4. A small high school holds its graduation ceremony in the gym. Because of seating constraints, students are limited to a maximum of four tickets to graduation for family and friends. The vice principal knows that historically 30% of students want four tickets, 25% want three, 25% want two, 15% want one, and 5% want none. (a) Let X ¼ the number of tickets requested by a randomly selected graduating student, and assume the historical distribution applies to this rv. Find the mean and standard deviation of X. (b) Let T ¼ the total number of tickets requested by the 150 students graduating this year. Assuming all 150 students’ requests are independent, determine the mean and standard deviation of T. (c) The gym can seat a maximum of 500 guests. Calculate the (approximate) probability that all students’ requests can be accommodated. [Hint: Express this probability in terms of T. What distribution does T have?]
Answers
Answer:
(a) The mean and standard deviation of X is 2.6 and 1.2 respectively.
(b) The mean and standard deviation of T are 390 and 180 respectively.
(c) The distribution of T is N (390, 180²). The probability that all students’ requests can be accommodated is 0.7291.
Step-by-step explanation:
(a)
The random variable X is defined as the number of tickets requested by a randomly selected graduating student.
The probability distribution of the number of tickets wanted by the students for the graduation ceremony is as follows:
X P (X)
0 0.05
1 0.15
2 0.25
3 0.25
4 0.30
The formula to compute the mean is:
\(\mu=\sum x\cdot P(X)\)
Compute the mean number of tickets requested by a student as follows:
\(\mu=\sum x\cdot P(X)\\=(0\times 0.05)+(1\times 0.15)+(2\times 0.25)+(3\times 0.25)+(4\times 0.30)\\=2.6\)
The formula of standard deviation of the number of tickets requested by a student as follows:
\(\sigma=\sqrt{E(X^{2})-\mu^{2}}\)
Compute the standard deviation as follows:
\(\sigma=\sqrt{E(X^{2})-\mu^{2}}\\=\sqrt{[(0^{2}\times 0.05)+(1^{2}\times 0.15)+(2^{2}\times 0.25)+(3^{2}\times 0.25)+(4^{2}\times 0.30)]-(2.6)^{2}}\\=\sqrt{1.44}\\=1.2\)
Thus, the mean and standard deviation of X is 2.6 and 1.2 respectively.
(b)
The random variable T is defined as the total number of tickets requested by the 150 students graduating this year.
That is, T = 150 X
Compute the mean of T as follows:
\(\mu=E(T)\\=E(150\cdot X)\\=150\times E(X)\\=150\times 2.6\\=390\)
Compute the standard deviation of T as follows:
\(\sigma=SD(T)\\=SD(150\cdot X)\\=\sqrt{V(150\cdot X)}\\=\sqrt{150^{2}}\times SD(X)\\=150\times 1.2\\=180\)
Thus, the mean and standard deviation of T are 390 and 180 respectively.
(c)
The maximum number of seats at the gym is, 500.
According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sum of values of X, i.e ∑X, will be approximately normally distributed.
Here T = total number of seats requested.
Then, the mean of the distribution of the sum of values of X is given by,
\(\mu_{T}=n\times \mu_{X}=390\)
And the standard deviation of the distribution of the sum of values of X is given by,
\(\sigma_{T}=n\times \sigma_{X}=180\)
So, the distribution of T is N (390, 180²).
Compute the probability that all students’ requests can be accommodated, i.e. less than 500 seats were requested as follows:
\(P(T<500)=P(\frac{T-\mu_{T}}{\sigma_{T}}<\frac{500-390}{180})\\=P(Z<0.61)\\=0.72907\\\approx 0.7291\)
Thus, the probability that all students’ requests can be accommodated is 0.7291.
Related Questions
Solve.
9x+9> 50.4
Enter the answer in the box.
X >
Answers
Rearrange unknown terms to the left side of the equation
\(\boldsymbol{\sf{ 9x > 50.4-9 \ \ \longmapsto \ \ \ [Subtract]}}\)
Calculate the sum or difference.
