A B C or D? I need help​

Answer:

-1.64

Explanation:

Multiple Choice Answers that were not provided in the question:

a. 0.103 .

b. None of the above.

c. -4.16

d. -1.45

e. 2.86

f .-1.64

The provided data is as below:

             Student 1  Student 2  Student 3  Student 4  Student 5  Student 6

Pre- test    80              76              76              50             48              67

Post- test   75              86              87              60            48               68

Further Explanation:

                    Student 1  Student 2  Student 3  Student 4  Student 5  Student 6

Pre- test             80              76              76              50             48              67

Post- test            75              86              87              60            48               68

Pretest-Postest   5               -10              -11              -10            0                 -1

Calculating the mean of the difference (Pretest-postest) we get d bar = -4.5

Calculating the standard deviation  of the difference  (Pretest-postest) we get sd= 6.716.

Since sample score is under 30 and population standard deviation is unknown, we will use a tscore to find the standardized test statistic

t = dbar/(sd/√n) = -4.5/(6.716√6) = -1.642 ≈ -1.64

The test statistic is -1.64.

Given:

Given that the radius of the circle is √98 units.

The circle is centered at the point (5.9, 6.7)

We need to determine the equation of the circle.

Equation of the circle:

The general form of the equation of the circle is given by

[tex](x-h)^2+(y-k)^2=r^2[/tex]

where (h,k) is the center and r is the radius of the circle.

Substituting the center point (h,k) = (5.9, 6.7) and r = √98, we get;

[tex](x-5.9)^2+(y-6.7)^2=(\sqrt{98})^2[/tex]

Simplifying, we get;

[tex](x-5.9)^2+(y-6.7)^2=98[/tex]

Thus, the equation of the circle is [tex](x-5.9)^2+(y-6.7)^2=98[/tex]

the equation of the circle with radius square root of 98 centered at (5.9, 6.7) is: [tex](x - 5.9)^2 + (y - 6.7)^2 = 98[/tex]

We know that the equation of circle is given by the formula:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

here h and k are the x and y coordinates of the center of circle and r is the radius. It is given to us that:

Radius = √98 units

Center at (5.9, 6.7)

Putting values into the equation we get:

[tex](x - 5.9)^2 + (y - 6.7)^2 = (\sqrt{98})^2\\\\ (x - 5.9)^2 + (y - 6.7)^2 = 98[/tex]

Therefore, the equation of the circle with radius square root of 98 centered at (5.9, 6.7) is: [tex](x - 5.9)^2 + (y - 6.7)^2 = 98[/tex]

By using multiplication, there are 68 cups is equal to 34 pints.

Given that,

Change the number 34 pint into cups.

Used the concept of measurement unit,

A measurement unit is a standard quality used to express a physical quantity. Also, it refers to the comparison between the unknown quantity with the known quantity.

Since we know that;

1 pint = 2 cups

Hence, we get;

34 pint = 34 x 2 cups

= 68 cups

Therefore, the number of cups in 34 pints is 68.

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Volume = length x width x height

120 = 15 x 4 x length

Simplify:

120 = 60 x length

Divide both sides by 60:

Length = 2 feet

Formula for the volume of a rectangular prism: V = length x width x height

120 = l x 4 x 15

120 = l x 60

l = 2

The length of the rectangular prism is 2 feet.

Hope this helps!! :)

The y-intercept is the y value when x = 0 --> (0, y) or the point where the line crosses through the y-axis.

The slope(m) is:

[tex]m=\frac{rise}{run}[/tex]

"rise" is the number of units you go up(+) or down(-) from each point

"run" is the number of units you go to the right from each point

You know:

y-intercept = -6 or (0, -6)

m = 2 or [tex]\frac{2}{1}[/tex] , so from each point you go up 2 units and to the right 1 unit to get to the next point.

#1: Locate the ordered pair (0, –6). From that point on the graph, move up 2, right 1 to locate the next ordered pair on the line. Draw a line through the two points.

This is true

#2: Locate the ordered pair (0, –6). From that point on the graph, move up 2, left 1 to locate the next ordered pair on the line. Draw a line through the two points.

This isn't accurate because the slope doesn't move left.

#3: Locate the ordered pair (–6, 0). From that point on the graph, move up 2, right 1 to locate the next ordered pair on the line. Draw a line through the two points.

