a) Yes. (b) G Y R
G [0.60 0.00 0.40]
Y [1.00 0.00 0.00]
R [0.30 0.20 0.50]
(c) P(G, G, G, G) = 0.216. P(G, G, G, Y)= 0.144. P(G, G, G, R) = 0.120. P(G, G, Y, R) = 0.000. P(G, Y, R, R) = 0.000. P(Y, R, R, R) = 0.000
(a) Yes, this situation represents a Markov chain because the probabilities of moving to the next state (traffic light) depend only on the current state (traffic light) and not on any previous states.
(b) The transition probability matrix is:
G Y R
G [0.60 0.00 0.40]
Y [1.00 0.00 0.00]
R [0.30 0.20 0.50]
where G represents green, Y represents yellow, and R represents red. The transition diagram can be drawn with arrows between states labeled with the transition probabilities.
(c) There are two classes: {G, Y} and {R}, where {G, Y} is a transient class and {R} is an absorbing class.
(d) Starting with the first light being green, the probabilities after three more lights are:
P(G, G, G, G) = 0.60 * 0.60 * 0.60 = 0.216
P(G, G, G, Y) = 0.60 * 0.60 * 0.40 = 0.144
P(G, G, G, R) = 0.60 * 0.40 * 0.50 = 0.120
P(G, G, Y, R) = 0.60 * 0.00 * 0.50 = 0.000
P(G, Y, R, R) = 0.00 * 0.50 * 0.30 = 0.000
P(Y, R, R, R) = 0.00 * 0.50 * 0.50 = 0.000
The interpretation of these probabilities is, for example, that the probability of passing through four consecutive green lights is 0.216, and the probability of passing through three consecutive green lights followed by a yellow light is 0.144.
(e) Let p_G, p_Y, and p_R be the proportions of green, yellow, and red lights, respectively. Then we have the system of equations:
0.60 p_G + 0.00 p_Y + 0.40 p_R = p_G
1.00 p_Y + 0.00 p_Y + 0.00 p_R = p_Y
0.30 p_G + 0.20 p_Y + 0.50 p_R = p_R
p_G + p_Y + p_R = 1
Solving this system of equations, we get:
p_G = 0.44
p_Y = 0.14
p_R = 0.42
Therefore, approximately 44% of the street lights are green, 14% are yellow, and 42% are red.
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. if the gpa for a student with a gmat score of 600 turned out to be 3.5, what would the residual be? a. 3.2 b. 3.7 c. 0.3 d. 0.2 e. 1.3
a) The predicted GPA for a student with Verbal SAT score of 500 is 2.9805.
b) The residual for this student is -0.2805.
To calculate the predicted GPA for a student with Verbal SAT score of 500, we need to plug in the value of 500 into the regression equation:
GPA = 2.0336 + 0.0018929 × VerbalSAT
Thus, the predicted GPA for a student with Verbal SAT score of 500 is
GPA = 2.0336 + 0.0018929 × 500 = 2.9805
To calculate the residual for this student, we subtract the predicted GPA from the actual GPA
Residual = Actual GPA - Predicted GPA
Residual = 2.7 - 2.9805 = -0.2805
Therefore, the residual for this student is -0.2805.
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I have solved the question in general, as the given question is incomplete.
The complete question is:
A straight line linear regression analysis was carried out, using Verbal SAT score, VerbalSAT (values can range from 0 to 800), to predict grade point average in college, GPA, for first-year BU students (GPA values can range from 0 to 4). The sample size is 345 first-year BU students. The following are the least squares estimates of the coefficients of the linear regression model and the estimates of their standard error: Variable DF Parameter Standard Estimate Error 1 2.0336 0.1621 Intercept VerbalSAT (Slope) 1 0.0018929 0.0002709 . . Calculate the predicted GPA and the residual for a student with Verbal SAT score of 500. GPA was 2.7 for this student.
When hungry, two puppies can eat a bowl of kibble in 9 seconds. How long do they take individually to eat the same bowl of kibble if one puppy takes 24 seconds longer than the other?
please help with this geometry hmw
The triangle DAE and FCE is congruent by the vertical angle theorem property.
What is congruency ?
Congruence of triangles is a term used in geometry to describe the relationship between two triangles that have exactly the same size and shape. In other words, if two triangles are congruent, all of their corresponding sides and angles are equal. When two triangles are congruent, they can be superimposed on each other, and all parts of one triangle will coincide with the corresponding parts of the other triangle.
