The probability generating function of the dis- crete nonnegative integer valued random variable X having probability mass function pj, j = 0, is defined by ø(s) = E[s] =Σp;si j=0 Let Y be a geometric random variable with param- eter p 1 s, where 0 < s < 1. Suppose that Y is independent of X, and show that ø(s) = P{XY}

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1A) To find out how much the hot air balloon rose each minute, we need to find the rate at which it rose. The rate can be calculated by dividing the change in altitude by the change in time. In this case, the change in altitude is 70 meters - 44 meters = 26 meters, and the change in time is 2 minutes - 3 minutes = -1 minute (since the time is decreasing). The rate is therefore 26 meters/-1 minute = -26 meters/minute.

1B) The hot air balloon started at an altitude of 44 meters - (-26 meters/minute) * 3 minutes = 44 meters - (-78 meters) = 122 meters.

1C) To find the equation that describes the relationship between the altitude of the hot air balloon and the elapsed time, we can use the information that we have. The altitude at time t=0 is 122 meters, and the rate at which the altitude changes is -26 meters/minute. The equation is therefore A = -26t + 122.

The hot air balloon rise 13 m each minute.

The hot air balloon was 5 m above the ground at start.

The equation that describes the relationship between the altitude of the hot air balloon in meters is A = 13t + 5.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

We have, After 3 minutes, the balloon was 44 meters above the ground.

After 2 minutes later, the hot air balloon had risen to 70 meters above the ground.

1. The rate of change

= (70-44)/ (5-3)

= 26/ 2

= 13 m / min

2. At start the hot air balloon is

= (44-13 x 3)

= 5 m above the ground

3. The equation that describes the relationship between the altitude of the hot air balloon in meters is

A = 13t + 5.

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Answer:

False.  They would form 4 right angles (90)

Step-by-step explanation:

Answer:

The correct answer is A. No, because 3(2) + 3 ≠ 15.

Step-by-step explanation:

because the total number of goals scored by Skylar and Wyatt was 15, and if Skylar scored 3 goals, then Wyatt would have scored 3 * 2 = 6 goals. Since the total number of goals scored by both players is 15, this scenario is not possible. Therefore, Skylar could not have scored 3 goals.

The quadrilateral abcd is a parallelogram because the slopes of opposite sides are equal.

In the given figure we have a quadrilateral  ABCD with A (-2,-2) , B(-3,4), C(2,2)

and D(3,-4).

We know that when the slope of two lines are equal then they are parallel.

In the given figure, Slope of BC= Slope of AD =

⇒ BC and AD are parallel .

Also, Slope of CD= Slope of BA =-6

⇒ CD and BA are parallel .

ABCD is a parallelogram because both pairs of opposite sides are parallel.

Hence, the correct reason for the given space is "slopes of opposite sides are equal"

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The number of bags filled by the pet shop is 879 and the number of treats they gave to the groomer is 4.

The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.

They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.

As per the data given in the question,

Total number of dog treats in the shop = 6157

Number of treats per bag = 7

Extra treats will be given to the groomer.

Then, the number of bags will be,

6157/7 = 879.57

This means that a total of 879 bags are there, with 7 pieces of treats per bag.

So, the total number of treats in 879 bags will be,

879 × 7 = 6153

So, the amount of treats left for the groomer is,

6157 - 6153 = 4 treats.

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Answer:

a : c = 3 : 20

Step-by-step explanation:

Given ratios:

The value of b is 3 and 5.

The lowest common multiple of 3 and 5 is 15.

Multiply each ratio by a factor of 15 so that b is 15.

Multiply ratio a : b by 3:

⇒ a : b = 6 : 15

Multiply ratio b : c by 5:

⇒ b : c = 15 : 40

Therefore:

⇒ a : b : c = 6 : 15 : 40

So a : c is:

⇒ a : c = 6 : 40

Simplest form:

⇒ a : c = 3 : 20

The value of x in the equation, 3/4x + 6 - 1/4x = 2/4x + 9, is: x = -2.