This isn't accurate because (-6, 0) isn't the y-intercept or a point on the y-axis

#4: Locate the ordered pair (–6, 0). From that point on the graph, move up 2, left 1 to locate the next ordered pair on the line. Draw a line through the two points.

This isn't accurate because (-6, 0) isn't the y-intercept or a point on the y-axis, and the slope doesn't move to the left.

Answer:

tis be A my friends

Step-by-step explanation:

Answer:

Step-by-step explanation:

This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = 60.8

For the alternative hypothesis,

µ ≠ 60.8

Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.

Since n = 8,

Degrees of freedom, df = n - 1 = 8 - 1 = 7

t = (x - µ)/(s/√n)

Where

x = sample mean = 66.9

µ = population mean = 60.8

s = samples standard deviation = 10.7

t = (66.9 - 60.8)/(10.7/√8) = 1.61

We would determine the p value using the t test calculator. It becomes

p = 0.076

Since alpha, 0.01 < than the p value, 0.076, then we would fail to reject the null hypothesis. Therefore, At a 1 % level of significance, the sample data showed that there is no significant evidence that μ ≠ 60.8

Therefore, this p-value leads to a decision to accept the null hypothesis

Answer:

B. One solution

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

-6y + 13 + 9y = 8y - 3

Step 2: Solve for y

∴ We can see by solving the equation, we get 1 solution only.

The linear equation has one solution after simplifying and isolating the variable y, which results in y = 16/5.

When solving the given linear equation −6y + 13 + 9y = 8y − 3, the first step is to simplify and collect like terms. Begin by combining the terms with y on the left side: 3y + 13 = 8y − 3. Next, move the terms with y to one side by subtracting 3y from both sides: 13 = 5y − 3. Lastly, isolate y by adding 3 to both sides and then dividing by 5: y =  rac{16}{5}. Since we have successfully isolated y and found a specific value for it, the equation has one solution.

Answer:

11.55 ft

Step-by-step explanation:

tan 60° = 20 / x

x = 20 / tan 60° = 20 / √3 = 11.55

The length of the shadow will be 11.55 ft. It is found by the help of the tangent formula of trigonometry.

Angle of depression is the angle formed by the horizontal and the place where your head came to a halt.

You keep your gaze level with the ground. When you need to keep an eye on anything, though, you raise your head and lower your gaze.

The given data in the problem is;

Angle of depression = 60°

Length of the shadow(x) = ?

Height of  flagpole = 20 ft

From trigonometry formula of tanΘ is;

[tex]\rm tan \theta = \frac{P}{B} \\\\ tan60^0=\frac{20}{x} \\\\ x= \frac{20}{tan60^0} \\\\ x= \frac{20}{\sqrt{3} } \\\\ x=11.55 \ ft[/tex]

Hence, the length of the shadow will be 11.55 ft.

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Answer: p-value  = 0.1085 and we will not reject the null hypothesis.

Step-by-step explanation:

Since we have given that

Hypothesis are :

[tex]H_0:p=0.3\\\\H_1:p>0.3[/tex]

Here, n = 200

x = 68

So, [tex]\hat{p}=\dfrac{68}{200}=0.34[/tex]

So, the test statistic value would be :

[tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}\\\\z=\dfrac{0.34-0.3}{\sqrt{\dfrac{0.3\times 0.7}{200}}}\\\\z=\dfrac{0.04}{0.0324}\\\\z=1.234[/tex]

So, the value of statistic value is 1.234.

And the p-value = 0.1085 at 5% level of significance.

So, 0.1085 <  1.234,

So, we will not reject the null hypothesis.

Hence, p-value  = 0.1085 and we will not reject the null hypothesis.

The p-value is a measure of the evidence against the null hypothesis in a hypothesis test. To calculate the p-value, we compare the observed proportion to the target percentage using a one-sample proportion test. The statistical decision when alpha = 0.05 is to reject the null hypothesis if the p-value is less than 0.05.

A. The p-value is a measure of the evidence against the null hypothesis in a hypothesis test. It represents the probability of observing a test statistic as extreme as the one obtained, assuming the null hypothesis is true.