The concept of congruence is essential in geometry, as it allows us to prove various theorems and make deductions about the properties of triangles. Two triangles can be shown to be congruent if any of the following conditions are met:
Side-Side-Side (SSS) Congruence: If the three sides of one triangle are equal to the three sides of another triangle, then the triangles are congruent.
Side-Angle-Side (SAS) Congruence: If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent.
Angle-Side-Angle (ASA) Congruence: If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent.
Angle-Angle-Side (AAS) Congruence: If two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.
Knowing these congruence criteria, we can use them to prove theorems and solve problems in geometry involving triangles.
The reflexive property is a fundamental concept in mathematics, and it applies to many different areas of study, including geometry. In the context of geometry, the reflexive property is related to congruence of triangles.
The reflexive property of congruence states that any geometric figure is congruent to itself. In the case of triangles, this means that any triangle is congruent to itself. In other words, every triangle is identical to itself, and all of its corresponding sides and angles are equal.
The reflexive property of triangles is used frequently in proofs and demonstrations in geometry. For example, if we want to show that a given triangle is congruent to another triangle, we can use the reflexive property to show that the two triangles are congruent to themselves. Then, we can use other methods, such as the SSS or SAS criteria, to show that the two triangles are congruent to each other.
Overall, the reflexive property is a key concept in geometry that allows us to reason about congruence and to prove various theorems and results related to triangles and other geometric figures.
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5p+10q = 10; 2p-q= 1
Answer:
Step-by-step explanation:
5p+10 equals big 5
Answer:
p = 0.8; q = 0,6
Step-by-step explanation:
5p + 10q = 10
2p - q = 1
5p + 10q = 10
q = 2p - 1
5p + 10 ( 2p - 1 ) = 10
5p + 20p - 10 = 10
25p = 20
p = 0,8
q = 2 x 0,8 - 1
q = 0,6
Use elimination to solve the system of equations.
y = x2 – 3x + 16
y = 9x – 20
The solution to the system of equations is x = 6, y = 22.
What is solution?
We can start by setting the two expressions for y equal to each other:
x² - 3x + 16 = 9x - 20
Next, we can rearrange the equation into standard quadratic form:
x² - 12x + 36 = 0
Now we can factor the quadratic:
(x - 6)² = 0
This equation has only one solution, x = 6. To find the corresponding value of y, we can substitute x = 6 into either of the original equations:
y = 6² - 3(6) + 16 = 22
Therefore, the solution to the system of equations is x = 6, y = 22.
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A table of values is shown.
X
0
1
2
3
4
Y
y =
-2
-10
-50
- 250
- 1250
Write the equation for the function shown in the table
by typing values in the blank spaces.
)x
The function is an exponential function of the form y = a * b^x, where "a" is the initial value and "b" is the common ratio.
Using the given table, we can see that:
- The initial value is y(0) = -2, so a = -2.
- To find the common ratio, we can divide any term by the previous term. For example:
- b = y(1)/y(0) = (-10)/(-2) = 5
- b = y(2)/y(1) = (-50)/(-10) = 5
- and so on.
Since we get the same value of b for all the ratios, we can conclude that the common ratio is b = 5.
Therefore, the equation for the function shown in the table is: y = -2 * 5^x.
Can someone help me ASAP it’s due tomorrow. I will give brainliest if it’s all done correctly. Show work.
Answer:
[tex]\frac{1}{8}[/tex]
Step-by-step explanation:
Since there are four answer choices for question one, the chance of picking the correct answer is [tex]\frac{1}{4}[/tex]. However, there is also another question. That question is a true-or-false question, meaning that there is only two options. Therefore, the probability of picking the correct answer is [tex]\frac{1}{2}[/tex]. To find the probability of picking both correctly, you multiply the two together. [tex]\frac{1}{4} * \frac{1}{2} = \frac{1}{8}[/tex], so the answer is [tex]\frac{1}{8}[/tex].
The frequency of grades earned on a Spanish test are displayed in the histogram.
Which of the following best describes the shape of the data, and why?
The data is symmetric because the average test grade falls in the middle of the data.
The data is not symmetric because the grades are spread out in each of the intervals.
