In a circle, an angle measuring 9.8 radians intercepts an arc of length 12.8. Find the
radius of the circle to the nearest 10th.

Answer:

238

Step-by-step explanation:

340 times 0.7 is 238

Answer:

238

Step-by-step explanation:

30% of 340

30/100×340

3/10×34

3×34

102 is the decrease

So,340-102

=238

The total number of red blood cells produced by human body in each minute is given by [ 1.2 × 10^8​ ] red blood cells

Number of red blood cells produced by human body = 4. 8 × 10^6

Time taken by human body to produce 4. 8 × 10^6 red blood cells

= 4×10^(−2)​ minute

Number of red blood cells produced by human body in one minute are :

4 × 10^(−2)​ minute = 4. 8 × 10^6 red blood cells

⇒ 1 minute =  [ 4. 8 × 10^6 / 4 × 10^(−2)​ ] red blood cells

⇒ 1 minute =  [ 1.2 × 10^( 6 - (−2) )​ ] red blood cells

⇒ 1 minute =  [ 1.2 × 10^( 6 + 2) )​ ] red blood cells

⇒ 1 minute =  [ 1.2 × 10^8​ ] red blood cells

Therefore, total number of red blood cells produced by human body in one minute is equal to [ 1.2 × 10^8​ ] red blood cells.

The above question is incomplete, the complete question is:

The human body produces about4. 8×10^6​ red blood cells in 4×10^(−2)​ minute. How many red blood cells does the body produce each minute? Write your answer in scientific notation and in standard form.

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a) To prove L(a) is an ideal of R, we show it is an additive subgroup and closed under multiplication by any element in R.

b) R is an integral domain if and only if L(a) = {0} for all a in R, meaning the only annihilator is zero.

a) To prove that L(a) is an ideal of R, we need to show that it satisfies two properties: (i) it is an additive subgroup of R, and (ii) for any x in L(a) and any r in R, the product rx and xr are also in L(a).

(i) Additive Subgroup:

L(a) is non-empty since 0 is always in L(a) (0a = 0).

For any x, y in L(a), we have (xa)y = 0y = 0 and x(ay) = x0 = 0, which means that (xa)y and x(ay) are also in L(a).

For any x in L(a), we have xa = 0, so (-x)a = -(xa) = -0 = 0. Thus, -x is also in L(a).

Therefore, L(a) is closed under addition and additive inverses, making it an additive subgroup of R.

(ii) Product Property:

For any x in L(a) and r in R, we have (rx)a = r(xa) = r0 = 0, so rx is in L(a).

Similarly, (xr)a = x(ra) = x0 = 0, so xr is also in L(a).

Since L(a) satisfies both properties, it is an ideal of R.

b) R is an integral domain if and only if L(a) = {0} for all a in R.

If L(a) = {0} for all a in R, it means that the only element that annihilates any element of R is the zero element. This implies that R has no non-zero zero divisors, making it an integral domain.

On the other hand, if R is an integral domain, it means that it has no non-zero zero divisors. This implies that the only element that annihilates any element of R is the zero element, i.e., L(a) = {0} for all a in R.

Therefore, R is an integral domain if and only if L(a) = {0} for all a in R.

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Answer: 0.6763 cm∧2

Step-by-step explanation: Variance is one of the measures of dispersion which is the the second central moment in probability. It is defined as a measure of by how much the values in a data set differs from the mean of the values. Thus it is the average of the squares of the deviations from the mean as this ensures that both the negative and positive deviations do not cancel each other out.

The sample variance would be calculated as follows:

Population size is 7 (5.6 4.9 6.0 5.1 5.5 5.1 7.5)

Mean: Sum of samples / population size ;

(5.6 4.9 6.0 5.1 5.5 5.1 7.5) / 7 = 5.67

Applying the formula for variance: [ Summation (x - mean) ] / population size =( |5.6 - 5.67| + |4.9 - 5.67| + |6.0 - 5.67| + (|5.1 - 5.67|) * 2 + | 5.5 - 5.67| + |7.5 - 5.67|) / 7 = 0.6763 cm^2

Answer:

Kate is 3 years old, Jane is 9 years old

Step-by-step explanation:

1.) First, assign variables to all of their ages. If we say Kate's age is x, Jane's age is 3 times this, which can be written as j, is 3x.

2.) Jane's age is also 2 less than twice of Kate's in 5 years. This means that her age is also 2(x+5) - 2 = j + 5. With a little simplification, you get that 2x + 8 = j + 5.