B. To calculate the p-value for the test statistic in this case, we need to perform a hypothesis test. We compare the proportion of viewers who would see the movie again (68/200 = 34%) to the target percentage of 30% using a one-sample proportion test.

C. The statistical decision when alpha = 0.05 is to reject the null hypothesis if the p-value is less than 0.05. This indicates strong evidence against the null hypothesis.

D. The managerial conclusion for this situation would depend on the p-value obtained. If the p-value is less than 0.05, we can conclude that there is strong evidence to suggest that more than 30% of the viewers would see the movie again. Otherwise, we cannot make a definitive conclusion.

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Answer:

24 cubic units

Step-by-step explanation:

4 times 2 times 3 equals 24

Answer:

2kg is the answer

ok well let's see it's 2000 grams

Given Information:

Population size = N = 210

Mean height of women population = μ = 64.4 in.

Standard deviation of height of women population = σ = 2.9 in.

Sample size = n = 36

Required Information:

Sample mean = μx = ?

Sample standard deviation = σx = ?

Answer:

Sample mean = μx = 64.4 in.

Sample standard deviation = σx = 0.44 in.

Step-by-step explanation:

We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.

The mean of the sample will be same as population mean that is

μ = μx = 64.4 in

Whereas the sample standard deviation is given by

[tex]\sigma_{x} = \frac{\sigma}{\sqrt{n} } \cdot \sqrt{\frac{N-n}{N-1} }[/tex]

Where σ is the standard deviation of height of women population, N is the population size and n is the sample size.

The term [tex]\sqrt{\frac{N-n}{N-1} }[/tex] is known as finite population correction factor and is used since the sampling is done without replacement.

[tex]\sigma_{x} = \frac{2.9}{\sqrt{36} } \cdot \sqrt{\frac{210-36}{210-1} }\\\sigma_{x} = 0.483 \cdot \sqrt{\frac{174}{209} }\\\sigma_{x} = 0.483 \cdot 0.912\\\sigma_{x} = 0.44[/tex]

Therefore, the standard deviation of sample is 0.44 in.

To find the mean (mu Subscript x overbar) and standard deviation (sigma Subscript x overbar) of the population of sample means, use the formulas provided.

To find the mean (mu Subscript x overbar) and standard deviation (sigma Subscript x overbar) of the population of sample means, we use the formulas:

In this case, the population mean (mu) = 64.4 inches, the population standard deviation (sigma) = 2.9 inches, and the sample size (n) = 36.

Using these values, we can calculate:

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Answer:

x,y(6.-6)

Step-by-step explanation:

{x=-y

6(-y)-5y=66

-6-5y=66

11y=66

y=6

-x-y=0

x=-y;

x=-6

Answer:

a) Recommended order quantity = 79.84 = 80

b) recorder point = 35

Safety stock = 10

Safety stock cost = $0/year

ci) P(stock out/cycle) = 0.1587

cii) Number of stock outs/ year = 2

Step-by-step explanation:

The pictures attached show a clear explanation of all the processes.

Final answer:

To determine the recommended order quantity, use the EOQ formula. The reorder point and safety stock can be calculated using the normal distribution. If the reorder point is set at 30, the probability of a stockout and the expected number of stockouts can be calculated.

Explanation:

To determine the recommended order quantity, we need to consider the economic order quantity (EOQ) model. The EOQ formula is given by:

EOQ = √((2 * D * Co) / Ch)

Where:

D is the annual demand (1000 units)

Co is the ordering cost per order ($25.50)

Ch is the holding cost per unit ($8)

Plugging in the values, we get:

EOQ = √((2 * 1000 * 25.50) / 8) = 79.79 (rounded to 2 decimal places)

Therefore, the recommended order quantity is 80 units.

To calculate the reorder point, we need to consider the lead-time demand. Since the lead-time demand follows a normal probability distribution with μ=25 and σ=5, we can use the normal distribution to find the reorder point.

To calculate the recorder point and safety stock for a desired probability of stockout of 2%, we need to find the Z value corresponding to the desired probability. We can use the Z-score table or a calculator to find the Z value. For a 2% probability of stockout, the Z value is approximately -2.05 (rounded to 2 decimal places).

