3. A rare species of aquatic insect was discovered in the Amazon rainforest. To protect the species, environmentalists declared the insect endangered and transplanted the insect to protected area. The population P(t) (in thousands) of insects in t months after being transplanted is
a. [3 pts] Determine the number of months until the insect population reaches 40 thousand (round to 2 decimal places).
b. [3 pts] What is the limiting factor on the insect population as time progresses? Explain your answer.
c. [3 pts] Sketch a graph of the function using the window and. Be sure to indicated the scale on the graph, label the axes, at least 2 points on the graph, and any asymptotes.
Answers
The number of months until the insect population reaches 40 thousand is 14.29 months and the limiting factor on the insect population as time progresses is 250 thousands.
Given that population P(t) (in thousands) of insects in t months after being transplanted is P(t)=(50(1+0.05t))/(2+0.01t).
(a) Firstly, we will find the number of months until the insect population reaches 40 thousand by equating the given population expression with 40, we get
P(t)=40
(50(1+0.05t))/(2+0.01t)=40
Cross multiply both sides, we get
50(1+0.05t)=40(2+0.01t)
Apply the distributive property a(b+c)=ab+ac, we get
50+2.5t=80+0.4t
Subtract 0.4t and 50 from both sides, we get
50+2.5t-0.4t-50=80+0.4t-0.4t-50
2.1t=30
Divide both sides with 2.1, we get
t=14.29 months
(b) Now, we will find the limiting factor on the insect population as time progresses by taking limit on both sides with t→∞, we get
[tex]\begin{aligned}\lim_{t \rightarrow \infty}P(t)&=\lim_{t \rightarrow \infty}\frac{50(1+0.05t)}{2+0.01t}\\ &=\lim_{t \rightarrow \infty}\frac{50(\frac{1}{t}+0.05)}{\frac{2}{t}+0.01}\\ &=50\times \frac{0.05}{0.01}\\ &=250\end[/tex]
(c) Further, we will sketch the graph of the function using the window 0≤t≤700 and 0≤p(t)≤700 as shown in the figure.
Hence, when the population P(t) (in thousands) of insects in t months after being transplanted by P(t)=(50(1+0.05t))/(2+0.01t) then the number of months until the insect population reaches 40 thousand 14.29 months and the limiting factor on the insect population is 250 thousand and the graph is shown in the figure.
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Related Questions
6
Select ALL the true statements about 388.33.
The value of the tens digit, 80, is 10 times the value of the ones digit, 8.
The value of the hundredths digit, 0.03, is 10 times the value of the tenths
digit, 0.3.
C. The value of the ones digit, 8, is the value of the tens digit, 80.
D.
The value of the hundredths digit, 0.03, is to the value of the tenths
digit, 0.3.
A.
B.
E. O The value of the tenths digit, 0.3, is 10 times the value of the hundredths
digit, 0.03.
Answers
The true statements about 388.33 are:
The value of the hundredth digit, 0.03, is 10 times the value of the tenth digit, 0.3.
The value of the tenth digit, 0.3, is 10 times the value of the hundredth digit, 0.03.
We have,
The statement "The value of the tens digit, 80, is 10 times the value of the one's digit, 8" is incorrect. The tens digit is actually 3, not 80.
The statement "The value of the hundredths digit, 0.03, is 10 times the value of the tenths digit, 0.3" is true.
The hundredth digit is 3 times smaller than the tenth digit, which means that the tenth digit is 10 times larger than the hundredth digit.
The statement "The value of the one's digit, 8, is the value of the tens digit, 80" is incorrect.
The tens digit is 3, not 80.
The statement "The value of the hundredths digit, 0.03, is to the value of the tenths digit, 0.3" is unclear and not a proper comparison, so it cannot be determined whether it is true or false.
Thus,
The true statements about 388.33 are:
The value of the hundredth digit, 0.03, is 10 times the value of the tenth digit, 0.3.
The value of the tenth digit, 0.3, is 10 times the value of the hundredth digit, 0.03.
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work out length x in the triangle below
if your answer is a decimal, give it to 1 d.p.
Answers
The length x in the triangle below is 16 m.
What is length?Length is the distance between two points.
To calculate the length of the triangle, we use the formula below
Formula:
A = absin∅/2...................... Equation 1Where:
A = Area of the triangle∅ = Included angle of the triangleFrom the question,
Given:
a = 15 mb = x∅ = 30°A = 60 m²Substitute these values into equation 1 and solve for x
60 = (15×x)sin30°/2120 = 15x(1/2)15x = 240x = 240/15x = 16 mLearn more about length here: https://brainly.com/question/28108430
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Instructions: Find the missing probability.
