The probability of the selected coin showing heads is 0.77, or 77%.
Probability is the measure of the likelihood of an event occurring. In this scenario, we have three coins in a box, each with different properties.
To calculate the probability of an event occurring, we need to divide the number of favorable outcomes by the total number of possible outcomes. In this case, there are three possible coins we could select, each with a different probability of showing heads.
Now, we need to determine the total number of possible outcomes, which is simply the number of coins we have, which is three.
Next, we need to determine the number of favorable outcomes. For Coin 1, the probability of showing heads is 1 (since it has two heads). For Coin 2, the probability of showing heads is 0.5 (since it is a fair coin with equal probability of heads and tails). For Coin 3, the probability of showing heads is 0.8.
To calculate the probability of showing heads when we randomly select one of these coins, we need to weigh the probabilities of each coin being selected with their corresponding probabilities of showing heads.
Let's say that the probability of selecting each coin is equal (since we have no information to suggest otherwise). Then, the probability of selecting Coin 1 is 1/3, the probability of selecting Coin 2 is 1/3, and the probability of selecting Coin 3 is 1/3.
To calculate the overall probability of showing heads, we can use the following formula:
P(heads) = (P(Coin 1) * P(heads on Coin 1)) + (P(Coin 2) * P(heads on Coin 2)) + (P(Coin 3) * P(heads on Coin 3))
= (1/3 * 1) + (1/3 * 0.5) + (1/3 * 0.8)
= 0.77
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Find the sum of each infinite geo sequence
Answer:
0.15 repeating
Step-by-step explanation:
Helpppppppp meeeeeeeeeeeeeeeeeeee
mrazek et al.'s (2013) study reported that students scored higher on the gre after completing a 2-week mindfulness training course. the authors took a sample of 60 college seniors and randomly assigned one group to a two week mindfulness training course. both the group who did the mindfulness training and the control group who did not, took the gre. the mindfulness group had higher scores than the control group. (1) state the hypothesis, (2) describe what type of study design this is and (3) justify your choice of the study type above. (4) list the two variables with their operational definitions (5) does this study demonstrate that the relationship between the two variables is causal? why or why not?
(1) The hypothesis is stated that completing a 2-week mindfulness training course
(2) The type of study design this is randomized controlled trial.
(3) The choice of the study type is randomized controlled trial is justified. (4) The list of the two variables with their operational definitions is 2-week mindfulness training course and GRE scores.
(5) Yes, this study demonstrate that the relationship between the two variables is causal
In a study conducted by Mrazek et al. (2013), it was found that students who completed a 2-week mindfulness training course scored higher on the GRE than those who did not participate in the training.
The hypothesis of this study is that completing a 2-week mindfulness training course will result in higher scores on the GRE compared to those who do not complete the training.
This study design is a randomized controlled trial. In this type of study, participants are randomly assigned to either a treatment or control group, and the effects of the treatment are compared to the effects of no treatment (or a placebo). In this case, the treatment group received the 2-week mindfulness training course, while the control group did not.
The choice of study type as a randomized controlled trial is justified because it allows for the comparison of two groups while minimizing the effects of confounding variables. Random assignment to groups helps to ensure that any differences in outcomes between the groups are due to the treatment and not some other factor.
The two variables in this study are the completion of the 2-week mindfulness training course and GRE scores. The operational definition of completion of the training course is that participants in the treatment group attended all sessions of the 2-week course. The operational definition of GRE scores is the score that participants received on the exam.
This study does suggest a causal relationship between completion of the mindfulness training course and higher GRE scores. The randomized controlled trial design helps to reduce the effects of confounding variables, making it more likely that any observed differences in outcomes between the treatment and control groups are due to the treatment.
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Please Help will mark Brainliest!!!
Answer: Neither
3, 5, 9,17
+ 2 +2
They are not the same #'s. For example, if you add 5 and 2 together you get 7. 9 does not equal 7. Not arithmetic, or geometric sequence.
Write a piece wise function for each function graphed below.
The piecewise function for the graph is given as follows:
y = -2, x < -4.y = 0.5x + 4, -4 < x ≤ 2y = -1.5x + 1, x > 1.How to define the piecewise function?A piecewise function is a function that has different definitions, depending on the input x of the function.
The three different definitions for the function in this problem are given as follows:
x < -4.-4 < x ≤ 2.x > 2.For x < -4, the function is constant at y = -2, hence:
y = -2, x < -4.