3.) Since j, Jane's age, is also 3x, we can substitute 3x in for j in the second equation. If you do this, you get 2x + 8 = 3x + 5.

4.) By moving the x onto one side and the numbers onto another, you get x = 3. X was Kate's age, meaning that Kate is 3 years old.

5.) Finally, since Jane's age is 3 times Kate's age, Jane's age is 3 * 3, which is 9. Jane is 9 years old.

Jane is 9 years old and Kate is 3 years old.To solve the problem, let's first establish variables for Jane and Kate's ages.

Let J represent Jane's age and K represent Kate's age.
According to the student question, Jane is 3 times as old as Kate, which can be represented as:
J = 3K
In 5 years, Jane's age will be 2 less than twice Kate's age, which can be represented as:
J + 5 = 2(K + 5) - 2
Now we can solve the equations step by step:

Substitute the first equation into the second equation to eliminate one of the variables:
3K + 5 = 2(K + 5) - 2
Distribute the 2 on the right side of the equation:
3K + 5 = 2K + 10 - 2
Simplify the equation by combining like terms:
3K + 5 = 2K + 8
Move the 2K term to the left side of the equation:
K = 3
now we know that Kate is currently 3 years old.
Substitute K's value back into the first equation to find Jane's age:
J = 3K
J = 3(3)
Simplify to find Jane's age:
J = 9
So, Jane is currently 9 years old.
Jane is 9 years old and Kate is 3 years old.

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There are 7 degrees of freedom.

In performing the pooled-variance t test, the degrees of freedom can be calculated using the formula:
df = (n1 - 1) + (n2 - 1)

Substituting the given values:
df = (4 - 1) + (5 - 1)
df = 3 + 4
df = 7

Therefore, there are 7 degrees of  freedom.

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There are 7 degrees of freedom for the pooled-variance t-test.

To perform a pooled-variance t-test, we need to calculate the degrees of freedom. The formula for degrees of freedom in a pooled-variance t-test is:

\(\[\text{{df}} = n_1 + n_2 - 2\]\)

where \(\(n_1\)\) and \(\(n_2\)\) are the sample sizes of the two independent samples.

In this case, \(\(n_1 = 4\)\) and \(\(n_2 = 5\)\). Substituting these values into the formula, we get:

\(\[\text{{df}} = 4 + 5 - 2 = 7\]\)

In a pooled-variance t-test, we combine the sample variances from two independent samples to estimate the population variance. The degrees of freedom for this test are calculated using the formula \(df = n1 + n2 - 2\), where \(n_1\)and \(n_2\) are the sample sizes of the two independent samples.

To understand why the formula is \(df = n1 + n2 - 2\), we need to consider the concept of degrees of freedom. Degrees of freedom represent the number of independent pieces of information available to estimate a parameter. In the case of a pooled-variance t-test, we subtract 2 from the total sample sizes because we use two sample means to estimate the population means, thereby reducing the degrees of freedom by 2.

In this specific case, the sample sizes are \(n1 = 4\) and \(n2 = 5\). Plugging these values into the formula gives us \(df = 4 + 5 - 2 = 7\). Hence, there are 7 degrees of freedom for the pooled-variance t-test.

Therefore, there are 7 degrees of freedom for the pooled-variance t-test.

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Answer:

✓ 45% = 9/20

Step-by-step explanation:

What box?

Answer:

9/20.

Step-by-step explanation:

45/100

= 45/5 /  100/5

= 9/20.

Answer:

solved graphically,

it's just the point where the two lines intersect

In analyzing the course grades of students in an elementary statistics course, a professor notices a pattern where seniors tend to perform better than sophomores.

This observation may lead the professor to be tempted to conclude that older students generally perform better than younger ones in statistics.

However, it is crucial to consider the presence of possible confounding variables that could influence this relationship and potentially lead to a biased conclusion.

One possible confounder in this situation is the students' prior knowledge or experience with statistics. It is reasonable to assume that seniors, who are closer to completing their undergraduate studies, have had more opportunities to take advanced courses that include statistical concepts.

They may have already gained exposure to statistical methods and developed a better understanding of the subject matter. On the other hand, sophomores, being in the earlier stages of their academic journey, may not have had as much exposure to statistics or have taken introductory courses that cover statistical concepts in depth.