P(B)=1/2P(A|B)=11/25P(AandB)=
Answers
P(A and B) = P(B) x P(A|B)
We are given:
P(B) = 1/2
P(A|B) = 11/25
Substituting these values into the formula, we get:
P(A and B) = (1/2) x (11/25) = 11/50
Therefore, P(A and B) = 11/50.
If the equation is an identity
Answers
The equation is an identity is discussed below.
An identity is a mathematical equation that holds true for all values of the variables involved.
In other words, it is true regardless of the specific values of the variables. When an equation is an identity, it means that both sides of the equation are equivalent and represent the same mathematical relationship.
For example, the equation 2x + 3 = 2(x + 1) is an identity because it holds true for all values of x.
When an equation is an identity, it provides a general statement or rule that is universally applicable and does not depend on specific values or conditions. Identifying an equation as an identity is important because it allows us to make general conclusions and deductions that apply in all cases.
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I have a deck of 52 cards, from which I draw 3 cards and I would like to make a probability tree diagram, with two events, drawing a spade, and not drawing a spade. These two events have to branches which are the same, drawing a spade and not drawing a spade. Once again these two branches have two more branches for each, drawing another spade and not drawing a spade. I need a tree diagram which includes these branches and events.
Answers
The probability is solved and the tree diagram is given
Given data ,
The tree diagram to draw 3 cards out of 52 cards from the given probability details are:
The two events, drawing a spade, and not drawing a spade. These two events have to branches which are the same, drawing a spade and not drawing a spade. Once again these two branches have two more branches for each, drawing another spade and not drawing a spade.
_______ Draw a Spade _______
/ \
______/______ ______\_______
/ \ / \
/ \ / \
/ \ / \
Spade Not Spade Spade Not Spade
| | | |
Draw another Spade Not Draw a Spade Draw another Spade Not Draw a Spade
Hence , the probability of deck of cards is solved
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Tres engranajes tangentes entre sí, cuyos radios miden 15, 16 y 17 cm, deben ser sostenidos por
una base triangular que tiene por vértices los centros de cada engranaje. Hallar los ángulos
interiores del triángulo y expresarlos según el sistema de medición radial.
Answers
Para resolver este problema, podemos utilizar el Teorema de los Cosenos para calcular los ángulos interiores del triángulo.
Sea A, B y C los vértices del triángulo correspondientes a los centros de los engranajes. Sea a, b y c las longitudes de los lados opuestos a los ángulos A, B y C respectivamente.
Dado que los radios de los engranajes miden 15 cm, 16 cm y 17 cm, podemos considerar que los lados del triángulo son a = 15 cm, b = 16 cm y c = 17 cm.
El Teorema de los Cosenos establece que en un triángulo con lados a, b y c, y ángulos opuestos A, B y C respectivamente, se cumple la siguiente fórmula:
c^2 = a^2 + b^2 - 2ab * cos(C)
Podemos aplicar esta fórmula para cada uno de los ángulos del triángulo.
Para el ángulo A, tenemos:
c^2 = b^2 + a^2 - 2ab * cos(A)
17^2 = 16^2 + 15^2 - 2 * 16 * 15 * cos(A)
Resolviendo la ecuación, encontramos que cos(A) = -1/8. Tomando el coseno inverso (arcocoseno), encontramos que el ángulo A es aproximadamente 135.2 grados en el sistema de medición radial.
Para el ángulo B, tenemos:
a^2 = c^2 + b^2 - 2cb * cos(B)
15^2 = 17^2 + 16^2 - 2 * 17 * 16 * cos(B)
Resolviendo la ecuación, encontramos que cos(B) = -7/17. Tomando el coseno inverso, encontramos que el ángulo B es aproximadamente 120.6 grados en el sistema de medición radial.
Para el ángulo C, tenemos:
b^2 = a^2 + c^2 - 2ac * cos(C)
16^2 = 15^2 + 17^2 - 2 * 15 * 17 * cos(C)
Resolviendo la ecuación, encontramos que cos(C) = -1/2. Tomando el coseno inverso, encontramos que el ángulo C es aproximadamente 120 grados en el sistema de medición radial.