For -4 < x ≤ 2, the function is linear, with an slope of 0.5 and intercept of 4, hence:
y = 0.5x + 4, -4 < x ≤ 2
For x > 2, the function is also linear, with slope of -1.5, hence at x = 0 it would assume a value of 1, thus:
y = -1.5x + 1, x > 1.
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Ships in a first generation video game were
modeled like the one shown.
130 in.
in.
2 in.
in.
3 in.
How many square inches of video screen did
one ship occupy?
A 71 in.2
B 9 in.2
C 10 in.2
D 11 in.²
The area occupied by the ship is 10 inches².
What is the area of parallelogram?The area of a parallelogram is -
A{||gm} = base x height
Given is that Ships in a first generation video game were modeled like the one shown in the image.
We can write the area occupied by the ship as -
Area = A{||gm} + A{triangle}
Area = {b x h} + {L x B}
Area = [tex]$(3\frac{2}{5}\times 2)\;+\; (3\frac{2}{5}-1)\times1\frac{1}{3}[/tex]
Area = (17/5 x 2) + (17/5 - 1) x (4/3)
Area = 34/5 + 12/5 x 4/3
Area = 34/5 + 16/5
Area = 50/5
Area = 10 inches²
Therefore, the area occupied by the ship is 10 inches².
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Question
You work with a carpenter who asks you to cut 4 boards to the following lengths: 7½ inches, 10½ inches, 9 inches, and 5½ inches. What is the total length, in inches, of the cut boards?
The total length, in inches, of the four cut boards is 130 inches.
What is Addition?Addition is one of the basic mathematical operations where two or more numbers is added to get a bigger number.
The process of doing addition is also called as finding the sum.
Given that, the length of each of the cut pieces of the board are 7½ inches, 10½ inches, 9 inches, and 5½ inches.
We have to find the total length of the board.
Total length of the board is found by adding each length.
Total length = 7½ + 10½ + 9 + 5½
Mixed fraction can be converted to improper fraction by cross multiplication.
7½ = (7 * 2 + 1) / 2, 10½ = (10 * 2 + 1) / 2 and 5½ = (5 * 2 + 1) / 2
Total length = 15/2 + 21/2 + 9 + 11/2
= (15/2 + 21/2 + 11/2) + 9
= 47/2 + 9
= 65/2
Again improper fraction can be converted to mixed fraction.
Total length of a board = 32 1/2 inches
But there are 4 boards.
Total length of the 4 boards = 4 × 65/2 = 130 inches
Hence the total length is 130 inches.
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Identify the function shown in this graph. PLEASEEE.
The function shown in this graph is y = x + 4
How to determine the function shown in this graphFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we can see a straight line
This means that the graph is a linear function
This can be represented as
y = mx + c
From the graph, we have
c = 4 (because the graph intersects the y-axis at y = 4)
m = 1 (because a unit change in x gives a unit change in y)
So, we have
y = x + 4
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If the trapezoid below is reflected across the x-axis, what are the coordinates
of B?
Answer:
C
Step-by-step explanation:
under a reflection in the x- axis
a point (x, y ) → (x, - y ) , then
B (3, 8 ) → B' (3, - 8 )
Need help with this question urgent please
Answer:
Step-by-step explanation:
-8^8 is -16777216.
-8^5 is -32768.
-16777216/-32768 is 512.
btw, is this bigideas? lol i remember this website
..........................................
Answer:
8^4
Step-by-step explanation:
8^8 divided by 8^4
Because they have the same base and it is divided, so we just need to take ^8 - ^4 and get the answer
8^4
Bob is interested in examining the relationship between the number of bedrooms in a home and its selling price. After downloading a valid data set from the internet, he calculates the correlation.
The correlation value he calculates is only 0.05. What does Bob conclude?
A. Bob gives up on his research because r=.05 means there is no relationship of any kind between bedrooms and selling price.
B. Bob continues his research because even though there is no linear relationship here, there could be a different relationship.
Option B. Bob continues his research because even though there is no linear relationship here, there could be a different relationship.
A correlation coefficient of 0.05 indicates a very weak linear relationship between the number of bedrooms in a home and its selling price. In other words, the number of bedrooms in a home does not seem to be a strong predictor of its selling price based on the data that Bob has analyzed. However, this does not mean that there is no relationship at all between these two variables. There could be a different type of relationship, such as a non-linear relationship, that is not captured by the linear correlation coefficient. It's possible that Bob will need to use other techniques, such as regression analysis, to better understand the relationship between the number of bedrooms in a home and its selling price.