\(\boldsymbol{\sf{9x > 41.4 }}\)
Convert decimal to fraction.
\(\boldsymbol{\sf{9x > \dfrac{414}{10} }}\)
Reduce the greatest common factor for both sides of the inequality.
\(\boldsymbol{\sf{x > \dfrac{46}{10} }}\)
Reduce the fraction
\(\red{ \boxed{\boldsymbol{\sf{\blue{ Answer \ \ \longmapsto \ \ x > \dfrac{23}{5} }}}}}\)
Hello!
Let's solve this inequality for x:
\(\begin{aligned} \sf{\Box\!\!\!\!\!\star{9x+9 > 50.4}\\\sf{9x > 41.4}\\\sf{x > 4.6} \end{aligned}\)
Therefore \(\bold{x > 4.6}\).
Hope that helps! :)
-art lover
Please help me on this. It's due Monday...
Answers
-184+53=-131
Then he goes down another -168 feet to -299 ft.
-131-168=-299
So, he is currently at -299ft, or 299 feet below the surface.
Given,
A miner is working 184 feet the the surface of the earth.
To get a tool , he climbs 53 feet.
And then descends 168 feet.
His current elevation below the surface of the earth
= (184 - 53) + 168
= 131 + 168
= 299 feet
3 6 9 12 15 18 21 24 27 30 is odd or even numbers?
Answers
Answer: Half of them are even and half of them are odd.
Step-by-step explanation:
The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.
The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.
Therefore, out of the given numbers, half of them are even and half of them are odd.
________________________________________________________
whats 2+2x8-16x18+24 divided by 4+2 equals?
lets see if yall smart :))
Answers
Answer:
its 46
Step-by-step explanation:
Based on the supply graph and the demand graph shown above, what is the price at the point of equilibrium?
Hint: Think about the point where they both meet. For example, if you were to place the graphs on top of each other, what would be the point of intersection?
Type the correct number below without the dollar sign.
Answers
Based on the supply graph and demand graph shown above, the price at the point of equilibrium is $ 30.
Demand refers to quantity of a commodity that the consumers are willing to, able to purchase at a given price during a given period of time. Supply refers to quantity of a commodity that the producers are willing to, able to offer for sale at a given price during a given period of time.
Demand curve slopes downward due to inverse relationship between price and quantity demanded whereas supply curve slopes upward due to direct relationship between quantity supplied and price. When both demand and supply curve intersect with each other balance is achieved. Intersection point between demand and supply curve is known as equilibrium.
At this point when prices are equal is known as equilibrium price and when quantiy demanded or supplied are equal it is known as equilibrium quantity. When we combine the given graph. Equilibrium is achieved at a point when price is equal to $ 30 and quantity is equal to 20 units.
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You pick a card at random. 5 6 7 What is P(odd or greater than 6)?
Answers
The answer to the question is 1/3.
There are three possible outcomes: 5, 6, or 7.
Out of these three outcomes, only two satisfy the condition of being odd or greater than 6: 7.
Therefore, the probability of picking a card that is odd or greater than 6 is 1/3, or approximately 0.333 or 33.3%.
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How many solutions does the system of equations below have? y=-3/4x+1/6
Answers
The solution is the point (0, 1/6) y = 1/6
Given the equation y = (-3/4)x + 1/6, which represents a linear equation, there is no "system" of equations involved since there is only one equation.
In this case, the equation is in slope-intercept form (y = mx + b),
where m represents the slope (-3/4) and b represents the y-intercept (1/6).
The slope-intercept form allows us to determine various properties of the equation.
Since there is only one equation, the solution to this equation is a single point on the Cartesian plane.
Each pair of x and y values that satisfy the equation represents a solution.
