Answer:
[tex]76.1\times 9.6=730.56[/tex]
Step-by-step explanation:
In this case, we need to find the value of [tex]76.1\times 9.6[/tex]. The numbers are in decimal form. It is understood that the final answer will have decimal point after two places from right.
For an instance, multiply remove decimals from both numbers. Now simply multiply 761 and 96 such that we will get 73056.
Now, keep the decimal point after two places from right. So, we will get 730.56.
Final answer:
The answer to the multiplication of 76.1 and 9.6 is 730 when rounded to two significant figures in accordance with the rules of significant figures in multiplication.
Explanation:
The student asked for the product of 76.1 and 9.6. To compute this, you multiply the two numbers. Since 76.1 has three significant figures and 9.6 has two significant figures, our final answer should be reported with two significant figures, owing to the least number of significant figures in the given numbers.
Now, calculating the product:
76.1 times 9.6 = 730.56
When rounding to two significant figures, the answer is 730.
In calculations involving significant figures, it is important to report your final answer with the correct number of significant figures. In multiplication and division, the number of significant figures in the final answer should be the same as the least number of significant figures in any of the numbers being calculated.
does this answer and help me with all subjects?
You are the engineer in charge of evaluating a new product for potential use in a hydraulic system. The manufacturer has sent 100 randomly chosen samples for you to test. You plan to go through with the deal as long as you can prove that less than 8% of the products you subsequently purchase will be defective. The engineering and business teams at your company believe a 90% confidence level is appropriate for the test.
(a) Specify the null and alternative hypotheses for your test.
(b) Describe (in words) a Type I error for this deal.
(c) Out of the 100 samples provided by the manufacturer, at most how many can be defective for you to agree to use the new product?
(d) For better or worse, your boss convinces you to go through with the deal. Turns out the minimum order is 5000 pieces. Assuming you purchase that many pieces of the new product, and that you found 6 defective pieces out of the 100, generate a 90% two-sided confidence interval for the number of pieces that will be flawed.
Answer:
a) The null hypothesis is represented as
H₀: p ≥ 0.08
The alternative hypothesis is represented as
Hₐ: p < 0.08
b) A type I error for this question would be that
we conclude that the proportion of defective products is less than 8% when in reality, the proportion of defective products, is more than or equal to 8%.
c) At most, the number of defective products in the sample for you to agree to use the new product = 7
d) If minimum of 5000 pieces are purchased, 90% confidence interval for minimum number of flawed pieces will be (103, 497)
Step-by-step explanation:
For hypothesis testing, the first thing to define is the null and alternative hypothesis.
The null hypothesis plays the devil's advocate and is usually stating the opposite of the theory is being tested. It usually maintains that random chance is responsible for the outcome or results of any experimental study/hypothesis testing. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.
While, the alternative hypothesis takes the other side of the hypothesis; that there is indeed a significant difference between two proportions being compared. It usually confirms the the theory being tested by the experimental setup. It usually maintains that other than random chance, there are significant factors affecting the outcome or results of the experimental study/hypothesis testing. It usually contains the signs ≠, < and > depending on the directions of the test
For this question, we want to prove that less than 8% of the products we subsequently purchase will be defective.
So, the null hypothesis will be that there is not enough evidence in the sample to say that less than 8% of the products we subsequently purchase will be defective. That is, the proportion of the sample that are defective is more than or equal to 8%.
And the alternative hypothesis is that there is enough evidence in the sample to say that less than 8% of the products we subsequently purchase will be defective.
Mathematically,
The null hypothesis is represented as
H₀: p ≥ 0.08
The alternative hypothesis is represented as
Hₐ: p < 0.08
b) A type I error involves rejecting the null hypothesis and accepting the alternative hypothesis when in reality, the null hypothesis is true. It involves saying that there is enough evidence in the sample to say that less than 8% of the products we subsequently purchase will be defective when in reality, there isn't enough evidence to arrive at this conclusion.