Solving an equation involves finding the value of the variable in the equation. The value, when plugged into the equation would make it true.

The equation given is, 3/4x + 6 - 1/4x = 2/4x + 9, to solve for the value of x, follow the steps below:

3/4x + 6 - 1/4x = 2/4x + 9 [given]

Combine like terms:

3/4x - 2/4x - 1/4x = 9 - 6

(3 - 2 - 1)/4x = 3

-6/4x = 3

Simplify

-3/2x = 3

Multiply both sides by -2/3:

-3/2x × -2/3 = 3 × -2/3

x = -6/3

x = -2

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6 + 12^2

12 squared would be 12 to the second power

since the directions say "the sum"

you would use addition to add 6 and 12^2

Answer: 3m+4=6m is the false equation

Step-by-step explanation:

Substitute 5 into the 4 equations to find whether they are true or false

3(5)+4=6(5)

15+4=30

19[tex]\neq[/tex]30 False

-5(5-7)=10

-5(-2)=10

10=10 true

17=4(5)-3

17=20-3

17=17 True

5+9=14

14=14 True

3m+4=6m is the false equation

The width of the rectangle is 6 inches and length of rectangle is 12 inches

We have given the perimeter of the rectangle and the length of a rectangle is 6 inches longer than its width.

Let x be the width of the rectangle and x+6 be the length of the rectangle.

Perimeter = p = 36 inches

We have to find the values of width and length of rectangle.

The formula to find the Perimeter is:

p = 2l+2w

36 = 2(x+6)+2(x)

36 = 2x+12+2x

36 = 4x+12

36-12= 4x

24 = 4x

x = 6 inches.

Hence, the width of the rectangle is 6 inches and length of rectangle is 12 inches.

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The exact answer to the definite integral ∫16^1^3/π of x dx using the fundamental theorem is 8/π^2.

The fundamental theorem of calculus states that if f(x) is a continuous function on the interval [a, b] and F(x) is an antiderivative of f(x), then:

∫a^bf(x)dx = F(b) - F(a)

To use the fundamental theorem to evaluate the definite integral ∫16^1^3/π of x dx, we need to find an antiderivative of x. The antiderivative of x is x^2/2 + C, where C is an arbitrary constant.

Therefore, the definite integral ∫16^1^3/π of x dx can be written as:

∫16^1^3/π x dx = (x^2/2 + C) |16^1^3/π

Evaluating this expression gives us:

(3/π)^2/2 + C - (1/π)^2/2 + C = (9/π^2 - 1/π^2)/2 + 2C

Since C is an arbitrary constant, it cancels out when we take the difference between the upper and lower limits of integration. Therefore, the definite integral ∫16^1^3/π of x dx is equal to:

(9/π^2 - 1/π^2)/2 = 8/π^2

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The probability is 0.7888.

Standard error of the mean [tex]$\sigma_{\bar{x}}=20$[/tex]

The population standard deviation (σ)=500

Standard deviation of [tex]$\bar{x}$[/tex] is given by:

[tex]\sigma_{\bar{x}} & =\frac{\sigma}{\sqrt{n}} \\\\\Rightarrow 20 & =\frac{500}{\sqrt{\mathrm{n}}} \\\\\Rightarrow n & =\left(\frac{500}{20}\right)^2 \\[/tex]=625

Probability that the point estimate [tex]$\bar{x}$[/tex] was within ±25 of the population mean is: [tex]$$p(\mu-25 < \bar{x} < \mu+25)$$[/tex]

At [tex]$\bar{x}[/tex]=μ-25, we have

[tex]z & =\frac{-25}{20} \\[/tex]=-1.25

Z=-1.25

At [tex]$\bar{x}[/tex]=μ+25, we have

[tex]z & =\frac{25}{20} \\[/tex]=1.25

Z=1.25

So the required probability is:

[tex]$$\begin{aligned}p(\mu-25 < \bar{x} < \mu+25) & =p(-1.25 < z < 1.25) \\& =p(z < 1.25)-p(z < -1.25) \\\end{aligned}$$[/tex]

                                     =0.8944-0.1056

                                     =0.7888

Therefore, probability that point estimate is within ±25 population mean is 0.7888.