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which of the following results in smaller sampling variation of , the ols estimator for the slope coefficient in the sample regression model? group of answer choices smaller sample size (smaller ) smaller error variance (smaller ) smaller variation in in the sample (smaller )
Smaller sample size results in smaller sampling variation of the OLS estimator for the slope coefficient in the sample regression model due to the fact that it reduces the amount of variability in the data. Smaller error variance also reduces sampling variation as it reduces the amount of overall variation in the data.
The sampling variation of the OLS estimator for the slope coefficient in the sample regression model is affected by a variety of factors. A smaller sample size will result in smaller sampling variation because it reduces the amount of variability in the data. This is due to the fact that a smaller sample size will contain less variation in the independent variable, and therefore the estimated slope coefficient will have less variation. Additionally, a smaller error variance will also reduce the sampling variation as it reduces the amount of overall variation in the data. Finally, smaller variation in the independent variable in the sample will also lead to smaller sampling variation of the OLS estimator. This is because the slope coefficient is estimated by minimizing the sum of squared residuals, which is a function of the variation in the independent variable. Thus, if the variation in the independent variable is reduced, the slope coefficient will have less variation. In conclusion, all three factors can lead to reduction in the sampling variation of the OLS estimator for the slope coefficient in the sample regression model.
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Use the Slope Formula to calculate the slope of a line with these two points. Find the slope of the line that passes through (1,9) and (4, 8).
helpppppppppppppppppppppp
Answer:
X Y
2 1
4 7
5 10
Step-by-step explanation:
You want to raise money for the local animal shelter. Your first step is outreach — spreading the word to as many people as you can. You create three outreach options:
• Option 3: Start a chain email, in which each person forwards your email to `2` new people. On the first day, you email `2` people. On the second day, those `2` people both forward your email to `2` new people, reaching a total of `4` people. This will continue for `28`days.
Starting with just 2 initial emails, the chain email will reach a total of 536,870,910 people over the 28-day period.
If we assume that the chain email will be forwarded to exactly 2 new people each day, and that there are no duplicates or dropouts, then we can use a geometric sequence to calculate the total number of people reached over the 28-day period.
On the first day, you email 2 people, so the total number of people reached is 2.
On the second day, each of the 2 people forwards the email to 2 new people, so the total number of people reached is 2 * 2 = 4.
On the third day, each of the 4 people forwards the email to 2 new people, so the total number of people reached is 4 * 2 = 8.
This pattern continues for 28 days, with the number of people reached doubling each day. Therefore, the total number of people reached over the 28-day period is:
2 + 4 + 8 + 16 + ... + 2^28
To calculate this sum, we can use the formula for the sum of a geometric series:
S = a(1 - r^n) / (1 - r)
where a is the first term (2), r is the common ratio (2), and n is the number of terms (28).
Plugging in these values, we get:
S = 2(1 - 2^28) / (1 - 2)
= 2(1 - 268,435,456) / (-1)
= 536,870,910
This is a very large number and could potentially have a significant impact on raising awareness and funds for the local animal shelter.
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The equation ŷ = 67.34x - 128,933.4 predicts a rodent population in a town in year x.
According to the equation, what was the rodent population in 2005?
Enter your answer in the box. Round to the whole number.
The predicted rodent population in the town in 2005 was approximately 6083.
What was the rodent population in 2005?From the question, we have the following parameters that can be used in our computation:
ŷ = 67.34x - 128,933.4
To find the rodent population in 2005, we need to substitute x = 2005 into the equation and solve for ŷ:
ŷ = 67.34(2005) - 128,933.4
So, we have
ŷ = 135016.7 - 128,933.4
Evaluate
ŷ = 6083
Hence, the predicted rodent population was 6083.
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2) The area of Norway's is 24% more than the area of Colorado. So Norway's area if
Colorado's area?
The area of Norway's is 24% more than the area of Colorado.So, the area of Colorado is approximately 260,449 square kilometers.
What is Area?
Area is a measurement of the amount of two-dimensional space occupied by a surface or an object. In mathematics, area is a scalar quantity that describes the size of a region in a plane. The units of area are typically square units, such as square meters, square centimeters, square inches, etc.
The formula for the area of a shape depends on the shape itself. For example, the area of a rectangle is equal to its length multiplied by its width, while the area of a circle is equal to π times the square of its radius. Other common shapes and their area formulas include triangles, parallelograms, and trapezoids.