If the professor solely focuses on the age difference between the two groups (seniors and sophomores) without accounting for the confounding factor of prior knowledge or experience, the conclusion that older students perform better would be flawed.

The observed difference in performance may be attributed more to differences in prior preparation rather than age itself. This confounding factor poses a threat to the internal validity of the study.

To properly evaluate the impact of age on student performance, it is essential to control for the confounding variable of prior knowledge or experience in statistics.

This can be achieved by considering additional variables such as previous coursework or exposure to statistical concepts. For instance, the professor could collect data on the number of statistics-related courses taken by each student or inquire about their familiarity with statistical methods prior to enrolling in the elementary statistics course.

By including these variables in the analysis, the professor can better isolate the effect of age on student performance and draw more accurate conclusions.

Controlling for confounding variables is crucial to ensure that the relationship between age and performance in statistics is accurately assessed.

Without accounting for potential confounders, the observed difference in grades between seniors and sophomores may lead to an incorrect conclusion.

By considering additional variables related to prior knowledge or experience, the professor can obtain a more comprehensive understanding of the factors influencing student performance and make more informed interpretations.

In conclusion, when analyzing the grades of students in an elementary statistics course, it is important to be cautious about drawing conclusions based solely on age differences.

The presence of confounding variables, such as prior knowledge or experience with statistics, can influence the observed relationship. To mitigate the influence of confounders, it is necessary to control for relevant variables and consider the broader context.

By taking these steps, the professor can obtain a more accurate understanding of the relationship between age and student performance in statistics.

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The percent of all adults who expect an inheritance is between 25% and 31%.

Hence option B is the correct answer.

It is given that (\(\hat{p}\)) = 28% = 0.28

                        \(\bar{E}\) = 3% = 0.03

We can use the formula;

                        Cl =  (\(\hat{p}\)) ±   \(\bar{E}\)

Confidence interval is calculated as :

                          Cl =  (\(\hat{p}\))  ± \(\bar{E}\)

                               = 0.28  ±  0.03

                          Cl = (0.25, 0.31)

Hence, the option (b)  the percent of all adults who expect an inheritance is between 25% and 31% is correct.

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Answer:

10.4476119402

Step-by-step explanation:

If you want a reasonable answer it would be 10.44 or 10.4!

The  probability of event A is P(A) = 1/4 or 0.25.

The formula to find P(A) for a series of simple events is:

P(A) = (number of outcomes that satisfy the event A) / (total number of possible outcomes)

For example, if you are tossing a coin and selecting a number at the same time, and event A is defined as getting a head and an even number, then:

- The number of outcomes that satisfy event A is 1 (getting a head and an even number, i.e., H2)
- The total number of possible outcomes is 4 (H1, H2, T1, T2)
- Therefore, the probability of event A is P(A) = 1/4 or 0.25.

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Answer:

Letter B matches the probability.

Step-by-step explanation:

Lucy throws a fair six sided dice.

Probability of the dice landing on a number between 1 and 6 = \(\frac{\text{Favorable outcome}}{\text{Number of events}}\)

= \(\frac{1}{6}\)

On a number line fraction \(\frac{1}{6}\) can be represented by,

An small section (A to B) will represent the fraction = \(\frac{1}{6}\)

Therefore, letter B will match the probability of a dice landing on a number between 1 and 6.

The joint probability mass function is determined to be p(x,y) = (2/3)xy, the conditional probability p(x > 1 | y = 1) is 1/2, E(X) is 10/3, and E(Y) is 2.

To find the value of k that makes the given function a probability mass function, we need to ensure that the sum of all probabilities over the entire sample space is equal to 1.

Let's calculate the sum of probabilities:

∑∑ p(x, y) = ∑∑ k(xy)

Since the function is defined as zero when x ≠ 1 and 2y ≠ 1, we only need to consider the cases where x = 1 and 2y = 1:

∑∑ p(x, y) = k(1 * y) + k(1 * (1/2))

To make this sum equal to 1, we need:

k(y + 1/2) = 1

Since this equation holds for all values of y, we can choose a value of y that satisfies the equation. Let's choose y = 1:

k(1 + 1/2) = 1

k(3/2) = 1

k = 2/3

So, the value of k that makes the function a probability mass function is 2/3.