For example, if we choose x = 0, we can substitute it into the equation to find the corresponding y value:
y = (-3/4)(0) + 1/6
y = 1/6
Therefore, the solution is the point (0, 1/6).
In summary, the given equation has a unique solution, represented by a single point on the Cartesian plane.
Any value of x plugged into the equation will yield a corresponding y value, resulting in a unique point that satisfies the equation.
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What is the range of the function? f(x)=3^x−1−2
Answers
The range of the equation f(x) = 3ˣ ⁻ ¹ - 2 is y > -2
Calculating the range of the equation?From the question, we have the following parameters that can be used in our computation:
f(x) = 3ˣ ⁻ ¹ - 2
The above equation is an exponential function
The rule of an exponential function is that
The domain is the set of all real numbersHowever, the range is always greater than the constant termIn this case, it is -2
So, the range is y > -2
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How would you name the triangle that is congruent to triangle XYZ?
Answers
The answer is triangle XWZ
write the english phrase as an algebraic expression. Let x represent the number
Answers
The english phrase "Seven less than four times a number" as an algebraic expression is 4x - 7
Writing the english phrase as an algebraic expressionFrom the question, we have the following parameters that can be used in our computation:
seven less than four times a number
Represent the number with x
So:
four times a number means 4x
So, we have
seven less than 4x
seven less than means - 7
So, we have
4x - 7
Hence, the english phrase as an algebraic expression is 4x - 7
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Complete question
write the english phrase as an algebraic expression. Let x represent the number
Seven less than four times a number
Deposits into a bank account are represented by positive numbers. Withdrawals from the
account are represented by negative numbers. Which amount represents a withdrawal of
less than $200 ?
$150
$-250
$250
$-150
Answers
\( \red{answer}\)
$-150
Use what you know about decomposing fractions to write 11/10 as a mixed number
Answers
Answer:
11/10 as a mixed number is 1 and 1/10
Step-by-step explanation:
10 out of 10 is 1 but there is still another tenth that needs to be added so it is 1 and one tenth.
3x+20=5x how many Solutions does it have
Answers
Answer:
one
Step-by-step explanation:
3x + 20 = 5x
20 = 5x - 3x
20 = 2x
x = 10
one solution
Emma is using this bar model
to plan how to cut 35 inches
of yarn into equal pieces.
35 inches
Part A
How many pieces of yarn does
Emma plan to cut?
5 pieces
Part B
How many inches long should
she make each piece?
inches
Answers
Emma is planning to cut 5 pieces of yarn and she should make each piece 7 inches long.
What is simplification?The acts of simplifying something to make it simpler to perform or comprehend, or the item that is simplified: The group offers guidance on streamlining trade processes.
Given, Emma is using this bar model to plan to cut 35 inches of yarn into equal pieces. As we can see in the picture she is planning to cut 5 pieces
Size of each yarn = 35/5 = 7
Therefore, Emma intends to cut five pieces of yarn, each measuring seven inches.
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Linda and seren had an equal number of balloons. After Linda used 16balloons. Serene had 3 times as many balloons as Linda. How many balloons does Serena have?
Answers
Answer:
The answer to the question is 19
Because it says 3 times more you just need to count 3 more numbers so 19 is the answer.
Help!
solve for x 13,14, and 16 only!!!
Answers
Answer:
13:
x= 86°
14:
x= 30°
16:
x= 59°
some body help meee!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
x=3
Step-by-step explanation:
This is a vertical line.
Vertical lines are of the form x= since the x value does not change
x=3
If 90% of a number is 110, find 9% of that number.
Answers
We can set up the equation :
0.9x = 110 ,
where x is the unknown number. To solve for x, we can divide both sides by 0.9 :
x = 110 ÷ 0.9
x = 122.22 (rounded to two decimal places)
So the unknown number is approximately 122.22.
To find 9% of that number, we can multiply 122.22 by 0.09 :
0.09 × 122.22 = 11.00 (rounded to two decimal places)
Therefore, 9% of the number is approximately 11.