Entonces, los ángulos interiores del triángulo son:
A ≈ 135.2 grados
B ≈ 120.6 grados
C ≈ 120 grados
Estos valores están expresados en el sistema de medición radial.
You pay for a fiction book, a nonfiction book, and a bookmark with three $5 bills. The fiction book costs $5.43. The nonfiction book costs $3.89. Your change is $3.45. How much does the bookmark cost?
Answers
Answer:
2.23
Step-by-step explanation:
You have 3 $5 bills which us 15 dollars. 15 dollars - 5.43 - 3.89 - 3.45 = 2.23 dollars for the bookmark.
To see if you are correct, you can add 3.45, 2.23, 3.89, and 5.43 to get your answer.
We have 3 $5
3 x 5 = 15
Now, we add the cost for both of the books and our remaining change
5.43 + 3.89 + 3.45 = 12.77
And then we subtract to 15
15 - 12.77 = 2.23
We can also check our answer by adding the costs of the bookmark and both books and subtracting it to 15
4.43 + 3.89 + 2.23 = 11.55
15 - 11.55 = 3.45
10.
A lunch menu consists of 8 different sandwiches, 5 different soups, and 3 different drinks. How many choices are there for ordering a sandwich, a bowl of soup, and a drink?
65 choices
120 choices
165 choices
16 choices
Answers
For the given menu, there are 120 choices for ordering a sandwich, a bowl of soup, and a drink.
Using the Multiplication PrincipleNumber of choices for ordering:
Sandwich = 8
Soup = 5
Drink = 3
According to the multiplication principle, multiply the number of options for each category to find the total number of choices:
Total choices = (Number of options for Sandwich) * (Number of options for Soup) * (Number of options for Drink)
Total choices = 8 * 5 * 3
Total choices = 120
Therefore, there are 120 choices for ordering a sandwich, a bowl of soup, and a drink from the given menu.
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please helppp!!! thank you!
Answers
The number line that shows the solution to the inequality is given as follows:
First number line.
How to solve the inequality?The inequality in the context of this problem is defined as follows:
-6x + 5 >= 17
-6x >= 12.
Due to the negative sign of the leading coefficient, we should change the sign of all terms, including the sign, as follows:
6x <= -12.
Then the solution is given as follows:
x <= -2.
Which is composed by the numbers to the left of the closed interval at x = -2, hence the first number line gives the solution to the inequality.
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The number line that shows the solution to the inequality is: C. graph C.
What is an inequality?In Mathematics and Geometry, an inequality refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;
Greater than (>).Less than (<).Greater than or equal to (≥).Less than or equal to (≤).Based on the information provided above, we have the following equation (inequality);
-6x + 5 ≥ 17
By subtracting 5 from both sides of the equation (inequality), we have;
-6x + 5 - 5 ≥ 17 - 5
-6x ≥ 12
x ≤ 12/6
x ≤ 2 (it would be shaded to the left with a closed circle at 2).
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A person places $12500 in an investment account earning an annual rate of 8.3%,
compounded continuously. Using the formula V = Pert, where V is the value of the
account in t years, P is the principal initially invested, e is the base of a natural
logarithm, and r is the rate of interest, determine the amount of money, to the nearest
cent, in the account after 12 years.
20 POINTS
Answers
When a person places $12,500 in an investment account earning an annual rate of 8.3%, compounded continuously, based on the formula V = Pe^rt, the amount of money (future value), to the nearest cent, in the account after 12 years, is $33,842.88.
How the future value is determined:Using the formula A = Pe^rt where V is the future value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest.
In this situation, we can use an online finance calculator to determine the future value compounded continuously as follows:
Principal (P): $12,500.00
Annual Rate (R): 8.3%
Compound (n): Compounding Continuously
Time (t in years): 12 years
Result:
A (Future Value) = $33,842.88
A = P + I where
P (principal) = $12,500.00
I (interest) = $21,342.88
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Please help me right now!
Thank you so much
Answers
The length of the arc KL in the given circle is 3.49 units
How to find the length of the arc KL?In a circle whose radius is R, the length of an arc defined by an angle x is given by:
Length = (x/360)*2*3.14*R
Here we know that the radius is 2 units, and the angle for the arc KL is 100°, then we can replace these values in the formula above so we get that the length of the arc is:
Length = (100/360)*2*3.14*2
Lenght = 3.49 units.