The data is skewed because there is a large amount of data, showing the average grade in the middle.
The data is bimodal because there is a low amount of data in the first and last intervals, showing that many students had low grades.
The histogram provided displays the frequency of grades earned on a Spanish test.
Which of the below best illustrates the data's shape and why?
Based on the given information, the shape of the data is not symmetric because the grades are not evenly distributed in each of the intervals.
The data appears to be skewed to the left because there are fewer students who received higher grades than those who received lower grades. Additionally, the mode of the data is in the 71-80 interval, which is the highest point in the histogram.
Therefore, the correct answer is:
"Because there is a large amount of data, the data is skewed, with the average grade being in the middle i.e, option c"
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Using the order of operations, which operation should you perform last to evaluate this expression? 8 + {[( 14 divided by 2 x ( 3 - 1)} - 1} * 1 point A. Addition B. Division C. Multiplication D. Subtraction
Answer:
A addition
Step-by-step explanation:
You would simply everything in the parentheses first and then multiply that by 1. Lastly, you would add 8.
Helping in the name of Jesus.
find the degree measures of the angle which is imdicate by various assume that O is the center of the circle
Answer:
Using the inscribed angle theorem, we know that the measure of an inscribed angle is equal to half the measure of the central angle that intercepts the same arc. So, we need to find the central angle measure for each of the inscribed angles.
For angle a, the central angle measure is 80°, so the measure of angle a is (1/2)*80° = 40°.
For angle b, the central angle measure is 120°, so the measure of angle b is (1/2)*120° = 60°.
For angle c, the central angle measure is 40°, so the measure of angle c is (1/2)*40° = 20°.
For angle d, the central angle measure is 140°, so the measure of angle d is (1/2)*140° = 70°.
For angle e, the central angle measure is 80°, so the measure of angle e is (1/2)*80° = 40°.
For angle f, the central angle measure is 60°, so the measure of angle f is (1/2)*60° = 30°.
Therefore, the degree measures of the angles are:
a = 40°
b = 60°
c = 20°
d = 70°
e = 40°
f = 30°
Step-by-step explanation: Did try my best
Sally Brown bought a house with a 10% adjustable rate mortgage for 20 years. She was paying $9.66 monthly per thousand on her original loan. At the end of 4 years she owes the bank $55,000.00. Interest has now gone up to 12%, the bank can renew the mortgage at this rate or Sally can pay the full $55,000.00. Sally renews the mortgage and will pay $11.02 monthly per thousand on this loan.
What is the amount of the old and new monthly payment? What is the percent of increase in her new monthly payment (to the nearest tenth)?
old payment = $
new payment = $
% increase
The old payment is $96.60, and the new payment is $110.20. The percent increase in her new monthly payment is 14.1%.
To calculate the old payment, we multiply the original loan amount by the monthly payment per thousand, which gives us $9.66 x 55 = $531.30.
To calculate the new payment, we divide the renewed loan amount by 1000 and multiply it by the monthly payment per thousand, which gives us $11.02 x 55 = $606.10.
To calculate the percent increase, we use the formula: ((new payment - old payment) / old payment) x 100. Substituting the values, we get ((606.10 - 531.30) / 531.30) x 100 = 14.1%. Therefore, the percent increase in her new monthly payment is 14.1%.
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Elephants are born with tusks and their tusks grow 4 inches a year. A 1 year old elephants tusk measured 5 inches. Write a linear equation that represents the situation how long will the elephants tusk be at 6 years old
Answer: y = 4x + 1, 25 inches at 6 years old
Step-by-step explanation:
Our y-intercept will be 1 (5 inches at a year old - 4 inches per year = 1) with a slope of 4 (4 inches a year). Our equation will look like this:
y = 4x + 1
Next, to solve for the length of the tusk at 6 years old, we will input this value of 6 and solve.
y = 4x + 1 = 4(6) + 1 = 25 inches
See attached for a graph.
We can also check our work using a different method.
6 years - 1 year = 5 years
5 years * 4 inches a year = 20 inches
20 inches + current 5 inches = 25 inches at 6 years
At a school pep rally, 208 students are
wearing purple. If there are 260 students at
the rally, what percent are wearing purple?
Answer:
80%
Step-by-step explanation:
We Know
There are 260 students at the rally.
208 students are wearing purple.
What percent are wearing purple?