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A researcher reports survey results by stating that the standard error of the mean is 20 . The population standard deviation is 500 . How large was the sample used in this survey

a. What is the probability that the point estimate was within ±25 of the population mean?

Answer:

Step-by-step explanation:

If a sample mean is 32, the range of possible values that best describes an estimate for the population mean is most likely (30, 38).

The sample mean is a statistic that is used to estimate the population mean. In general, the sample mean is a good estimate of the population mean, but it is not always perfectly accurate. There is always some degree of uncertainty or variability associated with any estimate, and this is especially true when the sample size is small.

One way to quantify this uncertainty is to use a confidence interval, which is a range of values that is likely to contain the population mean with a certain level of confidence. For example, a 95% confidence interval is a range of values that is likely to contain the population mean with 95% confidence.

In this case, if a sample mean is 32, a 95% confidence interval for the population mean would likely be a range of values centered around 32 and extending approximately 2 standard errors in either direction. For a sample mean of 32, a range of values extending 2 standard errors in either direction would be approximately (30, 38). Therefore, the range of possible values that best describes an estimate for the population mean is most likely (30, 38).

If a sample mean is 32, (30, 38) is most likely the range of possible values that best describes an estimate for the population mean. the correct option is option D.

Range serves as a statistical measure of dispersion in mathematics, or how widely spaced a particular data collection is from smallest to biggest. The range in a piece of data is the distinction between the highest and lowest number. The confidence interval of 95% for the population mean in this scenario, assuming the sample mean is 32, is likely to include a range of values centred around 32.

Extending around 2 standard errors in each direction. A range of results spanning two standard deviations in either way would result in around (30, 38) for a sample mean of 32. Thus, the range of potential values that most accurately captures an estimate of the population mean is (30, 38).

Therefore, the correct option is option D.

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To compare the sampling distribution, first I would simulate the machine by randomly generating n number of samples between 8 and 10 oz with a uniform distribution and calculate the 4th spread for each sample size. I would then repeat this experiment multiple times and take the average of the fourth spread values for each sample size to compare the sampling distributions.

To compare the sampling distributions of the fourth spread for sample sizes n = 5, 10, 20, and 30, I would simulate the machine by randomly generating samples between 8 and 10 oz with a uniform distribution. For each sample size, I would calculate the fourth spread for each sample and then repeat the experiment multiple times. Finally, I would take the average of the fourth spread values for each sample size to compare the sampling distributions. This way, I would be able to see how the fourth spread changes as the sample size changes. It would also allow me to see how the fourth spread is affected by the uniform distribution of the machine's output.

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Answer:  [tex]5.8\times 10^4[/tex]

Reason:

Place the decimal point between the 5 and the 8. So we have the value 5.8

To get back to 58000, we need to move the decimal point 4 spots to the right. This is why we have 4 as the exponent over 10.

All scientific notation values are of the form [tex]a \times 10^b[/tex]

where [tex]1 \le a < 10[/tex] or [tex]-10 < a \le 1[/tex]

The b value is an integer.

Answer:

Answer:

Below

Step-by-step explanation:

Domain is the set of values x can be for a function .....it looks like this one goes from -2 to 2 with asymptopes at these values:

-2< x < 2  

Range is the 'y' values a graph can have...this one goes from -1.5 -ish to 5.5 ish    

-1.5 <= y <= 5.5

Here is the graph with some lines on it:

The ordered pair for the vertices for r(90°, s)(QRST) include the following:

Q' = (-5, 1)

R' = (-3, -1)

S' = (0, 0)

T' = (-3, -2)

In Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).

