what is the probability that the mean annual salary of a random sample of 64 teachers from this state is less than $52,000?

Answer: 14%

Step-by-step explanation:

Our formula is i=prt but we're trying to find the rate (r) so we'll rearrange it to become r=i/pt.

i = $245

p = $7000

t = 3/12= 0.25 years

[tex]r=\frac{245}{(7000)(0.25)} \\r = 0.14[/tex]

Using simple interest we know the Total value of annual health coverage is $9000.

Borrowers must pay lenders simple interest as a fee in exchange for a loan.

Compound interest is excluded from the calculation and just the original principal is used.

Simple interest applies to all loans, not just specific ones.

Additionally, it refers to the kind of interest that banks give their customers on their savings accounts.

So, complete yearly health coverage calculation

Let x be the total annual healthcare budget.

Ruth contributes 18% of the entire cost of healthcare, or $67.50 for two weeks. (ie 15 days)

So, total paid for one month = 67.5 x 2 = 135

The total amount paid for the entire year is 135 x 12 = 1620.

She foots 18% of the overall annual health care costs, as was already established.

Then,

18% x = 1620

18 x / 100 = 1620

x = (1620 x 100) / 18

= $9000

Therefore, using simple interest we know the Total value of annual health coverage is $9000.

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Correct question:

Ruth contributes 18% of the total cost of her individual health care. This is a $67.50 deduction from each of her biweekly paychecks. What is the total value of her individual coverage for the year?

The weighted mean of the RORs for each portfolio, from best to worst, is:

Portfolio 3: 4.36%

Portfolio 2: 3.2%

Portfolio 1: 0.94%

To calculate the weighted mean of the RORs for each portfolio, we need to multiply each rate of return by its corresponding portfolio value, sum the results, and divide by the total value of the portfolios:

Weighted Mean ROR = sum of value / total amount

sum of value = portfolio value x rate of return

For Portfolio 1:

(0.089 x 850) + (-0.051 x 2425) + (0.124 x 280) + (0.042 x 1400) + (0.009 x 2330)

Sum of value = 75.65 - 123.68 + 34.72 + 58.8 + 20.97

                      = 61.46.

Weighted Mean ROR = 61.46 / (850 + 2425 + 280 + 1400 + 2330)

                                    = 61.46 / 7285

                                    = 0.0094 or 0.94% (third)

For Portfolio 2:

(0.089 x 1050) + (-0.051 x 1950) + (0.124 x 1295) + (0.042 x 745) + (0.009 x 1050)

Sum of value = 93.45 - 99.45 + 160.58 + 31.29 + 9.45

                      = 195.32.

Weighted Mean ROR = 195.32 / (1050 + 1950 + 1295 + 745 + 1050)

                                    = 195.32 / 6090

                                    = 0.032 or 3.2% (second)

For Portfolio 3:

(0.089 x 1175) + (-0.051 x 550) + (0.124 x 860) + (0.042 x 550) + (0.009 x 2000)

Sum of value = 104.58 - 28.05 + 106.64 + 23.1 + 18

                      = 224.27.

Weighted Mean ROR = 224.27 / (1175 + 550 + 860 + 550 + 2000)

                                    = 224.27 / 5,135

                                    = 0.0436 or 4.36% (first)

To compare the overall performance of the portfolios, we can rank them based on their weighted mean RORs, from highest to lowest:

Portfolio 3: 4.36%

Portfolio 2: 3.2%

Portfolio 1: 0.94%

Therefore, the overall performance of the portfolios, from best to worst, is Portfolio 3, Portfolio 2, and Portfolio 1.

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The inference is that,  Incorrect because of a failure to distinguish between incidence and prevalence.

What is inference drawn from statistics?

Utilising data analysis to determine characteristics of a probability distribution at play, statistical inference is the process. Through the use of estimation and hypothesis testing, inferential statistical analysis infers characteristics of a population. It is presumed that a bigger population than the observed data set was sampled for this data collection.

What distinguishes random assignment from random sampling inferences?

As a method of choosing participants for your study's sample, random selection or random sampling can be used. The sample can be divided into control and experimental groups using random assignment, however.