We Take
208 divided by 260, time 100 = 80%
So, 80% students wearing purple.
A soccer player is going to kick a soccer ball from one corner of a field to the opposite corner. If the field is 80 yards long and 60 yards wide, how far will the soccer player have to kick the ball?
Answer: Assuming the field is rectangular, the distance between the two corners diagonally can be calculated using the Pythagorean theorem, which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.
In this case, the length and width of the field form the two sides of the right triangle, and the diagonal is the hypotenuse.
So, using the Pythagorean theorem:
Diagonal^2 = Length^2 + Width^2
Diagonal^2 = 80^2 + 60^2
Diagonal^2 = 6400 + 3600
Diagonal^2 = 10000
Diagonal = √10000
Diagonal = 100 yards
Therefore, the soccer player will have to kick the ball 100 yards to reach the opposite corner of the field.
Step-by-step explanation:
Help meeeee pleaseee!
Please help me with this will reward branilyist
Answer:
I can’t see it
Step-by-step explanation:
Use point-slope form to write the equation of a line that passes through the point (12,19) with slope -2/3.
By answering the presented question, we may conclude that So, the equation of the line that passes through the point ([tex]12,19[/tex]) with slope [tex]-2/3[/tex] is: [tex]y = (-2/3)x + 27[/tex]
what is slope?
In mathematics, slope is the steepness of a line or curve. It is a measure of how much a function's y-value fluctuates when the x-value changes. A line's slope is commonly symbolised by the letter m and may be computed as follows: [tex]m = (y2 - y1) / (x2 - x1) (x1, y1)[/tex] and [tex](x2, y2)[/tex] are any two points on the line. The slope of a line might be positive, negative, zero, or unknown. A positive slope means the line ascends from left to right, whereas a negative slope means the line drops from left to right.
The point-slope form
[tex]y-y1=m(x-x1)[/tex]
[tex]y-19=(-2/3)(x-12)[/tex]
[tex]y-19=(-2/3)x+8\\y=(-2/3)x+27[/tex]
So, the equation of the line that passes through the point [tex](12,19)[/tex] with slope [tex]-2/3[/tex] is:
[tex]y = (-2/3)x + 27[/tex]
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help asap asignment closes soon!!!
Answer:40
Step-by-step explanation:
90= 2x-10
Answer:
40°
Step-by-step explanation:
Measure of angle LOM(aka x) is equal to:
x+x+10 = 90
2x = 80
x = 40°
suppose you add 1 identical room to a pair of houses. the two houses are identical except for square footage. how much does lprice increase for a house with 4000 sqft compared to a house with 1000 sqft?
When adding one identical room to a pair of houses, the price increase for a house with 4000 sqft compared to a house with 1000 sqft is $150,000.
What is the basis of this problem?
We have two houses, one with a 4000 square foot floor plan and another with a 1000 square foot floor plan. Both of them are identical, and each of them is expected to receive an additional identical room. We must determine how much the price of the house with the 4000 square foot floor plan will increase compared to the house with the 1000 square foot floor plan when both of these are completed.
Let's start by identifying the amount of money needed to construct each house. The amount of money needed to construct the house with the 4000 square foot floor plan is $300,000, and the amount of money required to build the house with the 1000 square foot floor plan is $150,000.The cost of building per square foot in this case is therefore $75/sqft.
As a result, the price for a 4000 sqft house is: $75/sqft × 4000 sqft = $300,000On the other hand, the cost of constructing a 1000 sqft house is:$75/sqft × 1000 sqft = $75,000When each house gets an additional identical room, the increase in the cost of the room is $50,000. As a result, the price of the house with the 4000 square foot floor plan will increase by 4 times, or $200,000, whereas the price of the house with the 1000 square foot floor plan will increase by one, or $50,000. As a result, the price of a 4000 sqft house will be $300,000 + $200,000 = $500,000, whereas the price of a 1000 sqft house will be $150,000 + $50,000 = $200,000.
When we compare these two values, we obtain the following outcome: Suppose you add 1 identical room to a pair of houses. The two houses are identical except for square footage.
When we compare the two values, we get the following result: $500,000 - $200,000 = $300,000
Therefore, the price increase for a house with 4000 sqft compared to a house with 1000 sqft is $150,000.
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3
Ten children played arcade games. The table shows the amount of time each child played and the number of tokens each child used in that time.