Now let's find p(x > 1 | y = 1):

p(x > 1 | y = 1) = p(x = 2 | y = 1) / p(y = 1)

To calculate p(x = 2 | y = 1), we use the joint probability mass function:

p(x = 2 | y = 1) = k(2 * 1) = 2/3

To calculate p(y = 1), we sum the probabilities over all x values:

p(y = 1) = ∑ p(x, 1) = p(1, 1) + p(2, 1) = k(1 * 1) + k(2 * 1) = 2/3 + 2/3 = 4/3

Therefore, p(x > 1 | y = 1) = (2/3) / (4/3) = 1/2.

To find E(X), we need to calculate the expected value of X using the joint probability mass function:

E(X) = ∑∑ x * p(x, y)

= 1 * p(1, 1) + 2 * p(2, 1)

= 1 * (k * 1 * 1) + 2 * (k * 2 * 1)

= 1 * (2/3 * 1 * 1) + 2 * (2/3 * 2 * 1)

= 2/3 + 8/3

= 10/3

Therefore, E(X) = 10/3.

To find E(Y), we need to calculate the expected value of Y using the joint probability mass function:

E(Y) = ∑∑ y * p(x, y)

= 1 * p(1, 1) + 1 * p(1, 2)

= 1 * (k * 1 * 1) + 1 * (k * 1 * 2)

= 1 * (2/3 * 1 * 1) + 1 * (2/3 * 1 * 2)

= 2/3 + 4/3

= 6/3

Therefore, E(Y) = 2.

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Answer:

A = 2b² + 15b + 7

Step-by-step explanation:

Assuming the figure is a trapezium , then

the area (A) is calculated as

A = \(\frac{1}{2}\) h (b₁ + b₂)

where h is the perpendicular height between the parallel bases b₁ and b₂

here h = b + 7 , b₁ = 3b - 5 , b₂ = b + 7 , then

A = \(\frac{1}{2}\) (b + 7)(3b - 5 + b + 7)

   = \(\frac{1}{2}\) (b + 7)(4b + 2) ← expand factors using FOIL

   = \(\frac{1}{2}\) (4b² + 30b + 14) ← distribute parenthesis by \(\frac{1}{2}\)

   = 2b² + 15b + 7

The cost of direct labor per unit is $5.628 per apple.

To calculate the cost of direct labor per unit, we need to determine the total labor hours required to produce one unit of output and then multiply it by the wage rate.

Let's denote the labor hours required for the first resource as "L₁" and the labor hours required for the second resource as "L₂".

The first resource has a capacity of 2.1 apples per hour, and the demand is 1.6 apples per hour. Therefore, the labor hours required for the first resource per unit of output are:

L₁ = 1 apple / (2.1 apples/hour) = 0.4762 hours/apple (rounded to 4 decimal places)

The second resource has a capacity of 4.4 apples per hour, and the demand is 1.6 apples per hour. Therefore, the labor hours required for the second resource per unit of output are:

L₂ = 1 apple / (4.4 apples/hour) = 0.2273 hours/apple (rounded to 4 decimal places)

Now, let's calculate the total labor hours required per unit:

Total labor hours per unit = L₁ (first resource) + L₂ (second resource)

= 0.4762 hours/apple + 0.2273 hours/apple

= 0.7035 hours/apple (rounded to 4 decimal places)

Finally, to calculate the cost of direct labor per unit, we multiply the total labor hours per unit by the wage rate:

Cost of direct labor per unit = Total labor hours per unit * Wage rate

= 0.7035 hours/apple * $8/hour

= $5.628 per apple (rounded to 3 decimal places)

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The given equation 3x^2 - y^2 + z^2 = 0 represents a surface known as an elliptic paraboloid. To sketch this surface using traces, we can fix one variable (either x, y, or z) and vary the other two to observe the resulting curve.

Let's fix x at a constant value of 0. Substituting x = 0 into the equation, we get -y^2 + z^2 = 0. This equation represents a pair of intersecting lines, forming a trace. By varying x and fixing y or z, we can obtain additional traces, which are also pairs of intersecting lines.

Thus, by considering multiple traces, we can sketch the elliptic paraboloid surface, which resembles a bowl or a saddle. The traces consist of intersecting lines that form a grid-like pattern on the surface.

Now, moving on to the second question, we are given two skew lines with parametric equations. To find the distance between these lines, we can use the closest distance formula.

First, we need to find a point on each line. By setting t = 0 in the first line's equations, we find a point (2, 3, 0). Similarly, setting s = 0 in the second line's equations gives us a point (1, 6, -2).

Next, we find the direction vectors for both lines. The direction vector for the first line is <1, 6, 2>, and for the second line is <2, 14, 5>.