That is, the proportion of defective products in reality, is more than or equal to 8% and we have concluded that the proportion is less than 8%.
c) Out of the 100 samples provided by the manufacturer, at most how many can be defective for you to agree to use the new product?
The engineer agrees to use the new product when less than 8% of the products we subsequently purchase will be defective.
8% of the product = 0.08 × 100 = 8.
Meaning that the engineer agrees to subsequently purchase the product if less than 8 out of 100 are defective.
So, the maximum number of defective product in the sample that will still let the engineer purchase the products will be 7.
(d) For better or worse, your boss convinces you to go through with the deal. Turns out the minimum order is 5000 pieces. Assuming you purchase that many pieces of the new product, and that you found 6 defective pieces out of the 100, generate a 90% two-sided confidence interval for the number of pieces that will be flawed.
Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample proportion) ± (Margin of error)
Sample proportion = 0.495
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error)
Critical value at 90% confidence interval for sample size of 100 using the t-tables since information on the population standard deviation.
Degree of freedom = n - 1 = 100 - 1 = 99
Significance level = (100-90)/2 = 5% = 0.05
Critical value = t(0.05, 99) = 1.660
Standard error of the mean = σₓ = √[p(1-p)/n]
p = 0.06
n = sample size = 100
σₓ = (0.06/√100) = 0.006
σₓ = √[0.06(0.94)/100] = 0.0237486842 = 0.02375
90% Confidence Interval = (Sample proportion) ± [(Critical value) × (standard Error)]
CI = 0.06 ± (1.660 × 0.02375)
CI = 0.06 ± 0.039425
90% CI = (0.020575, 0.099425)
90% Confidence interval = (0.0206, 0.0994)
If minimum of 5000 pieces are purchased, 90% confidence interval for minimum number of flawed pieces will be
5000 × (0.0206, 0.0994) = (103, 497)
Hope this Helps!!!
(a) The null hypothesis [tex]\(H_0\)[/tex] is that the proportion of defective products is 8% or less (b) A Type I error occurs when the null hypothesis is true (the actual proportion of defective products is 8% or less), but we incorrectly reject it (c) at most 12 defective products can be found in the sample for the deal to proceed. (d) the 90% two-sided confidence interval for the number of defective pieces in the order of 5000 is from 105 to 496.
(a) The null hypothesis [tex]\(H_0\)[/tex] is that the proportion of defective products is 8% or less. The alternative hypothesis [tex]\(H_1\)[/tex] is that the proportion of defective products is greater than 8%. Mathematically, this can be expressed as:
[tex]\(H_0: p \leq 0.08\) \(H_1: p > 0.08\)[/tex]
(b) A Type I error occurs when the null hypothesis is true (the actual proportion of defective products is 8% or less), but we incorrectly reject it, concluding that the proportion of defective products is greater than 8%. This would mean unnecessarily turning down a good deal and potentially incurring additional costs to find another supplier.
(c) To ensure a 90% confidence level with a maximum defective rate of 8%, we can use the binomial distribution to find the maximum number of defective products allowed in the sample of 100. The formula for a binomial confidence interval is given by:
[tex]\(n \cdot p \pm Z_{\alpha/2} \sqrt{n \cdot p \cdot (1 - p)}\)[/tex]
where [tex]\(n\)[/tex] is the sample size, [tex]\(p\)[/tex] is the defect rate, and [tex]\(Z_{\alpha/2}\)[/tex] is the Z-score corresponding to the desired confidence level. For a 90% confidence level, [tex]\(Z_{\alpha/2} = 1.645\)[/tex]. Plugging in the values:
[tex]\(100 \cdot 0.08 \pm 1.645 \sqrt{100 \cdot 0.08 \cdot (1 - 0.08)}\)[/tex]
[tex]\(8 \pm 1.645 \sqrt{100 \cdot 0.08 \cdot 0.92}\)[/tex]
[tex]\(8 \pm 1.645 \sqrt{7.36}\)[/tex]
[tex]\(8 \pm 1.645 \cdot 2.713\)[/tex]
[tex]\(8 \pm 4.46\)[/tex]
The interval is from [tex]\(8 - 4.46\) to \(8 + 4.46\)[/tex], which gives us a range from approximately 3.54 to 12.46. Since we cannot have a fraction of a defective product, we round down to 3. Therefore, at most 12 defective products can be found in the sample for the deal to proceed.