What is the measure of the unknown angle? n 120°
Answers
Since a full circle equals 360°, you would subtract 120° from 360° and get 240°.
You are traveling to a football game. You tell your friends you traveled 70 miles per hour while on the interstate. You know however, that at one point you glanced at your speedometer and it read 68 miles per hour. Which is your average speed and which is your instantaneous speed?
Answers
The average speed is 70 miles per hour and the instantaneous speed is 68
miles per hour.
The average speed is the total distance travelled divided by the elapsed time
while the instantaneous speed is the accurate speed covered by the object
at a given instant of time.
Mathematically,
average speed = total distance travelled by the object / total time taken by
the object
Instantaneous speed = distance of an instant / time of an instant.
Therefore,
The average speed is 70 miles per hour.
The instantaneous speed is 68 miles per hour.
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Write an equation for the function graphed below
Answers
The rational function graphed in this problem is defined as follows:
y = -2(x - 1)/(x² - x - 2).
How to define the rational function?The vertical asymptotes of the rational function for this problem are given as follows:
x = -1 and x = 2.
Hence the denominator of the function is given as follows:
(x + 1)(x - 2) = x² - x - 2.
The intercept of the function is given as follows:
x = 1.
Hence the numerator of the function is given as follows:
a(x - 1)
In which a is the leading coefficient.
Hence:
y = a(x - 1)/(x² - x - 2).
When x = 0, y = -1, hence the leading coefficient a is obtained as follows:
-1 = a/2
a = -2.
Thus the function is given as follows:
y = -2(x - 1)/(x² - x - 2).
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The image shows a sequence of transformations that were applied to quadrilateral CLIP, and resulted in the new image . The figure is rotated about the origin 270° counterclockwise followed by translation.
Answers
Here, we need to understand what is meant by rotating a shape or figure about the origin at an angle of 270 degrees counterclockwisely (against the direction of rotation of a clock)
When we make a rotation such as above, we are simply going to change the coordinates of the points in the figure.
Thus, by rotating a point R with coordinates (x,y) counterclockwisely at an angle of 270 about the origin, te new coordinates of point R becomes (y,-x)
We simply negate the x-value and switch its place with the y-value
In the given question, the coordinates of P is (3,2)
The coordinates of the rotation P' will be (2,-3)
Looking at the graph, we can see the coordinates of the point P'' which is the end of our tranformation.
The coordinates of P'' as seen in the graph is (4,-7)
So we have a change of position from P'(2,-3) to P''(4,-7)
What has simply happened here is that the value 2 (positive 2) was added to the x-coordinate value while the value -4 (negative 4) was further subtracted from the y-coordinate value
So for X , we have ( 2 + 2) and for y, Y we have (-3-4)
√(2) rational or irrational
Answers
Answer:
√2 is irrational.
Step-by-step explanation:
√2 = p/q, where 'p' and 'q' are integers, q ≠ 0 and p, q have no common factors (except 1). Thus, p and q have a common factor 2. This statement contradicts that 'p' and 'q' have no common factors (except 1). We can say that √2 is not a rational number.
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help with geometry please‼️‼️
Answers
c^2 = a^2 + b^2 - 2ab * cos(C)
Where c is the side opposite angle C, and a and b are the lengths of the other two sides.
In this case, side AB (c) has a length of 32, side AC (a) has a length of 23, and side BC (b) has a length of 20. We want to find the measure of angle A (m∠A).
Plugging the values into the Law of Cosines equation, we have:
32^2 = 23^2 + 20^2 - 2 * 23 * 20 * cos(A)
Simplifying:
1024 = 529 + 400 - 920 * cos(A)
1024 = 929 - 920 * cos(A)
920 * cos(A) = 929 - 1024
920 * cos(A) = -95
cos(A) = -95 / 920
Now, to find the measure of angle A, we can take the inverse cosine (cos^-1) of (-95 / 920):
m∠A = cos^-1(-95 / 920)
Using a calculator, we find:
m∠A ≈ 96.0 degrees
Therefore, the measure of angle A (m∠A) is approximately 96.0 degrees.