The reorder point is given by:

Reorder Point = μ + (Z * σ)

Where:

μ is the mean of the lead-time demand (25 units)

Z is the Z value (-2.05)

σ is the standard deviation of the lead-time demand (5 units)

Plugging in the values, we get:

Reorder Point = 25 + (-2.05 * 5) = 14.75 (rounded to 2 decimal places)

The safety stock is given by:

Safety Stock = Z * σ

Plugging in the values, we get:

Safety Stock = -2.05 * 5 = -10.25 (rounded to 2 decimal places)

Therefore, the recorder point is approximately 15 units (rounded to the nearest whole unit) and the safety stock is approximately 10 units (rounded to the nearest whole unit).

If the manager sets the reorder point at 30 units, we can use the normal distribution to find the probability of a stockout. The probability of a stockout can be calculated using the Z-score formula.

The Z value is calculated using the formula:

Z = (Reorder Point - μ) / σ

Where:

Reorder Point is the given reorder point (30 units)

μ is the mean of the lead-time demand (25 units)

σ is the standard deviation of the lead-time demand (5 units)

Plugging in the values, we get:

Z = (30 - 25) / 5 = 1 (rounded to 1 decimal place)

Looking up the Z value in the Z-score table, we find that the corresponding probability is approximately 0.8413. Therefore, the probability of a stockout on any given order cycle is approximately 0.1587 or 15.87% (rounded to 2 decimal places).

The number of times you would expect a stockout during the year can be estimated using the formula:

Number of Stockouts = (Annual Demand / EOQ) * (1 - Probability of Stockout)

Plugging in the values, we get:

Number of Stockouts = (1000 / 80) * (1 - 0.1587) = 10.69 (rounded to 2 decimal places)

Therefore, you would expect a stockout approximately 11 times during the year (rounded to the nearest whole number).

Answer:

[tex]\frac{7}{16}[/tex]

Step-by-step explanation:

[tex]\frac{7}{8}[/tex]×[tex]\frac{1}{2}[/tex]

Multiply straight forward:

So 7 and 1. 8 and 2.

7x1=7

8x2=16

[tex]\frac{7}{16}[/tex]

Answer:

Step-by-step explanation:

Let x represent the amount invested at 10%. Then 23000-x is the amount invested at 4%, and the total interest is ...

  0.10x +0.04(23000-x) = 1280

  0.06x = 360 . . . . . subtract 920, simplify

  x = 6000 . . . . . . . . divide by the coefficient of x

Ms Burke invested $6000 at 10% and $17000 at 4%.

The question is faulty written. I'll solve it assuming values for one variable and provide the answer to guide the student in their own question

Answer:

x=t

y=-1-9t

Step-by-step explanation:

Parametric Equations

Given an explicit relation between variables x and y, we can find expression for both of them in term of a third parameter t, such as

x=f(t)

y=g(t)

provided the main relation holds.

we have the equation

9x+y=-1

There are infinitely many forms to find parametric expressions for the variables, let's assume

x=t

Solving the equation for y

y=-1-9x=-1-9t

Thus the parametric equations are

x=t

y=-1-9t

Answer:

190 Jeans

Step-by-step explanation:

The daily production cost of the jeans manufacturer is given as:

[tex]C=0.3x^2-114x+11405[/tex]

To determine the number of Jeans,x that should be produced daily to minimize cost, C. We take the derivative of C and solve for its critical points.

[tex]C'=0.6x-114\\$When C'=0\\0.6x-114=0\\0.6x=114\\x=190[/tex]

Therefore, to minimize daily cost, 190 Jeans is the number of jeans that should be produced daily.

Answer: [tex]y=8x[/tex]

Step-by-step explanation:

For this exercise it is important to remember that the equation of a line that passes through the origin (this is located at the point [tex](0,0)[/tex]), has the following form:

[tex]y=mx[/tex]

Where "m" is the slope of the line.

In this case, according to the information given in the exercise, you know that 8 million tons of plastic waste enters the world’s oceans every year, apprdoximately.

Then, let the independent variable "x" represents the number of years.

 Analizing the data given, you can identify that the slope of that line is the following:

[tex]m=8[/tex]

So, knowing the value of "m", you can subsitute them into the equation  [tex]y=mx[/tex], in order to get the equation that shows that situation.

This is:

[tex]y=8x[/tex]

Answer:

The probability that the resident has both homeowner’s and automobile insurance with World Wide Insurance Company is 14% (P=0.1431).