(d) To generate a 90% two-sided confidence interval for the number of defective pieces out of 5000, given that 6 defective pieces were found out of 100, we first calculate the sample proportion of defective products:
[tex]\(\hat{p} = \frac{6}{100} = 0.06\)[/tex]
The formula for the confidence interval is:
[tex]\(\hat{p} \pm Z_{\alpha/2} \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}\)[/tex]
where [tex]\(n\)[/tex] is the sample size (100 in this case), and [tex]\(Z_{\alpha/2}\)[/tex] is the Z-score for a 90% confidence level (1.645). Plugging in the values:
[tex]\(0.06 \pm 1.645 \sqrt{\frac{0.06(1 - 0.06)}{100}}\)[/tex]
[tex]\(0.06 \pm 1.645 \sqrt{\frac{0.06 \cdot 0.94}{100}}\)[/tex]
[tex]\(0.06 \pm 1.645 \sqrt{\frac{0.0564}{100}}\)[/tex]
[tex]\(0.06 \pm 1.645 \cdot \sqrt{0.000564}\)[/tex]
[tex]\(0.06 \pm 1.645 \cdot 0.0237\)[/tex]
[tex]\(0.06 \pm 0.0391\)[/tex]
The interval is from [tex]\(0.06 - 0.0391\) to \(0.06 + 0.0391\)[/tex], which gives us a range from approximately 0.0209 to 0.0991. To find the number of defective pieces in the order of 5000, we multiply these proportions by 5000:
Lower bound: [tex]\(0.0209 \cdot 5000 = 104.5\)[/tex](round to 105)
Upper bound: [tex]\(0.0991 \cdot 5000 = 495.5\)[/tex] (round to 496)
Therefore, the 90% two-sided confidence interval for the number of defective pieces in the order of 5000 is from 105 to 496.
A simple random sample of size nequals10 is obtained from a population with muequals63 and sigmaequals18. (a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities involving the sample mean? Assuming that this condition is true, describe the sampling distribution of x overbar.
Answer:
The sample size is smaller than 30, so we need to assume that the underlying population is normally distributed.
The sampling distribution of x overbar will be approximately normally distributed with mean 63 and standard deviation 5.69.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem
The sample size is smaller than 30, so we need to assume that the underlying population is normally distributed.
If it is:
[tex]\mu = 63, \sigma = 18, n = 10, s = \frac{18}{\sqrt{10}} = 5.69[/tex]
The sampling distribution of x overbar will be approximately normally distributed with mean 63 and standard deviation 5.69.
The face of a clock is divided into 12 equal parts. The radius of the clock face is 6 inches. Assume the hands of the clock will form a central angle. Which statements about the clock are accurate? Check all that apply.
Step-by-step explanation:
Given, the face of a clock is divided into 12 equal parts.
Angle of each part = [tex]\frac{360}{12}[/tex] = 30°
(i) When one hand points at 2 and the other points at 4, this is can be divided into two parts, 2 to 3 and 3 to 4.
The angle formed = 2 (30) = 60°
Option (i) is correct
(ii) The circumference of the clock is ,
Circumference of circle = 2πr,
where r is the radius = 6 and π = 3.14.
Substituting the values in the formula, we get
Circumference of circle = 37.68.
Option (ii) is wrong.
(iii) With one hand at 5 and the other at 10, this is 5 parts
The angle formed= 30(5) = 150°.