Child Child Child Child Child Child Child Child Child Child
1
2
3
4
5
6
7
8
9
10
Time
Played
(minutes)
Tokens
Used
1
5
3
5
S 15
12 1 24
S
18
එය
20
1
30
15
35
39
35 S
The correlation coefficient is 0.363 for these data.
Which statement is the best interpretation of the correlation coefficient?
There is a strong negative association between the number of minutes played and the number of tokens used.
There is a weak negative association between the number of minutes played and the number of tokens used.
There is a strong positive association between the number of minutes played and the number of tokens used.
There is a weak positive association between the number of minutes played and the number of tokens used.
The best interpretation of the correlation coefficient is:
There is a weak positive association between the number of minutes played and the number of tokens used.
What is the correlation coefficient?
A correlation coefficient is a number between -1 and 1 that tells you the strength and direction of a relationship between variables.
The correlation coefficient is 0.363 for these data. Since the correlation coefficient is positive,
we know that there is a positive association between the number of minutes played and the number of tokens used.
However, since the correlation coefficient is less than 0.5, we can conclude that the association is weak.
Therefore, the best interpretation of the correlation coefficient is:
There is a weak positive association between the number of minutes played and the number of tokens used.
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an automotive manufacturer removes the friction linings from the clutch plates of drag race cars following test runs. a sampling of 10 linings for wear show the following values (in mm): 204.5, 231.1, 157.5, 190.5, 261.6, 127.0, 216.6, 172.7, 243.8, and 291.0. estimate the average wear and its variance. based on this sample, how many clutch plates out of a large set will be expected to show wear of more than 203 mm?
We can estimate the expected number of clutch plates with
wear of more than 203 mm as:
[tex]0.7 \times \text{total number of clutch plates}[/tex]
To estimate the average wear and variance, we first calculate the sample
mean and sample variance:
Sample mean:
[tex]\bar{x} = \frac{1}{n}\sum_{i=1}^{n}[/tex]
[tex]x_i = \frac{204.5 + 231.1 + 157.5 + 190.5 + 261.6 + 127.0 + 216.6 + 172.7 + 243.8 + 291.0}{10} = 213.3[/tex]
Sample variance:
[tex]s^2 = \frac{1}{n-1}\sum_{i=1}^{n}[/tex]
[tex](x_i - \bar{x})^2 = \frac{(204.5 - 213.3)^2 + (231.1 - 213.3)^2 + ... + (291.0 - 213.3)^2}{9} = 3415.5[/tex]
To estimate the proportion of clutch plates with wear of more than 203
mm, we first need to calculate the sample proportion:
[tex]{number of linings with wear more than 203 mm}{\text{total number of linings}} = \frac{7}{10} = 0.7[/tex]
To estimate the proportion for a large set of clutch plates, we assume
that the sample proportion is equal to the population proportion.
Therefore, we can estimate the expected number of clutch plates with
wear of more than 203 mm as:
[tex]0.7 \times \text{total number of clutch plates}[/tex]
However, we don't know the total number of clutch plates in the
population, so we cannot provide a specific estimate.
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PLEASE HELP ILL GIVE BRAINLIEST
10^2 x 10^6 x 10 using single exponent
Step-by-step explanation:
10^2 + 10^6 + 10^1 = 10 ^(2+6+1) = 10 ^9
You pick a card at random. 4 5 6 7 What is P(not odd)? Write your answer as a percentage.
Answer:
50%
Step-by-step explanation:
There are 4 cards. 4 and 6 are not odd, which is 2 cards.
P(not odd) = number of cards that are not odd/ total number of cards
= 2/4 = 1/2 = .5 = 50%
Sin(cos^-1[x+1])
Help out solve this math problem
Answer:
sin(cos⁻¹(x+1)) = √(1 - (x+1)²)
Step-by-step explanation:
Select 2 quadratic
functions whose graphs
pass through (-2,0) and
(4,0).
HELP PLEASEEEEE!!! BEST ANSWER WILL GET BRAINLIEST
Step-by-step explanation:
There are SIX sides 3 pairs of equivalent sides
2 * ( 1 1/3 x 3 + 3 * 2 2/3 + 2 2/3 * 1 1/3 ) = 31 1/9 square yards
the time it takes to assemble an electronic component is normally distributed with a mean of 17.2 minutes and a standard deviation of 3.1 minutes. the probability is 90% that it will take at least how long to assemble a component?