Let's call the area of Colorado "x". If Norway's area is 24% more than Colorado, then Norway's area can be represented as x + 0.24x = 1.24x.
To find the area of Colorado, we can set up an equation:
1.24x = area of Norway
x = area of Norway / 1.24
The area of Norway is 323,802 square kilometers. Therefore, the area of Colorado can be calculated as:
x = 323,802 / 1.24
x = 260,449 square kilometers
So, the area of Colorado is approximately 260,449 square kilometers.
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y = -2x + 1
4x + 2y = -1
(0, -3)
(-3,0)
No solution
Infinitely many solutions
The given equations having infinitely many solutions.
What is Solutions of system of equation?
A solution to a system of equations is a collection of variable values that satisfy all of the equations at the same time. To solve a system of equations, one must determine all of the sets of variable values that compose the system's solutions.
The solution to the system of equations y = -2x + 1 and 4x + 2y = -1 can be determined graphically by plotting both equations on the same set of axes and finding the points of intersection.
If there is exactly one point of intersection, then that point represents the unique solution to the system. If there are no points of intersection, then the system has no solution. If there are infinitely many points of intersection, then the system has infinitely many solutions.
Based on the information you provided, the system has two points of intersection: (0, -3) and (-3, 0). This means that the system has two solutions, and the solution set is the set of all points on the line that passes through these two points.
Therefore, The given equations having infinitely many solutions.
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Help fast please!!! Trigonometry word problems
Answer: pay attention
Step-by-step explanation:
Select the correct answer.
What is the justification for step 3 in the solution process?
0.8a - 0.1a = a - 2.5
Step 1: 0.7a = a - 2.5
Step 2: -0.3a = -2.5
Step 3:
a =8.3
O A.
the addition property of equality
O B. the subtraction property of equality
О C.
combining like terms
O D. the division property of equality
Answer: D. the division property of equality
Step-by-step explanation:
In step three you will be dividing -2.5 divided by -0.3 to get a.
Victor and his friends like to collect
and trade cards from a certain combat
card game. Victor used his allowance
to purchase 9 booster packs and 4
premade decks, which included a total
of 266 cards. For his birthday, he
received 10 booster packs and 5
premade decks, which included a total
of 320 cards. How many cards come in
every booster pack and every
premade deck?
The value of x and y in the system of equations, are 10 and 44, therefore, the number of booster pack and premade deck are 10 and 44 respectively.
What is a system of equation?A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
Given that, a deck contains 266 cards which have 9 booster packs and 4 premade decks, and 10 booster packs and 5 premade decks, which included a total of 320 cards.
Let the number of booster pack and premade deck be x and y,
Establishing the system of equations,
9x + 4y = 266....(i)
10x + 5y = 320
2x + y = 64...(ii)
Multiplying eq(ii) by 4 and subtract eq(ii) from eq(i)
(9x + 4y = 266) - (8x + 4y = 256)
x = 10
Put x = 10 in eq(ii)
20 + y = 64
y = 44
Hence, the value of x and y in the system of equations, are 10 and 44, therefore, the number of booster pack and premade deck are 10 and 44 respectively.
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32 children voted for thier favorite ice cream chocolate 3/8 so how may children voted for chocolate explanation step by step plssss
On solving the provided question we can say that The result of multiply the total number of kids by the proportion of those who enjoy chocolate is 12
What is Multiplication?Along with addition, subtractiοn, and division, multiplication is one of the four arithmetic operations. Multiplicatiοn in math refers to regularly adding groups of the same size. The formula for multiplication is multiplicand multiplier Equals prοduct.
Specifically, multiplicand: First number (factοr). divider: Second number (factor). After multiplying the multiplicand and the multiplier, the result is knοwn as the product. Multiple additiοns are made while adding numerals. as in 5 times 4 Equals 5 + 5 + 5 + 5 = 20, I multiplied 5 by 4 times. Multiplication is frequently referred tο as "doubling" because οf this.
The result of multiply the tοtal number of kids by the proportion of those who enjoy chocolate is
32 × 3/8 = 12
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four students, tamika, arianys, jin, and mohal, line up one behind the other. how many different ways can they stand in line?
There are 24 different ways they can stand in line.
By choosing some items from a set and creating subsets, permutation and combination are two approaches to represent a group of objects. It outlines the numerous configurations for a particular set of data. Permutations are the selection of data or objects from a set, whereas combinations are the order in which they are represented.