The arc length =[tex]\frac{150}{360}[/tex](37.68) = 15.7
Option (iii) is correct
(iv) When one hand points at 1 and the other points at 9, this is 4 parts,
30(4) = 120°. T
Option (iv) is wrong
(v) The length of the minor arc from 11 to 2, this is 3 parts
3(30) = 90°
minor arc from 7 to 10 is 3(30) = 90°
Option (v) is correct
Answer: options 1,3,5
1/4 divided by 7/16 give an example of real world situation that might involve this expression
Answer:
Step-by-step explanation:
if you have 1/4 of a rope and you need to give 7/16 to your friend how much rope did you give to your friend?
Final answer:
Divide 1/4 by the reciprocal of 7/16 to get 4/7. A real-world example is when needing ¼ cup of sugar with only a 7/16 cup measure, fill it approximately 4/7 full to obtain the needed amount of sugar.
Explanation:
To calculate 1/4 divided by 7/16, you would multiply 1/4 by the reciprocal of 7/16, which is 16/7. This would give you (1/4) * (16/7) = 16/28, which can be simplified to 4/7 after dividing both numerator and denominator by 4. A real-world situation involving this expression could be as follows: Imagine you have a recipe that requires 1/4 of a cup of sugar, but you only have a measuring cup that measures 7/16 of a cup.
To find out how many times you need to fill the 7/16 cup to get the 1/4 cup needed, you would calculate 1/4 divided by 7/16, which will give you 4/7. So, you would fill the 7/16 measuring cup approximately 4/7 of the way full to have 1/4 cup of sugar for your recipe.
Find the product of 0.032 and -1.9
Answer:
i think it's -0.0608
Step-by-step explanation:
Kirk goes to the gym every 3 days. Deshawn goes to the
gym every 4 days. If they join the gym on the same day,
when is the first day that they'll be at the gym together?
The day when they would meet first time after joining the gym together will be 12.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Kirk goes to the gym every 3 days.
Deshawn goes to the gym every 4 days.
If they join the gym on the same day.
Then the day when they would meet first time after joining the gym together will be
LCM of 4, 3 will be 12.
Then the day will be 12.
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Final answer:
Kirk and Deshawn will be at the gym together on the 12th day since they joined.
Explanation:
Gym memberships for Kirk and Deshawn occur every 3 days and 4 days respectively. To find the first day they'll be at the gym together, we need to find the lowest common multiple of 3 and 4.
LCM(3, 4) = 12. Therefore, Kirk and Deshawn will be at the gym together on the 12th day since they joined the gym.
If m∠A = 87° and m∠B = 32°, find m∠1.
Answer:
61 degrees
Step-by-step explanation:
87+32=119
180 (total degrees for triangle)-119=67 degrees
Function g can be thought of as a translated (shifted) version of f(x) = x2.
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Write the equation for g(2).
Given:
The given parent function is [tex]f(x)=x^2[/tex]
We need to determine the equation of the new translated (shifted) function g(x).
Vertical stretch:
The general rule to shift the graph f(x), to shift c units upward is [tex]g(x)=f(x)+c[/tex]
From the graph, it is obvious that the graph f(x) is shifted 1 unit upwards.
Thus, applying the above rule, we get;
[tex]g(x)=x^2+1[/tex]
Horizontal stretch:
The general rule to shift the graph f(x) to shift c units to the left is [tex]g(x)=f(x+c)[/tex]
From, the graph, it is obvious that the graph f(x) is shifted 2 units to the left.
Thus, applying the above rule, we have;
[tex]g(x)=(x+2)^2[/tex]
Equation of the new function g(x):
From the figure, it is obvious that the graph g(x) is shifted 1 unit upwards and 2 units to the left.
Thus, we have;
[tex]g(x)=(x+2)^2+1[/tex]
Therefore, the equation of the new function g(x) is [tex]g(x)=(x+2)^2+1[/tex]
Consider the polynomial p(s) = s2 + bs + c where b and c are real numbers. Show that all the roots of p(s) are both contained in the open left half plane {s : s < 0} if and only if b > 0 and c > 0. Hint: use the quadratic formula.