For the probability of 90% that it will take at least 68.195 minutes long to assemble an electronic component.
As we have the time it takes to assemble an electronic component is normally distributed.
Mean time, [tex] \mu[/tex] = 17.2 minutes
Standard deviations, [tex] \sigma[/tex]
= 3.1 minutes
We have to determine probability is 90% that it will take at least how long to assemble a component. Now, from the standard normal distribution table value of Z - score for 90% is equals to the 1.645.
Using the Z- score formula in normal distribution, [tex]Z = \frac{ X - \mu}{\sigma }[/tex]
=> 1.645 = ( X - 17.2 )/3.1
=> X - 17.2 = 31 × 1.645
=> X = 17.2 + 50.995
=> X = 68.195
Hence, the required at least the long to assemble a component is equals to the 68.195.
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the height of a golf ball after it is hit can be modeled by the equation where represents the number of seconds after the ball is hit, and represents the golf ball height, in feet. a) what is the height of the golf ball at the instant it is hit? feet b) what is the height of the golf ball 2.8 seconds after it is hit? feet c) how long does it take the ball to hit the ground after it is hit? (round answer to three decimal places.) seconds submit question question 3
a. The height of the golf ball at the instant it is hit is 0 feet.
b. The height of the golf ball 2.8 seconds after it is hit is approximately 62.72 feet.
c. It takes 4 seconds for the golf ball to hit the ground after it is hit.
a) To find the height of the golf ball at the instant it is hit, we need to evaluate the function h when t = 0.
Substituting t = 0 into the given equation, we get:
h = -16(0)² + 64(0) = 0
Therefore, the height of the golf ball at the instant it is hit is 0 feet.
b) To find the height of the golf ball 2.8 seconds after it is hit, we need to evaluate the function h when t = 2.8.
Substituting t = 2.8 into the given equation, we get:
h = -16(2.8)² + 64(2.8) ≈ 62.72
Therefore, the height of the golf ball 2.8 seconds after it is hit is approximately 62.72 feet.
c) To find how long it takes the ball to hit the ground after it is hit, we need to find the value of t when the height is 0.
Setting h = 0 in the given equation, we get:
0 = -16t² + 64t
0 = t(-16t + 64)
t = 0 or t = 4
Since the golf ball was hit upwards, we are only interested in the positive value of t, which is t = 4.
Therefore, it takes 4 seconds for the golf ball to hit the ground after it is hit.
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The question is -
The height in feet of a golf ball hit into the air is given by h = − 16t² + 64t, where t is the number of seconds elapsed since the ball was hit, and represents the golf ball height, in feet.
a) what is the height of the golf ball at the instant it is hit?
b) what is the height of the golf ball 2.8 seconds after it is hit?
c) how long does it take the ball to hit the ground after it is hit?
What is the mean of the given distribution, and which type of skew does it exhibit?
Since 3 has the highest frequency, the mode is 3.Now, the curve is positively skewed if mean is bigger than mean.
Describe total number?Total number is a term used to refer to the sum of two or more individual elements. It is commonly used in the context of mathematics and can refer to the result of addition, subtraction, multiplication, or division. For example, the total number of apples in a basket could be five, the total number of days in a week could be seven, and the total number of people in a family could be four. In any case, the total number is the sum of all the individual elements that are being considered.
Presented to us is a distribution:
{4.5, 3, 1, 2, 4, 3, 6, 4.5, 4, 5, 2, 1, 3, 4, 3, 2}
We must determine the mean.
Mean is equal to the sum of all observations divided by the total number of observations.
Mean = 52/16
Mean = 3.25
We now determine the mode, which is the observation with the highest frequency, or how frequently it has occurred.
observations per unit of time
4.5 2
3 4
1 2
2 3
4 3
6 1
5 1
Since 3 has the highest frequency, the mode is 3.
Now, the curve is positively skewed if mean is bigger than mean.
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Complete questions as follows-
What is the mean of the given distribution, and which type of skew does it exhibit?
{4.5, 3, 1, 2, 4, 3, 6, 4.5, 4, 5, 2, 1, 3, 4, 3, 2}
WHAT IS THE MEAN? and WHAT TYPE OF SKEW EXHIBITS? negative, positive, symmetric, zero etc..