10. Prime numbers from 1 to 100 are running a restaurant - PRIME SPOT, near a tourist point. On a winter holiday, 1 and the composite numbers up to 100 enter the restaurant for dinner after their picnic at the same point. The dining hall has tables with seating capacity 15 for each. If they occupy tables without leaving any chair free, how many tables are required? If each prime number attender has to serve equal number of customers, how many customers should each one get to serve?
Answers
6 tables are required. Each prime number attender should serve 3 customers each.
The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
All the numbers other than prime numbers are composite numbers.
The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.
Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.
Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables
Therefore, 6 tables are required.
Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.
Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.
Thus, each prime number attender should serve 3 customers each.
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PLEASE HELP URGENTTTTT
Answers
Answer:
8
Step-by-step explanation:
Because its a 2,2
Solve the given proportion X/4 = 3/6 X=
Answers
Answer:
X/4=3/6
Start off by cross multiplying the tops and bottoms, so X/4=3/6 turns into 6X=12. Now divide by 6 on both sides.
6X=12 X=2
Answer:
2
Step-by-step explanation:
Cross Multiple and Divide
X. 3
----. = ----
4. 6
So what you want to do is multiply diagonally:
(6)(X) = 6X
(3)(4) = 12
Now that we have our two answers, we put an equal sign between them.
6X = 12
Now to get X alone. Since it's being multiplied by 6, you want to do the opposite and divide.
So remember to divide on both sides to get rid of the 6.
6X divided by 6 is just X.
12 divided by 6 is 2
We got our answers, put the equal sign in-between
X = 2
An airplane descends 3.5 miles to an elevation of 5.25 miles. Find the elevation of the plane before its
descent.
Before its descent, the plane was at an elevation of
miles.
Answers
Answer: The initial elevation of the plane was 8.75 miles.
Step-by-step explanation:
Suppose that the initial elevation of the plane is E.
Then the plane descends 3.5 miles.
Then the new elevation of the plane will be:
E - 3.5 miles.
Now, we know that the new elevation of the plane is 5.25 miles, then:
E - 3.5 miles = 5.25 miles.
Now we need to solve this for E.
To solve this, we can add the same number to both sides of the equation, so we can add 3.5 miles to both sides to get:
(E - 3.5 miles) + 3.5 miles = 5.25 miles + 3.5 miles
E + (3.5 miles - 3.5 miles) = 5.25 miles + 3.5 miles
E = 8.75 miles.
The initial elevation of the plane was 8.75 miles.
Can someone help show me the steps to solve these subtraction problems using base five notation
Answers
The conversion and subtraction in the decimal base gives;;
a) 12 ten
b) 73 ten
What is the number base?The number base serves as the basis for carrying out a mathematical expression. In this case, we have been told that the number base in which the numbers that have been give are is base five and we are to convert the numbers to the decimal base.
For the first problem, we have;
34 five = 19 ten
12 five = 7 ten
We then have;
19 - 7 = 12 ten
For the second problem;
432 five = 117 ten
134 five = 44 ten
Then;
117 - 44 = 73 ten
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Iris has 120 songs on her playlist. Each week, she downloads 4 new songs. How do I write an expression to show the total number of songs on Iris's playlist after w weeks
Answers
The expression to show the total number of songs on Iris's playlist after {w} weeks is → y = 120 + 4w.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.
Given is that Iris has 120 songs on her playlist. Each week, she downloads 4 new songs.
We can write the expression to show the total number of songs on Iris's playlist after {w} weeks as -
y = 120 + 4w
Therefore, the expression to show the total number of songs on Iris's playlist after {w} weeks is → y = 120 + 4w.
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