Answer:
It is shown in the explanation
Step-by-step explanation:
p(s) = s² + bs + c
a = 1
b = b
c = c
We get Δ as follows
Δ = (b²-4*a*c) = b² - 4*1*c = b² - 4c > 0 ⇒ b² > 4c ⇔ c > 0
s = (-b + √(b² - 4c))/2(1)
⇒ s₁ = (-b + √(b² - 4c))/2
s₂ = (-b - √(b² - 4c))/2(1)
⇒ s₂ = (-b - √(b² - 4c))/2
We have that -b < 0 ⇔ b > 0
then s₁ < 0 and s₂ < 0 ⇔ c > 0 and b > 0
Answer:
For roots to lie on the left half plane, b ⊃ 0 and c ⊃0
Step-by-step explanation:
From quadratic formula, we have;
x = -b±√(b²-4ac)/2a
From the given expression p(s) = s² + bs + c,
x = s
a = 1
b = b
c = c
The quadratic formula can then be written as;
s = -b±√(b²-4*1*c)/2*1
= -b±√(b²-4c)/2
s₁ = -b+√(b²-4c)/2
s₂ = -b±√(b²-4c)/2
From the equation above,
Sum of root = -b
Product of root = c
If both the root lie on left side of the s-plane, then sum of roots will be negative. Hence, -b ∠0. That is, b ⊃0
Also, the product root will be positive, c ⊃ 0
Hence, for roots to lie on the left half plane, b ⊃ 0 and c ⊃0
Help me plz
Solve for X
20 points*
Answer:
x = 4
Step-by-step explanation:
14x - 15 + 139 = 180
(Alternate & Supplementary angles)
14x = 56
x = 4
Three forces act on a hook. Determine the magnitude of the resultant of the force.
Use Hooke's law... (just kidding)
Break down each force vector into horizontal and vertical components.
[tex]\vec F_1=(1000\,\mathrm N)(\cos30^\circ\,\vec x+\sin30^\circ\,\vec y)\approx(866.025\,\mathrm N)\,\vec x+(500\,\mathrm N)\,\vec y[/tex]
[tex]\vec F_2=(1500\,\mathrm N)(\cos160^\circ\,\vec x+\sin160^\circ\,\vec y)\approx(-1409.54\,\mathrm N)\,\vec x+(513.03\,\mathrm N)\,\vec y[/tex]
[tex]\vec F_3=(750\,\mathrm N)(\cos195^\circ\,\vec x+\sin195^\circ\,\vec y)\approx(-724.444\,\mathrm N)\,\vec x+(-194.114\,\mathrm N)\,\vec y[/tex]
The resultant force is the sum of these vectors,
[tex]\vec F=\displaystyle\sum_{i=1}^3\vec F_i\approx(-1267.96\,\mathrm N)\,\vec x+(818.916\,\mathrm N)\,\vec y[/tex]
and has magnitude
[tex]|\vec F|\approx\sqrt{(-1267.96\,\mathrm N)^2+(818.916\,\mathrm N)^2}\approx1509.42\,\mathrm N[/tex]
The closest answer is D.
To determine the magnitude of the resultant force acting on a hook when three forces are applied, you can use vector addition. If you have the information of the forces and the angles between them, you can calculate the resultant force using trigonometric functions.
Explanation:To determine the magnitude of the resultant force when three forces act on a hook, you must realize that forces are vector quantities. This means that they have both a magnitude (how much force is being applied) and a direction (the direction the force is being applied in).
If the forces are concurrent (i.e., they act at the same point), one usually uses the parallelogram law or the triangle rule to find the resultant force. You can add two forces to create a resultant, then add the third force to that resultant to find the total resultant. If the forces and the angles between them are known, you can use trigonometric functions to calculate the resultant force.
For instance, if the three forces are F1, F2, and F3, and the angles between them are θ1, θ2, and θ3, the resultant force R can be found using the following equation:
R = √[ (F1 + F2cosθ2 + F3cosθ3)^2 + (F2sinθ2 + F3sinθ3)^2 ]
This equation will give the magnitude of the resultant force. Please note that to use this equation, you must have enough information about the forces and the angles between them.