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A police radar gun is used to measure the speeds of cars on a highway. The speeds of cars are normally
distributed with a mean of 55 mi/hr and a standard deviation of 5 mi/hr. Roughly what percentage of cars
are driving less than 65 mi/hr? Use the empirical rule to solve the problem. (Round to the nearest tenth of a
percent)
Answers
The solution is : the percentage of cars that are driving less than 45 mi/hr is 2.3%
Here, we have,
Since the speeds of cars are normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = speeds of cars
µ = mean speed
σ = standard deviation
From the information given,
µ = 55 mi/hr
σ = 5 mi/hr
The probability that a car is driving less than 45 mi/hr is expressed as
P(x < 45)
For x = 45
z = (45 - 55)/5 = - 2
Looking at the normal distribution table, the probability corresponding to the z score is 0.023
Therefore, the percentage of cars that are driving less than 45 mi/hr is
0.023 × 100 = 2.3%
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What is the range of f(x) = sin(x)?
the set of all real numbers -2pi≤y≤2pi
the set of all real numbers -1≤y≤1
the set of all real numbers 0≤y≤2pi
the set of all real numbers
Answers
Answer:
the set of all real numbers -1≤y≤1
Step-by-step explanation:
according to the definition of 'sin'-function, the max value of it is '+1' and the min is '-1'. Finally, the correct answer is B. the set of all real numbers -1≤y≤+1.
One candle, in the shape of a right circular
cylinder, has a height of 7.5 inches and a
diameter of 5 inches. What is the volume of the
candle? Round your answer to the nearest
cubic inch.
Answers
Answer:
147
Step-by-step explanation:
V = h * S = h * Pi R^2 = h * Pi * d^2/4 = 7.5 * 3.14 * 25 / 4 = 147.188
The table of values below represents a linear function and shows the amount of snow that has fallen since a snowstorm began. What is the rate of change?
Snowfall Amount
Length of Snowfall
(hours)
Amount of Snow on the Ground
(inches)
0
3.3
0.5
4.5
1.0
5.7
1.5
6.9
2.0
8.1
1.2 inches per hour
2.4 inches per hour
3.3 inches per hour
5.7 inches per hour
Answers
The average rate of change for the snowfall amount is given as follows:
2.4 inches per hour.
How to obtain the average rate of change?The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function.
The change in the output is given as follows:
8.1 - 3.3 = 4.8.
(output is the amount of snow).
The change in the input is given as follows:
2 - 0 = 2.
(input is the time in hours).
Hence the average rate of change of the snowfall over time is given as follows:
4.8/2 = 2.4 inches per hour.
(change in the snowfall divided by the change in time).
Missing InformationThe table is given by the image presented at the end of the answer.
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13. Lindsay was going to visit her grandmother, shop at the mall, and then return home. The route she took was in the shape of a triangle. The distance between each place she visited was 10 miles. What type of triangle is formed by the route she traveled? Explain. answer please answer that question
Answers
A hemisphere is on top of a cylinder the radius of the hemisphere is 5 and the height of the cylinder is 8 what is the volume somehelp?
Answers
Answer:
V = π(5^2)(8) + (4/3)π(5^3)
= 200π + (500/3)π = (1,100/3)π
= about 1,151.92 cm^3
PLEASE I NEED HELP !!!!!
Answers
The weight of a pitaya seed in standard form is [tex]1 \times 10^-^6[/tex]ounce.
In standard form, the weight of a pitaya seed is expressed in scientific notation, where the number is a decimal between 1 and 10, and the exponent is a power of 10. The weight of a pitaya seed is given as [tex]1 x 10^-^3[/tex] ounce, which means that the seed weighs one-thousandth of an ounce.
To write this in standard form, we first convert the number to a decimal between 1 and 10 by moving the decimal point three places to the left. This gives us a decimal of 0.001. The exponent is already in the form of a power of 10, so we can leave it as [tex]10^-^3[/tex]. Thus, the weight of a pitaya seed in standard form is:
[tex]0.001 \times 10^-^3[/tex]
To simplify this expression, we can multiply the decimal and the exponent. This gives us:
[tex]1 x 10^-^6[/tex]
This means that the weight of a single pitaya seed is very small, and it takes many seeds to make up the weight of a whole pitaya fruit.
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The figure below shows a triangle with vertices, a and B on a circle and vertex c outside it. Side ac is tangent to the circle. Side bc is a secant intersecting the circle at point x. What is the measure of angle acb?
1.32
2.60
3.28
4.16
Answers
The measure of angle ACB is half the difference between 180 degrees and the measure of arc AB.
