To find the sample mean greater than 95% of possible sample means for a population mean of 3.25 and standard deviation of 1.75 with a sample size of 300, apply the Central Limit Theorem to calculate the standard error and use the 95th percentile z-score to compute the desired sample mean.
Explanation:To find the sample mean that is greater than exactly 95% of possible sample means given a population mean (μ) of 3.25 and a standard deviation (σ) of 1.75 for a sample size (n) of 300, we use the concept of a z-score in conjunction with the Central Limit Theorem.
The Central Limit Theorem states that the sampling distribution of the sample mean will be normally distributed if the sample size is large enough. Since we have a large sample size of 300, we can assume normality. The formula for the standard error of the mean (SEM) is given by σ divided by the square root of n, SEM = σ / √n. In this case, SEM would be 1.75 / √300.
To find the specific sample mean that would exceed 95% of the sample means, we need to find the z-score that corresponds to the 95th percentile, which is typically around 1.645 for a one-tailed test (since we're looking for means greater than a value). We then multiply this z-score by the SEM and add it to the population mean. The calculation is as follows:
Calculate SEM: SEM = 1.75 / √300 Find the z-score corresponding to the 95th percentile: z ≈ 1.645 Calculate the sample mean: sample mean = μ + (z * SEM)
By carrying out these calculations, we will obtain the sample mean that is greater than 95% of possible sample means.
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The sample mean that would be greater than exactly 95% of possible sample means is approximately 3.4164.
Given that the population mean [tex](\(\mu\))[/tex] is 3.25 and the population standard deviation [tex](\(\sigma\))[/tex] is 1.75, we can use the z-score formula to find the sample mean [tex](\(\bar{x}\))[/tex] that corresponds to the 95th percentile:
[tex]\[ z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}} \][/tex]
We know that for a standard normal distribution, the z-score that corresponds to the 95th percentile is approximately 1.645 (since we want the value that is greater than exactly 95%, we use the one-tailed z-score). We can rearrange the formula to solve for [tex]\(\bar{x}\)[/tex]:
[tex]\[ \bar{x} = \mu + (z \times \frac{\sigma}{\sqrt{n}}) \][/tex]
Now we plug in the values:
[tex]\[ \bar{x} = 3.25 + (1.645 \times \frac{1.75}{\sqrt{300}}) \] \[ \bar{x} = 3.25 + (1.645 \times \frac{1.75}{\sqrt{300}}) \] \[ \bar{x} = 3.25 + (1.645 \times \frac{1.75}{17.3205080756888}) \] \[ \bar{x} = 3.25 + (1.645 \times 0.1010101010101) \] \[ \bar{x} = 3.25 + 0.16641664166417 \] \[ \bar{x} = 3.4164166416642 \][/tex]
Prism A has a length of 2 units, height of 7 units, and width of 1 unit. Prism B has a length of 3 units, height of 2 units, and width of 3 units.
Which prism has a greater volume?
Prism
.
Prism B has larger volume than Volume of prims A.
What is volume?Volume is the scalar quantity of any object that specified occupied space in 3D.
For example, the space in our room is referred to as volume.
Volume has units of cube example meter³,cm³, etc.
Given that;
Prism A has a length of 2 units, height of 7 units, and width of 1 unit. Prism B has a length of 3 units, height of 2 units, and width of 3 units.
Since, The volume of the rectangular prism is given as,
V = length × height × width
Put length as 2 unit cubes, height as 7 unit cubes, and width as 1 unit cubes.
For prism A;
V = 2 x 7 x 1 = 14 units³.
Put length as 3 unit cubes, height as 2 unit cubes, and width as 3 unit cubes.
For prism B;
V = 3 x 2 x 3 = 18 units³.
Hence, Prism B has larger volume than Volume of prims A.
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IMagicCards.com is a website that allows its members to trade their Magic: The Gathering cards with other members. Since the website's founders do not trust the value of money in relation to the cards, they require members to use only Magic cards as currency rather than money. Which characteristic of money does this scenario best relate to?
A. acceptability
B. portability
C. divisibility
D. durability
E. stability
Answer:
Answer: A
Step-by-step explanation:
The scenario best correlates with the principle of 'Acceptability' in money characteristics, where the Magic cards are accepted in place of traditional currency for trades on IMagicCards.com.
Explanation:Magic Cards as Currency
The scenario you've described involves the trading of Magic: The Gathering cards on IMagicCards.com. This website uses the cards themselves as a form of currency instead of traditional money. Assessing the relation to characteristics of money, this system best correlates with Acceptability. Acceptability is a key attribute of money, signifying that it must be widely accepted for the purchase of goods and services. In this context, the acceptance of Magic cards for trades is equivalent to the principle of acceptability in currency.
The other options do not seem to fit as appropriately in this case. Portability involves the ease with which units of currency can be transported for use in purchasing or trade. Divisibility refers to the ability of money to be divided into smaller units without loss of value. Durability means the currency must withstand the physical wear and tear. Stability pertains to the value of the money remaining relatively stable over time.