There are four students, and each one can be in any one of the four positions in the line. Therefore, the total number of different ways they can stand in line is:
4 × 3 × 2 × 1 = 24
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TRIGONOMETRY PERIMETER
The perimeter of the triangle is
13.82 inHow to find the perimeter of the triangle'The perimeter of the triangle is sum of the length of the sides
The sides are solved as follows using trigonometry relations
Sin = opposite / hypotenuse - SOH
Cos = adjacent / hypotenuse - CAH
Tan = opposite / adjacent - TOA
Solving for NM using tan
tan 59 = 5 / NM
NM = 5 / tan 59 = 3
Solving for LN
sin 59 = 5 /LN
LN = 5 / sin 59 = 5.83
The perimeter of the triangle
= 5.83 + 5 + 3
= 13.82 in
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Hank came home from Trick-Or-Treating
with 8 Reece's, 12 Snickers, 5 Sour Patch
Kids, 4 Hershey's bars and 6 packs of
Skittles. Hank is allergic to chocolate.
Write the ratio of candy that Hank can
eat to the total amount Hank has.
Since Hank is allergic to chocolate, he cannot eat Reese's, Snickers, Hershey's bars, or any other type of chocolate candy.
Therefore, the only candy that Hank can eat is the Sour Patch Kids and Skittles.
The total number of Sour Patch Kids that Hank has is 5.
The total number of Skittles that Hank has is 6 packs, or 6 * the number of Skittles in one pack (let's assume it's 10 Skittles per pack). So, the total number of Skittles that Hank has is 6 * 10 = 60.
Adding the number of Sour Patch Kids and Skittles, the total number of candy that Hank can eat is 5 + 60 = 65.
The total amount of candy that Hank has is 8 Reece's + 12 Snickers + 5 Sour Patch Kids + 4 Hershey's bars + 6 packs of Skittles = 8 + 12 + 5 + 4 + 6 * 10 = 8 + 12 + 5 + 4 + 60 = 89.
The ratio of candy that Hank can eat to the total amount of candy he has is 65 / 89 = approximately 0.73, which can be expressed as a simplified fraction as 73 / 100.
Answer:
11:35
Step-by-step explanation:
no step by step explanation.
Nishtha has rs 1 coin , rs 2 coin , rs 5 coin, rs 10 coin. She needs to pay for a pencil rs 4. What is the probability of her using 5 rs coin
The probability of Nishtha using Rs 5 coin is [tex]\frac{1}{4}[/tex] , if she needs to pay for a pencil Rs 4.
P(E) = number of favorable outcomes / total number of outcomes
Denominations of coins = ₹1, ₹2, ₹5 and ₹10 each
Total number of coins = 4
Coins that can pay the amount = ₹5 and ₹10
Number of Favorable Outcomes = 2
For the probability of using two coins :-
P(E) = [tex]\frac{2}{4} = \frac{1}{2}[/tex]
we have to find the probability of using ₹5 coin. And here the probability of using of ₹5 coin and ₹10 coin are equal likely. So using of ₹5 coin is 50% of the probability of using both coin
P(rs5) = [tex]50\% \times \frac{1}{2}[/tex]
= [tex]\frac{1}{4}[/tex]
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There are purple, white and blue counters in a bag in the ratio 16:18:3
There are 78 more purple counters than blue counters.
How many white counters are there?
Answer:
Step-by-step explanation:
Step-by-step explanation:
Let's call the number of purple counters "x". This means that the number of blue counters is x - 78, and the number of white counters is 18x.
According to the ratio, the sum of the number of purple and blue counters is 16x + (x - 78) = 17x - 78.
And the sum of all counters is 16x + 18x + 3x = 37x.
Knowing that the sum of all counters is the same, we can set the two sums equal to each other:
37x = 17x - 78 + 37x
So, we have:
74x = 17x - 78 + 37x
57x = -78
x = -78/57
Since x can't be negative, we have to reject this solution.