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The complete question is -

At the initial examination in the Framingham study, coronary heart disease was found in 5 per 1,000 men aged 30yrs to 44yrs and in 5 per 1,000 women aged 30yrs to 44yrs. The inference that in this age group men and women have an equal risk of developing coronary heart disease is Selected Answer: A. Correct Answers: A. Correct B. Incorrect because of a failure to distinguish between incidence and prevalence C. Incorrect because a proportionate ratio is used when a rate is required to support the inference D. Incorrect because of failure to recognize a possible cohort phenomenon E. Incorrect because there is no control or comparison group.

If there are 90 pens in a box and 36 of them are red and the rest of them are black, the ratio of red pens to black pens in the box is 2:3.

The ratio of red pens to black pens in the box can be expressed as a fraction or as a simplified ratio. To do this, we need to determine the number of black pens in the box.

We know that there are 90 pens in total, and 36 of them are red. Therefore, the number of black pens can be found by subtracting the number of red pens from the total:

90 pens - 36 red pens = 54 black pens

Now we know that there are 54 black pens and 36 red pens in the box. To express this as a ratio, we can simplify it by dividing both numbers by their greatest common factor (GCF), which in this case is 18:

36/18 : 54/18

Simplifying further, we get:

2:3

This means that for every 2 red pens, there are 3 black pens in the box.

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the correct answer is A.

5,220,000 songs were downloaded in the year 2020.

The interpretation of s(2020) = 5,220,000 is "5,220,000 songs were downloaded in the year 2020".

Therefore, the correct answer is A. 5,220,000 songs were downloaded in the year 2020.

Interpretation refers to the process of explaining or giving meaning to information, data, or phenomena. It involves analyzing and making sense of information to draw conclusions or make decisions based on the findings.

Interpretation can involve subjective judgment and may depend on the perspective, assumptions, or biases of the interpreter.

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Using the functions f(x) and g(x) as F(x)=x²-16; g(x)=x+4, (f/g)(x) = (x^2 - 16)/(x + 4) when x = -4. So, the correct answer is option D.

To find (f/g)(x), we need to divide f(x) by g(x). The notation (f/g)(x) is another way of representing the function f(x)/g(x).

So, we first need to find f(x)/g(x) by dividing f(x) by g(x):

f(x)/g(x) = (x^2 - 16)/(x + 4)

Now, we can plug in the values of x in each option and see which one gives us the correct function.

Option A: (f/g)(-4) = ((-4)^2 - 16)/(-4 + 4) = undefined

Option B: (f/g)(4) = (4^2 - 16)/(4 + 4) = -1

Option C: (f/g)(4 - 4) = (0^2 - 16)/(4 - 4) = undefined

Option D: (f/g)(-4 - 4) = ((-4)^2 - 16)/(-4 - 4) = 0

Therefore, the correct answer is option D: (f/g)(x) = (x^2 - 16)/(x + 4) when x = -4.

Note that options A and C give undefined values because they have x + 4 in the denominator, which makes the function undefined at x = -4 and x = 4, respectively.

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Answer:

3 & 4

Step-by-step explanation:

Since you have 3 choice, you want to pick the options that can represent 3 options.

1. False, since a coin only has 2 sides.

2. False, black and red is two halves of a deck, meaning you only have 2 options.

3. True, 6 is divisible by three, so it can be used. Assuming each choice is represented by two number.

4. True, 3 choices is evenly represented by 3 sections

The probability of rolling a sum greater than 10 is 4/36, which simplifies to 1/9, or approximately 0.1111.

There are 36 possible outcomes when rolling two 6-sided dice. Each outcome is equally likely.

To find the probability of rolling a sum greater than 10, we need to count the number of outcomes where the sum is greater than 10, and then divide by the total number of outcomes.

The outcomes where the sum is greater than 10 are:

4 + 6 = 10

5 + 6 = 11

6 + 5 = 11

6 + 6 = 12

So there are 4 possible outcomes where the sum is greater than 10.

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We the best reason behind why we call National halothane study is an observational study rather than an experiment is: " In order to be an experiment, the treatments (choice of anesthetic) would have to be randomly assigned." So, option( b) is right one.