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U1.51.4
This excerpt mostly introduces
the character of King Henry, or Harry.
the setting of the port of Mars.
the conflict of a war between England and France.
the setting of the fields of war.
Answer: the character of king Henry, or Harry
Step-by-step explanation:
a psychologist contends that the number of facts of a certain type that are remembered after t hours is given by the following function. f(t)equals startfraction 85 t over 99 t minus 85 endfraction find the rate of change at which the number of facts remembered is changing after 1 hour and after 10 hours.
Answer:
At t=1, Rate of Change=-36.86
At t=10 hours, Rate of Change =-0.0088
Step-by-step explanation:
The function which describes the number of facts of a certain type which are remembered after t hours is given as:
[TeX]f(t)=\frac{85t}{99t-85}[/TeX]
To determine the Rate of Change at the given time, we first look for the derivative of f(t).
Applying quotient rule:
[TeX]f^{'}(t)=\frac{-7225}{{\left( 85 - 99\,t\right) }^{2}}[/TeX]
At t=1
[TeX]f^{'}(1)=\frac{-7225}{(85-99)^{2}}[/TeX]
=-36.86
At t=10 hours
[TeX]f^{'}(10)=\frac{-7225}{(85-99(10))^{2}}[/TeX]
=-0.0088
The rate of change of the function is calculated by finding its derivative and evaluated by substituting the respective hours (1 hour and 10 hours). The rate of change after 1 hour is approximately -106.25, implying a decline per hour, and after 10 hours is approximately -0.918, indicating a slower rate of decline per hour.
Explanation:The rate of change of a function is calculated by finding the derivative of the function. The derivative of a function gives the rate of change of the function at any given point. Let's calculate the derivative of the function f(t) = 85 t / (99 t - 85).
The first step is to use the quotient rule for differentiation, which is given by [f'(x) = (g'(x)h(x) - g(x)h'(x))/h(x)²]. In this case, g(t) = 85 t and h(t) = 99 t - 85.The derivative of g(t) is g'(t) = 85 and the derivative of h(t) is h'(t) = 99.Substitute these values into the quotient rule to obtain f'(t).We get f'(t) = (85*(99 t - 85) - (85 t)*99) / (99 t -85)² = (-850)/ (99 t - 85)². This is the rate of change of the function f(t).
To find the rate of change after 1 hour and 10 hours, substitute t = 1 and t = 10 into f'(t).
For t = 1, f'(1) = -850 / (99*1 - 85)² ≈ -106.25, suggesting a rate of decrease.For t = 10, f'(10) = -850 / (99*10 -85)² ≈ -0.918, also a rate of decrease but slower than in the first hour.Learn more about Rate of Change here:https://brainly.com/question/20816247
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¿Cuál de las siguientes fracciones es
equivalente al decimal 0.18?
~= Ello
Answer:
? necesitamos más información.. ¿dónde están los fracciones?
Step-by-step explanation:
Q 4.12: Suppose that a hypothesis test is conducted. 12 out of 100 subjects have the necessary qualities. The null hypothesis is that the proportion of the subjects who have the necessary qualities is equal to 0.2, while the alternative hypothesis is that this proportion is less than 0.2. The p-value is 0.023. Using a 5% significance level, state the conclusion to the hypothesis test in context.
Answer:
Because our p-value of .023 is lower than the alpha-level of .05, we reject the null hypothesis. There is sufficient evidence to conclude that the proportion of subjects who have the necessary qualities is less than .2. Our test provided a statistically significant result.
Note: An alpha-level of .05 is synonymous with a 5% significance level.Given EP = FP and GQ = FQ, what is the perimeter of ΔEFG?
Given:
In the given ΔEFG,
EP = FP and GQ = FQ
Again,
EP = [tex]4y+2[/tex]
FP = [tex]2x[/tex]
FQ = [tex]3x-1[/tex]
GQ = [tex]4y+4[/tex]
PQ = [tex]x+2y[/tex]
To find the perimeter of ΔEFG.
Formula
The perimeter of a triangle is the sum of all the sides.By Midpoint Theorem we get, a line segment joining the mid points of two sides of a triangle is parallel and half to the third side.In this given triangle, EG║PQ and EG = [tex]\frac{1}{2}[/tex]PQ
Now,
By given condition,
[tex]2x = 4y+2[/tex] ----- (1)
[tex]3x-1 =4y+4[/tex]---------(2)
From (1) we get, [tex]4y = 2x-2[/tex]
Putting this value into (2) we get,
[tex]3x-1 = 2x-2+4[/tex]
or, [tex]x = 3[/tex]
From (1) we get,
[tex]4y = 2(3)-2[/tex]
or, [tex]4y = 4[/tex]
or, [tex]y = 1[/tex]
So,
EF = [tex]2x+4y+2[/tex] = [tex]2(3)+4(1)+2 = 12[/tex] unit
FG = [tex]3x-1+4y+4 = 3(3)-1+4(1)+4 = 16[/tex] unit
PQ =[tex]3+2(1) = 5[/tex] unit
EG = [tex]2(5) = 10[/tex] unit
The perimeter of ΔEFG = EF+FG+EG = 16+10+12 unit = 38 unit
Hence,
The perimeter of the given triangle is 38 unit.