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i need this answered asap
It's a parallelogram, opposite sides congruent.
6x - 7 = 2x + 9
4x = 16
x = 4
12 = y + 3
9 = y
Answer: x=4, y=9
Answer:
x = 4 and y = 9
Step-by-step explanation:
This is a parallelogram, which we can tell because of the arrows. Basically, opposite sides are parallel. By definition, then, opposite sides of this polygon are equal: LM = ON and LO = MN. That means we can set the various expressions equal to each other:
LM = ON ⇒ 6x - 7 = 2x + 9 ⇒ 4x = 16 ⇒ x = 4
LO = MN ⇒ 12 = y + 3 ⇒ y = 9
Thus, x = 4 and y = 9.
Hope this helps!
An item originally priced at $55 is marked 25% off. What is the sale price?
Answer:
41.25$
Step-by-step explanation:
Answer:
41.25
Step-by-step explanation:
55/4=13.75
So 13.75 is 25% of 55
So then you would do 55-13.75
Because that is 25% off
The final answer would be $41.25 for the sale price.
A circle is centered on point B. Points A, C and D lie on it's circumference. If ADC measures 20 degrees, what does ABC measure
The Answer is : ABC = 40
Convert 4π/3 radians to degrees.
135°
180°
60°
240°
Answer:
240°
Step-by-step explanation:
[tex] \frac{4\pi^{c} }{3} = \frac{4 \times 180 \degree}{3} = 4 \times 60 \degree = 240 \degree \\ [/tex]
78.3 + -17 evaluate the expression
Answer:
it is 61.3
Step-by-step explanation:
Solve the system of linear equations by graphing.
y=−2x+2
y=−x−1
Answer:
(3; - 4)
Step-by-step explanation:
Blue: y = -x - 1
Red: y = -2x + 2
The given system of linear equations have solution as x = 3 and y = -4.
How to represent a straight line on a graph?To represent a straight line on a graph consider two points namely x and y intercepts of the line. To find x-intercept put y = 0 and for y-intercept put x = 0. Then draw a line passing through these two points.
The system of equations are given as,
y =−2x + 2 (1)
y = −x − 1 (2)
The above equations are linear equation in two variables.
Their graph are straight lines which shows their intersection at point (3, -4).
Hence, the solution of the given system of linear equations is x = 3 and y = -4.
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how much water does it take to completely fill a pool that is 50m long 25m wide and 2.5m deep
Answer:
[tex]3,125[/tex]
Step-by-step explanation:
If you want to fill a pool, you will use the formula for finding the volume:
[tex]v=l*w*h[/tex]
In this case, height being depth:
[tex]v=l*w*d[/tex]
Insert values
[tex]v=50*25*2.5[/tex]
Simplify
[tex]v=1,250*2.5\\v=3,125[/tex]
You would need a lot of water.
Answer:
3125000 liter
Step-by-step explanation:
hope i helped
if i can be brainliest that would be great
What is your favorite color? A larger survey of countries, including the United States, China, Russia, France, Turkey, Kenya, and others, indicated that most people prefer the color blue. In fact, about 24% of the population claim blue as their favorite color. Suppose a random sample of n = 75 college students were surveyed and x = 19 of them said that blue is their favorite color. Does this information imply that the proportion of college students who prefer blue differs from that of the general population? Use ???? = 0.05.
Answer:
[tex]z=\frac{0.253 -0.24}{\sqrt{\frac{0.24(1-0.24)}{75}}}=0.264[/tex]
[tex]p_v =2*P(z>0.264)=0.792[/tex]
So the p value obtained was a very high value and using the significance level given [tex]\alpha=0.05[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of students said that blue is their favorite color is not different from 0.24
Step-by-step explanation:
Data given and notation
n=75 represent the random sample taken
X=19 represent the students said that blue is their favorite color
[tex]\hat p=\frac{19}{75}=0.253[/tex] estimated proportion of students said that blue is their favorite color
[tex]p_o=0.24[/tex] is the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level
Confidence=95% or 0.95
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value (variable of interest)
Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the true proportion is different from 0.24.:
Null hypothesis:[tex]p=0.24[/tex]
Alternative hypothesis:[tex]p \neq 0.24[/tex]
When we conduct a proportion test we need to use the z statisitc, and the is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].
Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
[tex]z=\frac{0.253 -0.24}{\sqrt{\frac{0.24(1-0.24)}{75}}}=0.264[/tex]
Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level provided [tex]\alpha=0.05[/tex]. The next step would be calculate the p value for this test.
Since is a bilateral test the p value would be:
[tex]p_v =2*P(z>0.264)=0.792[/tex]
So the p value obtained was a very high value and using the significance level given [tex]\alpha=0.05[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of students said that blue is their favorite color is not different from 0.24
Answer:
0.792
Step-by-step explanation:
In a bag of candy, there are 2 cinnamon, 1 butterscotch, and 2 peppermints. What is the probability of randomly selecting a peppermint?
Answer:
2/5
Step-by-step explanation:
The total number of candies are 2+1+2 = 5 candies
P (peppermint) = number of peppermints/total
=2/5
Answer:
2/5
Step-by-step explanation:
The probability is 2/5.There are five in all and two peppermint.Put it as a fraction and you get 2/5.
What is the place value of 4 in 4.09
Toby skated from his house to the beach at a constant speed of 8 88 kilometers per hour, and then skated from the beach to the park at a constant speed of 7 77 kilometers per hour. The total distance Toby skated was 20 2020 kilometers, and it took him twice as long to get to the park.
Answer:
8b+7p=20
p=2b
Step-by-step explanation:
You're welcome. Thou shall complete thou work without any trouble.
What is the relationship between x and y
Given:
Given that the table with values of x and y.
We need to determine the relationship between x and y.
Slope:
The slope of the relation can be determined using the formula,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substituting the points (2,11) and (4,9), we get;
[tex]m=\frac{9-11}{4-2}[/tex]
[tex]m=\frac{-2}{2}[/tex]
[tex]m=-1[/tex]
Thus, the slope of the relation is m = -1.
y - intercept:
The y - intercept of the relation is the value of y when x = 0.
Hence, from the table, it is obvious that when x = 0, the value of y is 13.
Thus, the y - intercept of the relation is b = 13.
Relationship between x and y:
The relationship between x and y can be determined using the formula,
[tex]y=mx+b[/tex]
Substituting m = -1 and y =13, we get;
[tex]y=-x+13[/tex]
Thus, the relationship between x and y is [tex]y=-x+13[/tex]
If the sphere shown above has a radius of 17 units, then what is the approximate volume of the sphere?
Answer:
Approximately 20,579 units.
12x+7<-11 and 5x-8>= 40
Answer:
no solution
Step-by-step explanation:
First inequality:
12x < -18 . . . . subtract 7
x < -18/12 . . . divide by 12
x < -1.5 . . . . . . write as decimal
__
Second inequality:
5x -8 ≥ 40
5x ≥ 48 . . . . . . add 8
x ≥ 9.6 . . . . . . . divide by 5
__
There are no solutions to this pair of inequalities. No value of x can be both less than -1.5 and greater than 9.6.
When telephone subscribers call from the National Magazine Subscription Company, 18% of the people who answer stay on the line for more than one minute. If 800 people are called in a day, find the probability that a. at least 150 stay on the line for more than one minute. (Use normal approximation to binomial). b. more than 200 stay on the line. (Use Normal approximation to Binomial).
Answer:
a) 30.50% probability that at least 150 stay on the line for more than one minute.
b) 0% probability that more than 200 stay on the line for more than one minute.
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this problem, we have that:
[tex]n = 800, p = 0.18[/tex]
So
[tex]\mu = E(X) = np = 800*0.18 = 144[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{800*0.18*0.82} = 10.87[/tex]
a. at least 150 stay on the line for more than one minute.