We have data from the National Halothane Study that correlates with important research into the safety of anesthetics used in surgery. The above shows the death rate and aesthetic. There is a relationship between the anesthetic used and the death of the patient. The data was collected after that the anesthesia was administered is started. In the observational study, interesting observer in the subjects & any treatment that the subjects recive are beyond the council of the investigators. Here the motion of anaesthesia is anesthetics used her determined by the doctors and the investigators are simply observing. So, it is an observational study due to because in order to be an experiment, the treatments (choice of anesthetic) would have to be randomly assigned. Instead, a patient's anesthetic is selected by his or her doctor(s).

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Complete question:

The National Halothane Study was a major investigation of the safety of anesthetics used in surgery. Records of over 850,000 operations performed in 34 major hospitals showed the following death rates for four common anesthetics:27 Anesthetic A Death rate B CD 1.7% 1.7% 3.4% 1.9% There is a clear association between the anesthetic used and the death rate of patients. Anesthetic C appears dangerous.

a) in order to be an experiment, the subjects would have to be randomly selected from the population. however, these are hospital patients who all have some disease or condition and have not been randomly selected from the population, which includes both healthy and sick people.

b) in order to be an experiment, the treatments (choice of anesthetic) would have to be randomly assigned. instead, a patient's anesthetic is selected by his or her doctor(s).

c) there is not enough information to say for sure, but it is safer to assume that it is only an observational study, so that we are not overconfident about the results.

d) actually, it is an experiment and not an observational study.

V=π(d

2)2h=π·(20.12

2)2·6.4≈2034.42618m

Answer: 228 yards

Step-by-step explanation:

Answer:

228

Step-by-step explanation:

Answer:

A = 40 in²

Step-by-step explanation:

the area (A) of a trapezoid is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂)

where h is the height between the bases b₁ and b₂

here h = 8 , b₁ = 4 , b₂ = 6 , then

A = [tex]\frac{1}{2}[/tex] × 8 × (4 + 6)

   = 4 × 10

   = 40 in²

Answer: C 70%

Step-by-step explanation:

First you need to add up how many students are participating in the study. 4+6+12+8+4=34. There are 24 people who own more than 5 video games. This means that it is 24/34. This equals about 70%

Answer:

Can i see the full answer so I can help you?

Step-by-step explanation:

Using a trigonometric relation we can see that the correct option is the last one;

4. 348.5 ft​

We have a right triangle, so we can use trigonometric relations.

The angle at the top of the triangle is a, and it must solve the equation:

a + 19° = 90°

a = 90° - 19° = 71°

Now we can use the trigonometric relation:

tan(a) = (opposite cathetus)/(adjacent cathetus)

REplacing what we know:

tan(71) = ?/120 ft

120ft*tan(71) = ? = 348.5ft

That is the distance.

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So, the matrix representation of T relative to the basis B = {f1, t, t²} is:
| 2.5  3  0 |
|  0   4  0 |
|  0   0  6 |

To find the matrix representation of the linear transformation T relative to the basis B = {f1, t, t²}, we need to apply T to each element of the basis and then express the result as a linear combination of the basis elements.
Let's apply T to each element of the basis B:
1. T(f1) = T(1) = 2(1) + 0.5(1) = 2.5
2. T(t) = T(c) = 3(c) + 4(c²) = 3f1 + 4t
3. T(t²) = T(c²) = 6(c²) = 6t²
Now, we can express the results as linear combinations of the basis elements:
1. T(f1) = 2.5f1 + 0t + 0t²
2. T(t) = 3f1 + 4t + 0t²
3. T(t²) = 0f1 + 0t + 6t²
Finally, we can form the matrix representation of T relative to the basis B by using the coefficients of the linear combinations as the columns of the matrix:
T matrix = | 2.5  3  0 |
                  |  0   4  0 |
                  |  0   0  6 |

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The matrix representation of t with respect to the basis b = [tex]{f1, t, t^2}[/tex] is:

[1/2   -4/3      1 ]

[1       8/3      0 ]

[0     -5/2   3/2 ].