However, the number of white counters can be found by multiplying 18 by the number of purple counters:
18 * x = 18 * (x/57) = (18/57) * x = (18/57) * 78 = 72
Therefore, there are 72 white counters in the bag.
a tank contains 1120 l of pure water. solution that contains 0.08 kg of sugar per liter enters the tank at the rate 4 l/min, and is thoroughly mixed into it. the new solution drains out of the tank at the same rate. (a) how much sugar is in the tank at the begining?
a) 0 kg of sugar is in the tank at the beginning., b) ds/dt = 0.08-(S/1120)*4, c) 0.32 kg of sugar is in the tank after 1 minute., d) 2.59 kg of sugar is in the tank after 84 minutes.
a) At the beginning, there is no sugar in the tank since it contains only pure water.
b) Let S(t) be the amount of sugar in the tank at time t (in minutes). The rate of change of S is given by the rate at which sugar enters the tank minus the rate at which it leaves. Since the solution enters at a rate of 4 L/min, and contains 0.08 kg of sugar per liter, the rate at which sugar enters is 0.08 kg/L * 4 L/min = 0.32 kg/min. Since the solution leaves at the same rate, the differential equation that models the situation is:
dS/dt = 0.32 - (S/1120) * 4
c) To find the amount of sugar after 1 minute, we need to solve the differential equation from part (b) with the initial condition S(0) = 0 (since the tank initially contains only water). One possible way to solve the differential equation is to use separation of variables:
dS/dt + (4/1120) S = 0.32
Multiplying both sides by dt and dividing by (0.32 - (4/1120) S), we get:
(1/S) dS = (4/0.32 - (1120/4)) dt
Integrating both sides from t = 0 to t = 1 and from S = 0 to S = S(1), we get:
ln(S(1)) - ln(0) = (1.25 - 280) * 1
S(1) = [tex]e^{0.25} * 1120[/tex] ≈ 300.92 kg
Therefore, after 1 minute, there is approximately 300.92 kg of sugar in the tank.
d) To find the amount of sugar after 84 minutes, we can solve the differential equation from part (b) numerically using an appropriate method such as Euler's method, or we can use an integrating factor to solve it analytically. One possible way to use an integrating factor is to multiply both sides of the differential equation by exp(4t/1120):
exp(4t/1120) dS/dt + (S/280) exp(4t/1120) = 0.32 exp(4t/1120)
This can be written as:
d/dt [S exp(4t/1120)] = 0.32 exp(4t/1120)
Integrating both sides from t = 0 to t = 84, we get:
[S(84) exp(4/1120 * 84)] - [S(0) exp(4/1120 * 0)] = ∫(0 to 84) 0.32 exp(4t/1120) dt
Since S(0) = 0 and exp(4/1120 * 84) is a constant, we can simplify this to:
S(84) = (1/exp(4/1120 * 84)) ∫(0 to 84) 0.32 exp(4t/1120) dt
Using integration by substitution with u = 4t/1120, we get:
S(84) = (1/exp(4/1120 * 84)) * (1120/4) * (0.32/4) * [exp(4/1120 * 84) - 1]
S(84) ≈ 301.53 kg
Therefore, after 84 minutes, there is approximately 301.53 kg of sugar in the tank.
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The complete question is:
A tank contains 1120 L of pure water. At a rate of 4 L/min, a solution that contains 0.08 kilogramme of sugar per litre enters the tank. At the same rate that it drains from the tank, the solution is mixed.
a) How much sugar is in the tank when it first starts?
b) With S representing the amount of sugar (in kg) at time t, write a differential equation which models the situation.
c) After 1 minute, calculate the sugar content (in kilogramme).
d) After 84 minutes, calculate the sugar content (in kg).
What is the standard deviation of the data set {2,1,1,2,2,3}?
You may use the desmos calculator to assist you.
Enter your answer as a number, rounded to the nearest tenth
The standard deviation of the data set is 0.7.
How to calculate standard deviation?First, calculate the mean of the data set:
(mean) = (2+1+1+2+2+3)/6 = 11/6 ≈ 1.8
Next, calculate the deviation of each data point from the mean:
2 - 1.8 = 0.2
1 - 1.8 = -0.8
1 - 1.8 = -0.8
2 - 1.8 = 0.2
2 - 1.8 = 0.2
3 - 1.8 = 1.2
Now square each deviation:
0.2² = 0.04
(-0.8)² = 0.64
(-0.8)² = 0.64
0.2² = 0.04
0.2² = 0.04
1.2² = 1.44
The sum of the squared deviations is:
0.04 + 0.64 + 0.64 + 0.04 + 0.04 + 1.44 = 2.84
To find the variance, we divide by the number of data points:
variance = 2.84/6 ≈ 0.4733
Finally, take the square root of the variance to get the standard deviation:
standard deviation = √(0.4733) ≈ 0.69
Therefore, the standard deviation of the data set {2,1,1,2,2,3} is approximately 0.7 (rounded to the nearest tenth).
Learn more on standard deviation here: https://brainly.com/question/24298037
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