Note: The point S represents the center (origin) of this geometric figure.

By applying a rotation of 90° counterclockwise to the vertices for r, the coordinates of the vertices of the image point r' are as follows:

(x, y)                               →            (-y, x)

Ordered pair Q  = (1, 5) → Ordered pair Q' = (-5, 1)

Ordered pair R = (-1, 3) → Ordered pair R' = (-3, -1)

Ordered pair S = (0, 0) → Ordered pair S' = (0, 0)

Ordered pair T = (-2, 3) → Ordered pair T' = (-3, -2)

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For the study about cholestrol levels of people was taken by medical researcher.

a) Null and Alternative hypothesis for study is

H₀ : μd ≥0

Hₐ : μd <0

where μd --> average

b) The value of t-statistic is 3.78118

c) The critical value for t-test is - 2.015.

d) We fail to reject null hypothesis, H₀

e) There is sufficient evidence to support the claim of researcher that cholesterol level decreases on average.

The above table represents the patients and their cholesterol levels before and after they showed the film about the effect of high cholesterol levels. The "d" column shows the difference in their cholesterol levels.

Singnificance level, α =0.05

∑d = 122, n = 6 , ∑d² = 3348

Xd -bar = 122/6 = 20.33

Standard deviations, σ = √(∑d² - ∑d/n)/(n-1)

σ = √(3348 - 20.33)/5 = 13.170

a) The Null and Alternative hypothesis are

H₀ : μd ≥0

Hₐ : μd <0

b) test- statistic,

t - value = (Xd-bar - μd)/σ /√n

=> t = (20.33 - 0)/13.17/√6

=> t = 20.33/5.37662

=> t = 3.78118

c) degree of freedom, df = n-1 = 5

The critical t-value for a given confidence level c and sample size n is obtained by computing the quantity tα/2 for t-distribution with (n-1) degrees of freedom.

α = 0.05 , α/2 = 0.25 , df = 5

t(₀.₂₅, ₅) = - 2.015

d) Decision: As we seen t-value= 3.781 and t-critical value = - 2.015

so, t -value > critical value. Therefore, we fail to reject null hypothesis.

e) Conclusion: There is sufficient evidence to claim that the cholesterol level decrease on average.

Hence, we got all required answers.

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Complete question:

Cholesterol Levels A medical researcher wishes to see if he can lower the cholesterol levels through diet in 6 people by showing a film about the effects of high cholesterol levels. The data are shown. At =α0.05 , did the cholesterol level decrease on average? Use the P -value method and tables. Patient 1 2 3 4 5 6 Before 250 219 218 224 209 223 After 216 203 192 190 207 213 State the hypotheses and identify the claim with the correct hypothesis. H0 : ▼(Choose one) H1 : ▼(Choose one) This hypothesis test is a ▼(Choose one) test. Compute the test value. Always round t score values to three decimal places. t= Find the interval for the P -value. The correct interval is Make the decision. ▼(Choose one) the null hypothesis. Summarize the results. There is ▼(Choose one) that the mean heights are different

Answer:

6*3 + 6*2

6*5

6(3+2)

Step-by-step explanation:

All of these equations lead to the same answer which is 30.

The two diagrams are basically the same but they are just separated apart. When you look for the area of both diagrams, it leads to the same answer.

Answer:

Step6x3 = 18. And. 2x6 = 12. Then you add the amounts, 18+12 = 30-by-step explanation:

The product of a,b and c from the fraction is 6/125

The product is the result of the multiplication of the numbers

From the given exponential fractions, we have

=(3x³y²/³)÷(125³*¹/³y³*¹/³

Simplifying the expression to have

(3x³y²/³)(125)(1)

⇒3/125x³y²/³

The expressed form is [tex]ax^{b} y^{c}[/tex]

a=3/125 b=3 c 2/3

Simplify further to have

⇒3/125*3/1*2/3

Simplify further to get your final answer as

=6/125

Therefore, the product of the fractional exponents is 6/125

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Although part of your question is missing, you might be referring to this full question: Write an expression that describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for the first term. –1, 0, 1, 2, ...