To find the matrix representation of the linear transformation t with respect to the given basis, we need to apply t to each of the basis vectors and represent the result as a linear combination of the basis vectors.

The coefficients of these linear combinations will form the columns of the matrix representation.

First, we apply t to each of the basis vectors:

[tex]t(1) = a0 + a1t + a2t^2 = a0 + a1f1 + a2t - (a1/2)f1 - (3a2/2)t^2[/tex]

[tex]t(t) = a0 + (4/3)a1t + (5/6)a2/t = a0 + (4/3)t + (5/6)t^2 - (4/3)f1 - (5/2)t^2[/tex]

[tex]t(t^2) = a0 + (3/2)a2/t^3 = a0 + (3/2)t^2 - (3/2)f1[/tex]

Next, we represent these results as linear combinations of the basis vectors:

[tex]t(1) = (a0 - a1/2)f1 + (a1 + a2)t - (3a2/2)t^2[/tex]

[tex]= 1f1 + 0t + 0t^2 + (-1/2)f1 + 1t + 0t^2 + 0f1 - (3/2)t^2[/tex]

[tex]= (1/2)f1 + 1t - (3/2)t^2[/tex]

[tex]t(t) = (-4/3)f1 + (a0 + 4/3)t + (5/6)t^2[/tex]

[tex]= 0f1 + 1t + 0t^2 + (-4/3)f1 + (4/3)t + (5/6)t^2 + 0f1 + 0t - (5/2)t^2[/tex]

[tex]= (-4/3)f1 + (8/3)t - (5/2)t^2[/tex]

[tex]t(t^2) = f1 + (a0 - 3/2)t^2[/tex]

[tex]= 0f1 + 0t + 1t^2 + 1f1 + 0t + 0t^2 + 0f1 + (1/2)t^2[/tex]

[tex]= 1f1 + 0t + (3/2)t^2[/tex]

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Answer:

below

Step-by-step explanation:

58.

(72 + 75 + 68 + 70 + 73 + 72 + 76 + 72 + 69 + 72 ) divided by 10 = 71.9

59.

order- 68, 69, 70, 72 , 72, 72, 72, 73, 75, 76

median = (72 + 72) divided by 2 = 72

61.

I dont know what MAD means

this is all I could do rn

Answer:

Using similar triangles, we can set up a proportion:

(tree height)/(tree shadow) = (building height)/(building shadow)

Plugging in the given values, we get:

8/4 = 24/x

Solving for x, we get:

x = (24 x 4)/8 = 12 feet

Therefore, the length of the building's shadow is B. 12 feet.

For the maximum volume of , the value of x must be smaller that is x = 2.90 inch. Size of square = 8.41 sq. in.

The issue is an application of maxima and minima, where the unknown quantity is located using the first derivative. Keep in mind that the height of a box is equal to a side of the cut square when the sides are bent upward. Moreover, the box formula's volume is

Volume = length * width * height

Given:

Volume of new box = (32 - 2x)(12 - 2x)x

Rearranging terms:

V = 4x³ - 88x² + 384x

For maximum volume, V' = 0 (first derivative)

V' = 12x² - 167x + 384

V' = 0

12x² - 167x + 384 = 0

Solve using quadratic formula:

x = [-b ± √(b² - 4ac)] / 2a

a = 12 , b = - 167 , c = 384

x = [167 ± √(167² - 4*384*12)] / 2*12

x =  [167 ± 7√193] / 24

Now,

x =  [167 + 7√193] / 24

x = 11.01 inch

and,

x = [167 - 7√193] / 24

x = 2.90 inch

For the maximum volume of , the value of x must be smaller that is x = 2.90 inch.

Size of square = x²

Size of square = 2.90²

Size of square = 8.41 sq. in.

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The annual percentage rate is approximately 9.97% when rounded to the nearest hundredth of a percent.