The measure of angle ACB can be determined using the properties of tangents and secants intersecting a circle.
Since side AC is tangent to the circle, angle BAC is a right angle (90 degrees).
According to the tangent-secant theorem, the measure of angle ACB is equal to half the difference between the intercepted arcs AB and AX.
Since angle BAC is a right angle, the intercepted arc AX is a semicircle, which means its measure is 180 degrees. The intercepted arc AB is an arc of the circle and is less than 180 degrees since it is not a full circle.
Therefore, the measure of angle ACB is half the difference between 180 degrees and the measure of arc AB.
To find the exact measure, more information is needed about the length of arc AB or the relationship between the lengths of the sides of the triangle. Without this additional information, we cannot determine the precise measure of angle ACB.
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Help me please! I’m really struggling on how to do this
Answers
Answer:
12 feet
Step-by-step explanation:
1 inch= 8 feet
1/2 inch= 4 feet
1/4 inch= 2 feet
(2x2)/2= 2 (one triangle)
2x4=8 (rectangle)
2+2=4 +8=12
^2 was added 2 times cause there are 2 triangles
(you did not need a 3rd measurement cause the triangle measurements were equal)
Lai Lal Chinese Restaurant has seven items in its breakfast menu. The management of Lai Lai has just acquired some data and they would like to find out both popularity and profitability of its breakfast menu items based on their selling price, food cost percentage, sales volume and contribution margin (CM) from the past period. The financial data for the selling price, sales volume, and individual food cost dollar amounts are presented in the table below:
Breakfast Selling Price Food Cost Menu Item ($) (52 Sales Volume А $10.00 $3.00 250 B $16.00 $6.00 50 с $18.45 $8.00 60 D $14.75 $4.25 300 E $8.75 $2.50 80 F $12.50 $5.75 180 G $9.00 $2.60 280 TOTAL 1.200
Based on the information given in the table above, what are the specific classification of the breakfast menu items based on their profitability and popularity in order?
Answers
Based on the contribution margin and the sales volume, Menu Item D is the most profitable and popular.
What is the contribution margin?The contribution margin is the profitability that is shown in the difference between the selling price and the variable cost per unit of an item.
The contribution margin can be computed per unit or in total. Using the sales volume to multiply the contribution margin per item gives the total contribution margin in dollars.
Breakfast Selling Price Food Cost Sales Contribution Margin
Menu Item ($) ($) Volume Unit Total
А $10.00 $3.00 250 $7.00 $1,750
B $16.00 $6.00 50 $10.00 $500
C $18.45 $8.00 60 $10.45 $627
D $14.75 $4.25 300 $10.50 $3,150
E $8.75 $2.50 80 $6.25 $500
F $12.50 $5.75 180 $6.75 $1,215
G $9.00 $2.60 280 $6.40 $1,792
TOTAL 1,200
Thus, we can conclude that Menu Item D enjoys the highest profitability and popularity.
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9. Find m DF
m
140°
DF:
=
E
44°
20. Find
mZPQR.
131*
m/POR=
Need done asap please show work
Answers
According to the angles between intersecting secant and tangent, the value of
angle DF is 52 degrees
angle PQR = 49 degrees
How to solve for angle DFThe value of angle DF is solved using the angles of intersecting secant out side the circle
The theorem give the formula in the form
44 = 1/2 (140 - DF)
88 = 140 - DF
DF = 140 - 88
DF = 52 degrees
Using intersection of tangents, for the second figure
exterior angle = 1/2 (major arc - minor arc)
major arc = 360 - 131 = 229
PQR = 1/2 (229 - 131)
PQR = 49 degrees
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1.1.4 Express 25/75 as a percentage.
Answers
Answer:
Hi
Please mark brainliest ❣️
Step-by-step explanation:
25/75 × 100/1
= 33.3%
Determine which set of sides measurements could be used of form a right triangle 14,5,15 3,4,5 9,14,16 5,2,7
Answers
Answer: 14,5,15 is correct
Step-by-step explanation:
Please help find the x.
Answers
Answer:
The answer is 64°
Step-by-step explanation:
opposite angles are equal
x=64°
Answer:
X is 64 degrees.
Step-by-step explanation:
X is directly across from 64 degrees. These angles are equal. So are angle y and 18, and angle z and the blank angle at the bottom.
Haleigh decides that instead of throwing away old candles, she can use the last bit of wax combined together to make new candles. Each candle has 10% of it's original wax left. How many 5 ounce candles can she make if she has five 20 oz candles, 5 five ounce candles, and twenty-five one-ounce candles?