The expression that describes the given sequence is: aₙ = –2 + n

This is an arithmetic sequence. Arithmetic sequence is a sequence of numbers in which every term (except the first term) is provided by adding a constant number to the previous term.

An arithmetic sequence can be defined by an explicit formula in which aₙ = d (n – 1) + c, where d is the common difference between consecutive terms, and c = a₁.

In this case, the given sequence is –1, 0, 1, 2, ...

This is an arithmetic sequence with common difference.

Because of:

0 – (–1) = 1

1 – 0 = 1

2 – 1 = 1 …

Then, a₁ = –1

Now, substitute the value of a₁ = –1, d = 1 into the formula.

aₙ = d (n – 1) + c

aₙ = 1 (n – 1) + (–1)

aₙ = n + (–2)

aₙ = –2 + n

Hence, the expression that describes the given sequence is: aₙ = –2 + n.

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To solve this inequality, we can start by converting the mixed numbers to improper fractions. The mixed numbers in this inequality are 1/3 and -2 1/4. The negative sign in front of 2 1/4 indicates that the resulting fraction will be negative. To convert 1/3 to an improper fraction, we can multiply the denominator (3) by the whole number (1) and add the result to the numerator (1). This gives us 1/3 = 4/3. To convert -2 1/4 to an improper fraction, we can multiply the denominator (4) by the whole number (-2) and add the result to the numerator (1). This gives us -2 1/4 = -9/4.

Next, we can combine the two fractions on the left side of the inequality by adding their numerators and denominators. This gives us m + 4/3 + -9/4. We can then simplify this expression by combining like terms. This gives us m - 9/12 + 4/3. We can further simplify this expression by adding the fractions with unlike denominators. To do this, we can find a common denominator by multiplying the two denominators together, which gives us 12 * 3 = 36. We can then convert the fractions to have this common denominator by multiplying the numerator and denominator of each fraction by the appropriate value. For m - 9/12 + 4/3, we have m - (9 * 3)/(12 * 3) + (4 * 12)/(3 * 12), which simplifies to m - 27/36 + 48/36. We can then combine like terms to get m + 21/36.

Finally, we can solve for m by moving all of the terms with m to one side of the inequality and all of the other terms to the other side. To do this, we can subtract 21/36 from both sides of the inequality, which gives us m + 21/36 - 21/36 < -2 1/4 - 21/36. This simplifies to m < -2 1/4 - 21/36, which we can further simplify by converting -2 1/4 - 21/36 to an improper fraction. To do this, we can multiply the denominator (4) by the whole number (-2) and add the result to the numerator (1), which gives us -2 1/4 = -9/4. We can then add -9/4 and -21/36 to get -9/4 - 21/36 = -105/36. Finally, we can convert this to a mixed number by dividing the numerator (-105) by the denominator (36) and taking the quotient (-2) as the whole number and the remainder (27) as the numerator of the fraction. This gives us -105/36 =

The value of missing angles in the given figure are as follow:

m∠1= 56  ,m∠2= 56 and m∠3= 74.

As given in the question,

In the figure, MPQ is a triangle

We know that sum of the angles in the triangle is 180.

m∠ MPQ + m∠ PMQ + m∠1 =180

⇒58 + 66 + m∠1=180

⇒124 + m∠1= 180

⇒m∠1= 180 - 124

⇒m∠1=56

so m∠1=56.

∠1 and ∠2 are vertically opposite angles so ,

⇒m∠1= m∠2

therefore, m∠2=56.

Now in triangle QNO

∠QON + m∠2 + m∠3 =180

⇒50 + 56 +m∠ 3=180

⇒106 + m∠3= 180

⇒m∠3= 180 - 106

⇒m∠3=74

Therefore, the measure of the angles in the given figure are m∠1= 56  ,m∠2= 56 and m∠3= 74.