To find the annual percentage rate (APR), we can use the following formula:

APR = (finance charge / loan amount) / (loan period in years) x 100%

First, let's calculate the loan amount by subtracting the finance charge from the total cost of the furniture:

Loan amount = $1,860 - $308.25 = $1,551.75

Next, let's convert the loan period of 2 years to the decimal form of 2:

Loan period = 2 years = 2.0 years

Now we can plug in the values into the formula and solve for the APR:

APR = ($308.25 / $1,551.75) / (2.0) x 100%

APR = 0.0997 x 100%

APR ≈ 9.97%

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The major flaw of the linear probability model is, Option d, which allows predicted values to range from above 1 to below 0

The binary dependent variable, which accepts values of 0 and 1, and the independent variables are assumed to have a linear relationship under the linear probability model.

The anticipated values from the linear probability model, however, can range from 0 to 1, and in some circumstances, they can be either above or below 0. This goes against the dependent variable's probabilistic character and can produce inaccurate forecasts.

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The measure of angle A and angle B are 28.61 and 61.39 rounded to two decimal place, using trigonometric ratio of tangent for the respective angles.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

tan B = 6/11 {opposite/adjacent}

B= tan⁻¹(6/11) {cross multiplication}

B = 28.6105.

tan A = 11/6 {opposite/adjacent}

A= tan⁻¹(11/6) {cross multiplication}

A = 61.3895.

Therefore, the measure of angles A and B are 28.61 and 61.39 rounded to two decimal place, using trigonometric ratio of tangent for the respective angles.

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The depreciation rate of Nancy is 15%.

Depreciation is the reduction in the value of an asset over time due to wear and tear, obsolescence, or other factors. It is a non-cash expense that is recorded on a company's income statement, which reflects the decrease in the asset's value during its useful life. Depreciation is commonly used in accounting to allocate the cost of an asset over its useful life, and it helps businesses to accurately reflect the true value of their assets on their financial statements.

In mathematics, a function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output.

The given function V(t) = [tex](30000*0.85)^{t}[/tex]represents the value of Nancy's car after t years.

Depreciation rate is the rate at which the value of an asset decreases over time. In this case, the depreciation rate of Nancy's car is 1 - 0.85 = 0.15 or 15%.

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(a) The linear programming model to maximize the profit is written as,

Maximize Z = 2(4x1)(100) + 1.5(6x2)(100) + 4(2x3)(1000) - 2(100x1 + 100x2 + 50x3) - 40(10x1 + 12x2)

(b) The optimal solution is x1 = 0, x2 = 8/3, x3 = 8, x4 = 0, and the maximum profit is $40.

(a) Linear programming model:

Let x1, x2, and x3 be the number of acres allocated to lemon, peach, and cherry trees, respectively. Then, the objective function we want to maximize is:

Maximize Z = 2(4x1)(100) + 1.5(6x2)(100) + 4(2x3)(1000) - 2(100x1 + 100x2 + 50x3) - 40(10x1 + 12x2)

The first term represents the revenue from selling lemons, the second term represents the revenue from selling peaches, the third term represents the revenue from selling cherries, the fourth term represents the cost of fertilizer, and the last term represents the cost of labor.

The constraints are:

x1 + x2 + x3 ≤ 200 (total available land)

10x1 + 12x2 + 10x3 ≤ 20000 (total available labor hours)

x1, x2, x3 ≥ 0 (non-negativity constraints)

(b) Simplex algorithm:

Convert the linear programming model into standard form by introducing slack variables and expressing all variables in terms of these variables.

Maximize Z = 2(4x1)(100) + 1.5(6x2)(100) + 4(2x3)(1000) - 2(100x1 + 100x2 + 50x3) - 40(10x1 + 12x2)

Subject to:

x1 + x2 + x3 + x4 = 200

10x1 + 12x2 + 10x3 + x5 = 20000

x1, x2, x3, x4, x5 ≥ 0

In this case, the entering variable is x1, as it has the highest coefficient in the objective function.

Step 5 (continued):

1.6 0.1 0 1 -48 32 <- Z

0.4 0.9 1 1/10 0 40 <- x1

8.4 3.3 0 -1/10 1 1840 <- x5

The entering variable is x3, as it has the highest coefficient in the objective function.