Using the closest distance formula, we can calculate the distance between the two lines as follows:

distance = |(2-1, 3-6, 0+2) · (1, 6, 2) x (2, 14, 5)| / |(1, 6, 2) x (2, 14, 5)|

Simplifying this expression will give us the distance between the skew lines.

Please note that the exact calculations are omitted here, but following the steps outlined above will provide the desired distance.

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The Equation of circle is (x-2)² +(y+ 8)² = 7²

The standard form of a circle with center (h, k) and radius r is given by the equation:

(x-h)²  + (y-k)² = r²

In this equation, (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle.

In this case, the center of the circle is (2, -8) and the radius is 7.

Plugging these values into the equation, we have:

(x- 2)² + (y- (-8))² = 7²

Simplifying further:

(x-2)² +(y+ 8)² = 7²

So, the equation in standard form for the circle with center (2, -8) and radius 7 is:

(x-2)² +(y+ 8)² = 7²

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The probability that the numbers are selected and multiplied to be a multiple of 196 is 1/3.

196 is the multiple we require.We list the components of 196, which are 14*14=2*7*2*7.

Therefore, the required numbers that will be present in any product must have at least these as its factors.So, we choose 98 now, and it's possible that all it takes to achieve 196 is to multiply that by 2. Therefore, if we take 98 as one of our numbers, the other numbers that must be multiplied are 2,4,12,14,28. That makes 5 pairs necessary.

So, we choose 98 now, and it's possible that all it takes to achieve 196 is to multiply that by 2. Therefore, if we take 98 as one of our numbers, the other numbers that must be multiplied are 2,4,12,14,28. That makes 5 pairs necessary. We can now take pairings like (21,28) and (14,28) based on the prime factorization (14,28).

The total number of possible pairs is ⁷C₂ = 21

Therefore, the required probability =7/21=1/3

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Each installment will be approximately $15,280.55.

To calculate the equal six-monthly installment, we can use the formula for the present value of an annuity.

Principal amount (P) = $500,000

Interest rate (r) = 12% per annum = 12/100 = 0.12 (compounded monthly)

Number of periods (n) = 20 (since there are 20 equal six-monthly installments)

The formula for the present value of an annuity is:

\(P = A * (1 - (1 + r)^(-n)) / r\)

Where:

P = Principal amount

A = Equal installment amount

r = Interest rate per period

n = Number of periods

Substituting the given values into the formula, we have:

$500,000 = \(A * (1 - (1 + 0.12/12)^(-20)) / (0.12/12)\)

Simplifying the equation:

$500,000 = A * (1 - (1.01)^(-20)) / (0.01)

$500,000 = A * (1 - 0.6726) / 0.01

$500,000 = A * 0.3274 / 0.01

$500,000 = A * 32.74

Dividing both sides by 32.74:

A = $500,000 / 32.74

A ≈ $15,280.55

Therefore, each installment will be approximately $15,280.55.

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Answer:

the coefficient is 1.

Step-by-step explanation:

it is not visible or necessarily written

Answer:

Step-by-step explanation:

The total distance of the outer sides of a closed figure is known as the perimeter. It is the total length of all sides of a polygon. The unit of the perimeter of any polygon will remain the same as the unit of its respective sides.

Answer:

To find the perimeter of a regular polygon, we take the length of each side, and multiply it by the number of sides.

hope it helps

plzz mark it as brainliest...

So, the y-value of the solution to the system of equations 3x + 5y = 17 and 4x + 4y = -13 is not possible to find, because the system is inconsistent and has no solution.

To find the y-value of the solution to the system of equations 3x + 5y = 17 and 4x + 4y = -13, we can use one of the methods for solving systems of equations, such as substitution, elimination, or graphing. In this case, we will use elimination method.

The first step of elimination method is to eliminate one of the variables by adding or subtracting the equations. In this case, we will multiply the first equation by 4 and the second equation by -3 and add them:

4(3x + 5y) = 4(17)

12x + 20y = 68

-3(4x + 4y) = -3(-13)

-12x - 12y = 39

then we can add these two equations:

12x + 20y = 68

-12x - 12y = 39

0 = 29

This is an impossible equation, which means that the system has no solution.

Therefore, the y value of the solution to the system of equations 3x + 5y = 17 and 4x + 4y = -13 is not possible to find, because the system is inconsistent and has no solution.