Step-by-step explanation:

The probability of having homeowner’s insurance (H) with the company is P(H)=0.53.

The probability that, given that the resident has homeowner insurance with the company, also had a automobile insurance is P(A|H)=0.27.

We have to calculate P(A&H): probability of having automovile and homeowner:

[tex]P(A\&H)=P(H)*P(A|H)=0.53*0.27=0.1431[/tex]

Answer:

The probability that the resident has both homeowner’s and automobile insurance with World Wide Insurance Company is 0.143 OR 14.3%.

Step-by-step explanation:

We are given that:

53% of the residents had homeowner's insurance i.e. P(H) = 0.53

Of these people, 27% also had automobile insurance i.e. they had automobile insurance given that they had homeowner's insurance. So, P(A|H) = 0.27.

We need to find out the probability that the resident has both homeowner's and automobile insurance i.e. P(A and H) or P(A∩H). To compute P(A∩H) we will use the conditional probability formula:a

P(A|B) = P(A∩B)/P(B)

Here we have:

P(A|H) = P(A∩H)/P(H)

P(A∩H) = P(A|H) * P(H)

            = 0.27 * 0.53

P(A∩H) = 0.143

The probability that the resident has both homeowner’s and automobile insurance with World Wide Insurance Company is 0.143 OR 14.3%.

Answer:

[tex]v = \pi {r}^{2} \frac{h}{3} \\ \: \: \: \: = \pi \times 20 \frac{40}{3} \\ \: \: \: \: = 16755.16 {cm}^{3} [/tex]

hope this helps you

Answer:

Scalene Triangles

Step-by-step explanation:

Isosceles triangles have one pair of equivalent edges, and equilateral triangles of course have all equivalent edges, it would obviously be the scalene triangles.

I am joyous to assist you at any time.

Answer:

The answer is 0.75.

Step-by-step explanation:

To use probability of a complement event, we need to find the situation where none of the couples are sitting next to each other which can happen either two husbands are sitting in the seats 2 and 3 or two wives are sitting in the seats 2 and 3. Also in the first scenario, the wives would need to be sitting at the opposite ends to their husbands and vice versa for the second scenario.

So there are in total 4 scenarios where no couple is sitting next to each other.

There are a total of 16 different ways that they can be seated so the probability of compelement is 16 - 4 = 12, which is 3/4 of the total, meaning that the probability of at least one of the wives sittting next to her husband is 0.75 or 75%.

I hope this answer helps.

Answer:

Length of the longest metal rod which can be carried horizontally around the right-angle turn is 21.21ft

Step-by-step explanation:

Length of the longest metal rod which can be carried horizontally around the right-angle turn, can be determined at the point at where the distance between one end of rod and the 7feet corridor is same as the distance between other end of the rod and the 8feet corridor. How do I mean.

The length of longest metal rod will be determined when distance between the one end of rod and the 7feet corridor and the distance between other end of the rod and the 8feet corridor are both 15ft (7ft + 8ft).

See attachment for illustration.

Therefore using Pythagoras theorem we can find the length of longest metal rod that can be carried horizontally around the right angle turn

See illustration in attachment

i.e

Hyp² = opp²+adj²

Hyp = √(15²+15²)

Hyp = √450

Hyp = 21.21ft

Step-by-step explanation:

csc²u − cos u sec u

csc²u − 1

cot²u

Answer:

f(x)= 3x + 1

Step-by-step explanation:

Let's set the unknown variable as b, since it's a linear equation.

Using the point given (-3, -8), we can find b by plugging in the known numbers and solving.

-8 = -3 (3) + b

-8 = -9 + b

b = 1

If you want, you can check it by forming the complete equation and plugging in -3.

f(x)= 3x + 1

f(-3) = -9 + 1

f(-3) = -8 = -8

I hope this helped!

Answer:

the graph that matches the function is

Step-by-step explanation:

Answer:

$125.25

Step-by-step explanation:

8.75*h+11.25*e

h is hours regular pay and e is extra pay for overtime. Since its an extra $2.50 for overtime, add that to the regular pay. Put in the hours:

[tex]8.75*8+11.25*5[/tex]

Simplify by multiplying 8.75 by 8

[tex]70+11.25*5[/tex]

Simplify by multiplying 11.25 by 5

[tex]70+56.25[/tex]

Add

[tex]70+56.25=126.25[/tex]

Since it says how much did each earn, as in individually, leave it as it is (unless regular pay was $2.18 an hour, which would be a rip-off). I'm pretty sure including the number of employees was meant to throw you off.

