - 2h)/(π))^2 + h * (9 - 2h)/(π)
Simplifying this equation, we get:
A = (1/2)(9h - h^2/π)
To find the maximum area, we differentiate the area function with respect to h, set it equal to zero, and solve for h:
dA/dh = 9/2 - h/π = 0
Solving this equation, we find:h = 9π/2
Substituting this value of h back into the area function, we get:
A = (1/2)(9 * 9π/2 - (9π/2)^2/π) = (81π/2 - 81π/4) = 81π/4
Therefore, the maximum area of a Norman window with a perimeter of 9 feet is 81π/4 square feet.
Learn more about area here:
https://brainly.com/question/2607596
#SPJ8
PLEASE HEEEEEEEEELLLLLLLLLPPPPPPP WILLING TO GIVE BRAINLIEST.
Answers
Answer:
Maria is 5
Steve is 2
Steve
Step-by-step explanation:
10/2=5
6/3=2
10.43=s-7.52 solve for s
Answers
Explanation: have a nice day/night :)
10 . 43 = S - 7.52
S = 17.95
If y varies inversely as x and y= 24 when x = 4. find y when x = 3.
A. 32
B. 18
C. 2
D. 288
Answers
Answer:
A. 32
Step-by-step explanation:
y varies inversely as x
y = k/x
-------------------------
y = 24 when x = 4
find k, the constant of variation
24 = k/4
multiply both sides by 4
96 = k
----------------------------
find y when x = 3
using k = 96
y = 96/3
y = 32
An insect population in a lab has 2 ¹² insect. If the population double how many insect will be there?
Answers
Answer:
8192
Step-by-step explanation:
2 ¹²= 4096
4096 x 2 = 8192
answer this for me pls
Answers
Answer:
Slope = 2
Step-by-step explanation:
Find the slope by using the slope equation:
\(\frac{y^2 - y^1}{x^2 - x^1}\)
Plug in the numbers to the slope equation:
\(\frac{8 - (-8)}{2 - (-6)}\)
Which is equal to:
\(\frac{16}{8}\)
Which is simplified to:
2.
What is the next number in the sequence 3,5,8,12,17?
Answers
Answer:
it would be 23
Step-by-step explanation:
5-3=2
5-8=3
12-8=4
17-12=5
23-17=6
What function represents this graph
Answers
Answer:
f(x) = 10^x -4
Step-by-step explanation:
The horizontal asymptote of this exponential function is at y=-4, so there is a vertical translation of -4 added to the function. That is, the function is expected to be of the form ...
y = a·b^x -4
The graph crosses 1 unit above the horizontal asymptote at x=0, so there is no horizontal translation. Effectively, a=1 in the above equation.
The graph crosses 10 units above the horizontal asymptote at x=1, so the base of the exponent is b = 10.
The function appears to be ...
f(x) = 10^x -4
With your team, create a piecewise-defined function with at least three “pieces.” The function does not need to be a step-function with horizontal line segments, but it needs to meet the definition of a function. Make a table and a graph for your function, and write an equation for each part. Be sure to state the domain for each part, as well as the domain for the whole function.
Answers
On solving the provided question we can say that The following is the data table of the function.
what is function?The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.
here,
the provided functions that can be formed are
x -infinity < x < -10
f(x) = 2x + 10 -10 < x < 10
4X - 10 10 < x < infinty
The following is the data table of the function.
x y
-20 -20
-15 -15
-10 -10
-5 0
0 10
5 20
10 30
15 50
20 70
To know more about function visit:
https://brainly.com/question/28193995
#SPJ1
An example of the piecewise defined function is: \(f(x)= \begin{cases}x & -\infty < x \leq-10 \\ 2 x+10 & -10 < x \leq 10 \\ 4 x-10 & 10 < x < \infty\end{cases}\)
what is function?The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output.
A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or range.
Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.
The following is the data table of the function.
x y
-20 -20
-15 -15
-10 -10
-5 0
0 10
5 20
10 30
15 50
20 70
The provided functions that can be formed are
\(f(x)= \begin{cases}x & -\infty < x \leq-10 \\ 2 x+10 & -10 < x \leq 10 \\ 4 x-10 & 10 < x < \infty\end{cases}\)
To know more about function visit:
brainly.com/question/28193995
#SPJ1
cultural anthropologists distinguish between ideal behavior (what people are expected to do) and real behavior (what people actually do)
Answers
Because cultural anthropologists are studying culture as it is and not as it would like it to be, anthropologists are concerned with actual behavior as opposed to ideal behavior.
A given group's social behavior, customs, achievements, and values are collectively referred to as its culture. It is the only thing that unites everyone in a society, regardless of country, social class, ethnicity, or religion. These things can be both material and immaterial, such as the importance of family or the customary dishes of a culture.
Anthropologists are unable to gather data with accuracy when people idealize their actions in front of them. Their entire study may be in jeopardy if they use false data.
Real culture is defined as the observed and quantified values, customs, and beliefs of a particular civilization. There may be a right and incorrect way to accomplish something in a culture, but exceptions are always possible. While some goals might be seen or expected, there is always room for the rules to be bent or even ignored in some circumstances because no civilization on Earth is genuinely an ideal society. As a result, there are lots of ambiguities.The ideals, customs, and viewpoints that a particular civilization professes to uphold or wants to do so are referred to as ideal culture in contrast to real culture. Instead of the reality that can be seen, it is the aim of a particular culture. Civilization is said to have an ideal culture when all of its members adhere to indisputable values and norms and act in ways that are generally seen as immoral. In an ideal culture, there are fewer exceptions and more clear-cut "rules." No society can, however, really live up to all of its values because people are fallible and frequently break the law.to know more about ' anthropology' try:
https://brainly.com/question/1799013
#SPJ4