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Answer:

whither what I got npthing

Answer:

x = 1, y = 3

Step-by-step explanation:

use substitution method since the second equation is already solved for 'x'

substitute '2y-5' for 'x' in the first equation:

2y - 5 + 3y = 10

5y - 5 = 10

5y = 15

y = 3

now substitute 3 for y to find out what x equals:

x + 3(3) = 10

x + 9 = 10

x = 1

Answer:

Step-by-step explanation:

a.v = 10 * 5 * 7 = 350cm^3

b.because 1m^3=1000dm^3=1000000cm^3

so 1cm^3=0.000001m3

350cm^3=0.00035m^3

Answer:

that you're positive that you should be trying out these difficult math questions, let’s get right to it! The answers to these questions are in a separate section below, so you can go through them all at once without getting spoiled.

#1:

body_ACT_0506_-_56

#2:

body_ACT_0506_-_59

#3:

body_ACT_0809_-_38_J

#4:

body_ACT_0809_-_54

#5:

body_ACT_0809_-_55-1

#6:

body_ACT_0809_-_56

#7:

body_ACT_0809_-_57-1

#8:

body_ACT_0809_-_60

#9:

body_ACT_1112_-__48-1

#10:

body_ACT_1112_-_45

#11:

body_ACT_1112_-_51-1

#12:

body_ACT_1112_-_52

#13:

body_ACT_1112_-_53

#14:

body_ACT_1112_-_58

#15:

body_ACT_1314_-_55-1

Step-by-step explanation:

Answer:

-8.72811548...   i think

Step-by-step explanation:

a² + b² = c²

8.3² + 2.7² = c²

68.89 + 7.29 = c²

76.18 = c²

√76.18, -√76.18 = c

c = 8.72811548…, −8.72811548…

I think because it's depression, it's -8.72811548...

The 95% confidence interval for the mean weight of bags of that specific brand of candies is approximately 2.4461 ounces to 2.5539 ounces.

To construct a 95% confidence interval for the mean weight of the bags of that specific brand of candies, we can use the following formula:

Confidence Interval = Sample Mean ± (Critical Value)× (Standard Deviation / √Sample Size)

First, let's calculate the critical value. Since the population distribution is assumed to be normal and the sample size is small (n = 16), we can use a t-distribution instead of a z-distribution.

The critical value can be obtained from the t-distribution table or using statistical software. For a 95% confidence level with 15 degrees of freedom (n - 1 = 16 - 1 = 15), the critical value is approximately 2.131.

Now, we can plug in the given values into the formula:

Sample Mean = 2.5 ounces (given)

Standard Deviation = 0.1 ounces (known)

Sample Size (n) = 16 (given)

Critical Value = 2.131 (from t-distribution)

Confidence Interval = 2.5 ± (2.131)× (0.1 / √16)

Calculating the standard error (Standard Deviation / √Sample Size):

Standard Error = 0.1 / √16 = 0.1 / 4 = 0.025

Confidence Interval = 2.5 ± (2.131) × (0.025)

Calculating the bounds of the confidence interval:

Lower Bound = 2.5 - (2.131) ×(0.025)

Upper Bound = 2.5 + (2.131)×(0.025)

Lower Bound ≈ 2.5 - 0.0539 ≈ 2.4461 ounces

Upper Bound ≈ 2.5 + 0.0539 ≈ 2.5539 ounces

Therefore, the 95% confidence interval for the mean weight of bags of that specific brand of candies is approximately 2.4461 ounces to 2.5539 ounces.

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The 95% confidence interval for population mean is (19.8, 22.2).

The confidence interval for population mean using the Student's t-distribution is:

CI = x ± \(t_{\frac{\alpha }{2}, (n -1) }\) \(\frac{s}{\sqrt{n} }\)

Given:

x = 22

s = 3

n = 27

α = n - 1 = 26

The critical value of t for α = 0.05 and degrees of freedom, (n - 1) = 19 is:

\(t_{\frac{\alpha }{2} , (n -1)}\) = \(t_{\frac{0.05}{2,19} }\)

            = 2.093

Compute the 95% confidence interval for population mean as follows:

   CI = X + \(t_{\frac{\alpha }{2}, (n -1) }\frac{s}{\sqrt{n} }\)

⇒ CI = 21± 2.093 × 3/√27

        = 21 ± 1.20

        = (22.2, 19.8)

Thus, the 95% confidence interval for population mean is (19.8, 22.2).

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