Answer:

The p-value for the hypothesis test is 0.0042.

Step-by-step explanation:

We are given that the supervisor of a production line wants to check if the average time to assemble an electronic component is different from 14 minutes.

Assume that the population of assembly time is normally distributed with a standard deviation of 3.4 minutes. The supervisor times the assembly of 14 components, and finds that the average time for completion is 11.6 minutes.

Let [tex]\mu[/tex] = average time to assemble an electronic component.

SO, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 14 minutes  {means that the average time to assemble an electronic component is equal to 14 minutes}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 14 minutes   {means that the average time to assemble an electronic component is different from 14 minutes}

The test statistics that will be used here is One-sample z test statistics as we know about the population standard deviation;

                        T.S.  = [tex]\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

where, [tex]\bar X[/tex] = sample average time for completion = 11.6 minutes

             [tex]\sigma[/tex] = population standard deviation = 3.4 minutes

             n = sample of components = 14

So, test statistics  =  [tex]\frac{11.6-14}{\frac{3.4}{\sqrt{14} } }[/tex]  

                               =  -2.64

Now, P-value of the hypothesis test is given by the following formula;

         P-value = P(Z < -2.64) = 1 - P(Z [tex]\leq[/tex] 2.64)

                                              = 1 - 0.99585 = 0.0042

Hence, the p-value for the hypothesis test is 0.0042.

The p-value for the hypothesis test is approximately 0.0082

To calculate the p-value for the hypothesis test, follow these steps:

1. State the null and alternative hypotheses:
  - Null hypothesis (\(H_0\)): The average assembly time is 14 minutes. \( \mu = 14 \)
  - Alternative hypothesis (\(H_1\)): The average assembly time is different from 14 minutes. \( \mu \ne 14 \)

2. Determine the test statistic:
  Since the population standard deviation (\(\sigma\)) is known, use the \( z \)-test for the mean. The test statistic is calculated using the formula:
[tex]\[ z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}} \][/tex]
  where:
  - \(\bar{x}\) is the sample mean,
  - \(\mu\) is the population mean under the null hypothesis,
  - \(\sigma\) is the population standard deviation,
  - \(n\) is the sample size.

  Given:
  [tex]\(\bar{x} = 11.6\) minutes,\\ \(\mu = 14\) minutes,\\ \(\sigma = 3.4\) minutes,\\ \(n = 14\).[/tex]

  Plug these values into the formula:
  [tex]\[ z = \frac{11.6 - 14}{3.4 / \sqrt{14}} \][/tex]

3. Calculate the value of the test statistic:
  [tex]\[ z = \frac{11.6 - 14}{3.4 / \sqrt{14}} = \frac{-2.4}{3.4 / \sqrt{14}} \approx \frac{-2.4}{0.9087} \approx -2.64 \][/tex]

4. Find the p-value:
  The p-value for a two-tailed test is calculated by finding the probability that the test statistic is at least as extreme as the observed value, under the null hypothesis.

  [tex]\[ p\text{-value} = 2 \times P(Z \leq z) \][/tex]

  Since we have a \( z \)-score of -2.64, we look up the cumulative probability for \( Z = -2.64 \) in the standard normal distribution table or use a calculator to find:
  [tex]\[ P(Z \leq -2.64) \approx 0.0041 \][/tex]

  Therefore:
  [tex]\[ p\text{-value} = 2 \times 0.0041 = 0.0082 \][/tex]

5. Interpret the results:
  Compare the p-value to the significance level (\(\alpha\)) to make a decision. Typically, \(\alpha\) is set at 0.05. If the p-value is less than \(\alpha\), we reject the null hypothesis.

  In this case:
  [tex]\[ p\text{-value} = 0.0082 \][/tex]

  Since \(0.0082 < 0.05\), we reject the null hypothesis. There is significant evidence to suggest that the average assembly time is different from 14 minutes.

So, the p-value for the hypothesis test is approximately 0.0082.