Answers
We cannot have a fractional number of candles, Haleigh can make a maximum of 2 five-ounce candles using the available wax from the 20-ounce and 1-ounce candles.
To determine the number of 5-ounce candles Haleigh can make using the remaining wax from her existing candles, we need to calculate the total amount of wax available and divide it by the amount of wax needed for each 5-ounce candle.
Let's calculate the total amount of wax available:
The five 20-ounce candles have 10% of their original wax remaining, so each candle has 2 ounces of wax left.
Therefore, the total wax from the five 20-ounce candles is 5 candles [tex]\times[/tex] 2 ounces = 10 ounces.
The five 5-ounce candles already have wax, so we don't need to consider them.
The twenty-five 1-ounce candles have 10% of their original wax remaining, so each candle has 0.1 ounces of wax left.
Therefore, the total wax from the twenty-five 1-ounce candles is 25 candles * 0.1 ounces = 2.5 ounces.
Adding up the wax from the 20-ounce and 1-ounce candles, we have a total of 10 ounces + 2.5 ounces = 12.5 ounces of wax available.
To determine how many 5-ounce candles can be made, we divide the total available wax by the amount of wax needed for each 5-ounce candle:
Number of 5-ounce candles = Total available wax / Wax needed per 5-ounce candle
Number of 5-ounce candles = 12.5 ounces / 5 ounces
Number of 5-ounce candles ≈ 2.5 candles.
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A 50 foot rope is stretched tight from the roof of a building to a spot 20 feet from the base of the
building. How tall is the building? Round your answer to TWO decimal places.
Answers
47.17 feet is the height of the building.
We can use the Pythagorean theorem to solve the problem:
Let h be the height of the building.
Then we have a right triangle with legs 20 and h, and a hypotenuse 50.
Using the Pythagorean theorem, we have:
[tex]50^2 = 20^2 + h^2[/tex]
Simplifying and solving for h, we get:
[tex]h = \sqrt{(50^2 - 20^2)[/tex]
h ≈ 47.17 feet (rounded to two decimal places)
Therefore, the height of the building is approximately 47.17 feet.
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What is the answer to the question please ?
Answers
Answer:
Step-by-step explanation:
easy its A tell me if u got it correct good job (:
Solve. |7x-20|=|2x+20|
Answers
To solve the equation |7x - 20| = |2x + 20|, we need to consider two cases based on the absolute values.
Case 1: (7x - 20) = (2x + 20)
Simplifying this equation, we get:
7x - 20 = 2x + 20
Subtracting 2x from both sides:
5x - 20 = 20
Adding 20 to both sides:
5x = 40
Dividing both sides by 5:
x = 8
Case 2: (7x - 20) = -(2x + 20)
Simplifying this equation, we get:
7x - 20 = -2x - 20
Adding 2x to both sides:
9x - 20 = -20
Adding 20 to both sides:
9x = 0
Dividing both sides by 9:
x = 0
Therefore, the solutions to the equation |7x - 20| = |2x + 20| are x = 8 and x = 0.
Thirty-four percent of workers in the Unites States are college graduates. Suppose a random sample of 120 workers is obtained and 35 of them have a college degree.
a) What are the mean and standard deviation of the number of workers with a college degree respectively?
b) What is the probability that the number of workers with a college degree is at least 35?
Answers
The mean number of workers with a college degree is 40.8, and the standard deviation is 5.37.
The probability that the number of workers with a college degree is at least 35 is 0.976, or 97.6%.
Given Sample size (n) is 120 workers
Proportion of workers who are college graduates (p): 34% or 0.34
a) Mean and Standard Deviation:
The mean (μ) of a binomial distribution is given by μ = np, and the standard deviation (σ) is given by σ =√np(1 - p).
Substituting the values:
μ = 120 ×0.34 = 40.8
σ = √120 × 0.34 × (1 - 0.34)) = 5.37
To find the probability that the number of workers with a college degree is at least 35
we need to calculate the cumulative probability of the binomial distribution from 35 to the maximum possible value, which is 120 in this case.
Using a binomial probability calculator or a statistical software, we can find this probability.
Assuming a binomial distribution with parameters n = 120 and p = 0.34, the probability can be calculated as follows:
P(X ≥ 35) = 1 - P(X < 35)
The probability that the number of workers with a college degree is at least 35 is 0.976, or 97.6%.
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