The leaving variable is x1, as it has the smallest ratio of RHS to its coefficient in the x3 column.

x2 x1/12 x3 x5/120 x4 RHS

2.5 1/5 0 -1/60 0 40 <- Z

0.5 -1/5 1 1/60 0 8 <- x3

0.5 2/15 0 1/60 1/10 8/3 <- x2

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It has been proved that the lines MN and PR are parallel because they have the same slope.

We are given the coordinates of the points P, Q and R as:

P(-3, -6)

Q(1, 4)

R(5, -2)

Since M is the midpoint of PQ, we have:

M = (-3 + 1)/2, (-6 + 4)/2

M = (-1, -1)

N is the midpoint of QR and so:

N = (1 + 5)/2, (4 - 2)/2

N = (3, 1)

Slope of MN = (1 + 1)/(3 + 1) = 1/2

Slope of PR = (-2 + 6)/(5 + 3)

Slope of QR = 4/8 = 1/2

Both slopes are equal and as such they are parallel lines

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Subway ridership data can reveal useful patterns through calculations with multiple operators, informing decisions about infrastructure and scheduling to better serve riders' needs.

The subway ridership dataset can reveal a wealth of information through calculations with multiple operators. One such calculation is the average increase or decrease in ridership during specific time intervals. By comparing ridership during peak and off-peak hours or weekdays versus weekends, it is possible to determine when the subway system is busiest and when it is underutilized.

Another useful calculation is the average percentage change in ridership between different stations or subway lines. This can help identify the most popular stations or lines and can inform decisions about where to allocate resources and infrastructure improvements.

Additionally, it is possible to explore the correlation between ridership and other factors such as weather, events, or holidays. By analyzing how ridership fluctuates in response to external factors, transportation planners can adjust schedules and routes to better serve the needs of riders.

Calculations with multiple operators can also reveal patterns in ridership based on time of year or day of the week. By analyzing the average change in ridership on different days or months, transportation planners can make informed decisions about scheduling and staffing.

Finally, regression analysis can be used to identify the overall trend in ridership over time. By examining long-term ridership trends, transportation planners can identify areas for improvement and plan for future infrastructure projects to better meet the needs of subway riders.

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The diameter of the circle is √74. Answer: C.

What is circle?

A circle is a geometric shape that consists of all points in a plane that are equidistant from a fixed point called the center. It can also be defined as the set of points that are a fixed distance (called the radius) away from the center point.

To find the diameter of the circle, we need to find the distance between points A and B, which will give us the length of the diameter.

Using the distance formula, we have:

d = √[(x2 - x1)² + (y2 - y1)²]

where (x1, y1) = (-3, 6) and (x2, y2) = (-8, -1).

Plugging in the values, we get:

d = √[(-8 - (-3))² + (-1 - 6)²]

= √[(-5)² + (-7)²]

= √[25 + 49]

= √74

Therefore, the diameter of the circle is √74. Answer: C.

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The probability that the sample mean would differ from the population mean by greater than 3 millimetres is 0.0033 + 0.0033 = 0.0066, rounded to four decimal places.

We are given that the population mean diameter of the steel bolts manufactured by Thompson and Thompson is μ = 137 millimeters and the variance is = 49.

We need to find the probability that the sample mean would differ from the population mean by greater than 3 millimeters.

The standard deviation of the sample means is given by the formula:

[tex]\sigma_{\bar{x}} = \frac{\sigma}{{\sqrt{n}}}[/tex]

Substituting the given values, we have:

[tex]\sigma \bar{x}=\frac{\sqrt{49}}{\sqrt{48}}=1.118[/tex]

To find the probability that the sample mean would differ from the population mean by greater than 3 millimeters,

we need to calculate the z-score:

[tex]z=\frac{(\bar{x}-\mu)}{ \sigma _{\bar{x}}}[/tex]

Substituting the given values, we have:

[tex]z=\frac{\bar{x}-137}{1.118}[/tex]

We want to find the probability that |z| > 3/1.118 = 2.683.

Using a standard normal distribution table, we find that the probability of z > 2.683 is 0.0033.

Since this is a two-tailed test, the probability of z < -2.683 is also 0.0033.

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