Using continuity correction, [tex]P(X \geq 150 - 0.5) = P(X \geq 149.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 149.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{149.4 - 144}{10.87}[/tex]
[tex]Z = 0.51[/tex]
[tex]Z = 0.51[/tex] has a pvalue of 0.6950
1 - 0.6950 = 0.3050
30.50% probability that at least 150 stay on the line for more than one minute.
b. more than 200 stay on the line.
Using continuity correction, [tex]P(X \geq 200 + 0.5) = P(X \geq 200.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 200.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{200.5 - 144}{10.87}[/tex]
[tex]Z = 5.2[/tex]
[tex]Z = 5.2[/tex] has a pvalue of 1
1 - 1 = 0
0% probability that more than 200 stay on the line for more than one minute.
"Tongue Piercing May Speed Tooth Loss, Researchers Say" is the headline of an article. The article describes a study of 51 young adults with pierced tongues. The researchers found receding gums, which can lead to tooth loss, in 19 of the participants. (a) Construct a 95% confidence interval for the proportion of young adults with pierced tongues who have receding gums. (Round your answers to three decimal places.) ( .138 Incorrect: Your answer is incorrect. , .503 Incorrect: Your answer is incorrect. )
Answer:
The 95% confidence interval for the proportion of young adults with pierced tongues who have receding gums is (0.24, 0.506).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 51, \pi = \frac{19}{51} = 0.373[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.373 - 1.96\sqrt{\frac{0.373*0.627}{51}} = 0.24[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.373 + 1.96\sqrt{\frac{0.373*0.627}{51}} = 0.506[/tex]
The 95% confidence interval for the proportion of young adults with pierced tongues who have receding gums is (0.24, 0.506).
The following gambling game has been proposed, which a player must pay to play. First, a value U is chosen uniformly from the set [0, 10]. Next, a number is chosen according to a Poisson random variable with a parameter U. Letting X be the number chosen, the player receives $X. Find E[X], which is the amount a player should pay to make this a fair game HINT: Use the Law of Total Probability for Expectations, E[X]
Answer:
The player should be required to pay $5 to make this a fair game.
Step-by-step explanation:
U ~ Uniform(0, 10)
E[U] = (0 + 10)/2
= 5
X | U ~ Poisson(U)
E[X | U] = U
By law of total probability for expectations,
E[X] = E[E[X|U]] = E[U] = $5
Therefore the player should be required to pay $5 to make this a fair game.
A rectangular box is to have a square base and a volume of 72 ft3. If the material for the base costs $0.62/ft2, the material for the sides costs $0.15/ft2, and the material for the top costs $0.18/ft2, determine the dimensions (in ft) of the box that can be constructed at minimum cost.
a. length
b. width
c. height
Answer:
a. length = 0.7211 ft
b. width = 0.7211 ft
c. height = 140.3846 ft
Step-by-step explanation:
This is an optimiztion with restriction problem.
We have to minimize the cost, with the restriction of the volume being equal to 72 ft3.
As the cost for the sides is constant, we know that length and width are equal.
Then, we can express the volume as:
[tex]V=x\cdot y\cdot z=x^2z=73[/tex]
being x: length and z: height
We can express the height in function of the length as:
[tex]x^2z=73\\\\z=73x^{-2}[/tex]
Then, the cost of the box can be expressed as:
[tex]C=0.62(x^2)+4*0.15(xz)+0.18(x^2)=(0.62+0.18)x^2+0.60xz\\\\C=0.8x^2+0.60x*x^{-2}=0.8x^2+0.6x^{-1}[/tex]
To optimize C, we derive and equal to zero
[tex]\dfrac{dC}{dx}=\dfrac{d}{dx}[0.8x^2+0.6x^{-1}]=1.6x-0.6x^{-2}=0\\\\\\1.6x=0.6x^{-2}\\\\x^{1+2}=0.6/1.6=0.375\\\\x=\sqrt[3]{0.375} =0.7211[/tex]
The height z is then
[tex]z=73x^{-2}=\dfrac{73}{0.7211^2}=\dfrac{73}{0.52}=140.3846[/tex]