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The correct statement is-number of students in the data set

In research and data collecting, something that is being measured and whose values can change is referred to as a variable.

Given that we have a range of alternatives from January to December, the aforementioned example demonstrates how the student birth month is a variable. The student's ability to indicate whether they support particular political parties or not makes their political affiliation another variable. Since they are college students, the age of the student is another variable, with replies falling within a range of 20 to 25.

Since students will give different answers, whether they live at the same address or a different one, student address is also a variable.

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Answer:

D

Step-by-step explanation:

6^(4+0) = 6^4

6^(-10) : 6^4

6^(-10-4)

6^(-14)

1/6^(14)

Answer:can you copy and paste it?

Step-by-step explanation:

We reject null hypothesis when hypothesis test, draw conclusions at significance level 0.08.

Given that,

Consider an NFL team that says the average weight of its defensive players is 315 pounds. A opposing team believes that their defensive players' average weight is lower than the 315 pounds they state. Consider that they take 15 defensive players as a sample and discover that the average weight of the players is 300 pounds, with an 8-pound sample standard deviation.

We have to create a suitable hypothesis test, draw conclusions at significance level 0.08, and then. Suppose that the weights are evenly distributed.

We know that,

Weights are normally distributed.

We are given μ = 315 , n= 15 , x = 300, s = 8, α = 0.08

The hypothesis are :

H₀ : μ = 315   v/s  H₁ : μ ≠ 315

The test statistic is given by,

z=x-μ/σ/√15

=300-315/8/√15

=-7.26

The critical value = z(α)  = z(0.04) = -1.75 and z(1-α)  = z(1-0.04)  = 1.75

Here calculated value of z > critical value of z

Therefore, we reject null hypothesis when hypothesis test, draw conclusions at significance level 0.08.

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The table with constant of proportionality between x and y is table A

We should be able to know that constant of proportionality shows a type of relationship between two variables that shows a constant relationship or same ratio.

The given fraction is 8/5

Rewrite 8/5 as a ratio of two numbers

8:5

Constant of proportionality is written as

y=k/x

Making k the subject, k=y/x

Where k is a constant.

From table A,

The constant  (K) is 4/1 = 4:1

Now multiply 4*8=32

8*1=5

Therefore 32/5 is a proportion of 8/5

Also using the constant k=10

⇒10:1   Then 10*8=80

And 1*5=5

⇒ 80/5=16

Also in the last constant K=11, we have 11:1

⇒[tex]\frac{11*8}{1*5}[/tex] =88/5

In conclusion option A gives the table that has constant of proportionality to 8/5

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For a 90% confidence interval the upper and lower bound is 11.50 and 9.56 respectively.

Confidence interval means the probability that a population parameter will fall between a set of values.

The formula for confidence interval is C.I = u ± z (sd/[tex]\sqrt{n\\}[/tex] ) where u is the mean, sd is the standard deviation and z is the confidence level value. For an area of 90% around the mean, which makes 45% on each side, for the confidence level we will find the z-score at 0.45+0.5 = 0.95 area, and then double it since we need for both sides. At 0.95, the z-score is approximately 1.64. Thus, z is 3.28.

Plugging the values in the formula for C.I gives the upper bound as 10.53 + 0.968 = 11.50 and the lower bound as 10.53 - 0.968 = 9.56

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The required sample size of the given value is 577.

What is margin of error?

The formula to calculate the sample size  :-

n = (p(1-p)((Zα/₂)/E)²

Given :  Estimated proportion  p = 0.60

Margin of error : E = 0.04

Significance level : α = 1-0.95 = 0.05

Critical value : Zα/₂ = 1.96

Now, the required sample size will be :-

n = (0.60)(0.11)(1.96/0.04)²

= 6.6 * (0.0784)²

= 0.57744

Hence, the required minimum sample size of the given is 577.

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