The perimeter of the ΔEFG when EP = FP and GQ = FQ should be 38 units.
Calculation of the perimeter:Since
EP = 4y + 2
FP = 2x
FQ = 3x - 1
GQ = 4y + 4
PQ = x + 2y
So,
2x = 4y +2 ..(1)
4x - 1 = 4y + 4........(2)
So,
3x - 1 = 2x - 2 + 4
y = 1
Now
= EF + FG + FG
= 16 + 10 + 12
= 38 units
hence, The perimeter of the ΔEFG when EP = FP and GQ = FQ should be 38 units.
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An angle is inscribed in a circle. The arc intercepted by this angle is 40°. What is the measure of the inscribed angle?
Answer:
20°
Step-by-step explanation:
Given:
Angle of Intercepted arc = 40°
If an angle is inscribed in a circle, the measure of the inscribed angle is half the measure of the intercepted arc.
Therefore, since the angle of Intercepted arc is 40°, the measure of inscribed angle will be:
[tex] \frac{1}{2} * 40 [/tex]
= 20
Answer:
the answer is 20 degrees
Step-by-step explanation:
just took it
The results of a random survey show that 40 out of 75 people plan to vote for Mr.beston for a position on the local school board. Which is the best prediction of the number of people who will vote for Mr.beston if 3,000 people vote
Answer:
1,600
Step-by-step explanation:
3000/75=40
40*40=1,600
Final answer:
The best prediction for the number of people who will vote for Mr. Beston out of 3,000 voters is found through a simple proportion, resulting in an estimated 1,600 votes for Mr. Beston.
Explanation:
The question asks for a prediction of the number of people who will vote for Mr. Beston if 3,000 people vote, based on the results of a survey where 40 out of 75 people indicated they would vote for him. To find this prediction, we use a simple proportion. We set up a ratio of the number of people who plan to vote for Mr. Beston to the total number surveyed and set this equal to the unknown number of people who will vote for Mr. Beston out of 3,000 total voters.
The ratio or survey proportion is 40/75. We set up the following proportion to find the predicted number of votes:
40/75 = x/3000,
where x is the number we want to find. By cross-multiplying, we get:
40 * 3000 = 75 * x,
which simplifies to:
120,000 = 75x.
Now, we divide both sides by 75 to isolate x:
x = 120,000 / 75,
x = 1600.
Therefore, the best prediction is that 1,600 people out of 3,000 will vote for Mr. Beston.
According to a poll, 55 % of Americans do not know that GOP stands for Grand Old Party (Time, October 17, 2011). Assume that this percentage is true for the current population of Americans. Let p ^ be the proportion in a random sample of 953 Americans who do not know that GOP stands for Grand Old Party. Find the mean and standard deviation of the sampling distribution of p ^ and describe its shape.
Answer:
[tex]\hat p \sim N (p , \sqrt{\frac{p(1-p)}{n}}) [/tex]
The mean is given by:
[tex] \mu_{\hat p} = 0.55[/tex]
And the deviation:
[tex] \sigma_{\hat p} =\sqrt{\frac{0.55*(1-0.55)}{953}}= 0.0161[/tex]
Step-by-step explanation:
For this case we assume that the true population proportion of Americans do not know that GOP stands for Grand Old Party is 0.55 and we select a random sample of n = 953 americans
For this case we assume that we satisfy the conditions to use the normal approximation for [tex]\hat p[/tex]
1) np >10 , n(1-p)>10
2) Independence
3) Random sample
4) The sample size is less than 10% of the population size
We assume that all the conditions are satisfied and the distribution for [tex]\hat p[/tex] would be:
[tex]\hat p \sim N (p , \sqrt{\frac{p(1-p)}{n}}) [/tex]
The mean is given by:
[tex] \mu_{\hat p} = 0.55[/tex]
And the deviation:
[tex] \sigma_{\hat p} =\sqrt{\frac{0.55*(1-0.55)}{953}}= 0.0161[/tex]
State the complement of each of the following sets: (a) Engineers with less than 36 months of full-time employment. (b) Samples of cement blocks with compressive strength less than 6000 kilograms per square centimeter. (c) Measurements of the diameter of forged pistons that do not conform to engineering specifications. (d) Cholesterol levels that measure greater than 180 and less than 220.
Answer:
(a) Engineers with greater than 36 months of full-time employment.
(b) Samples of cement blocks with compressive strength greater than 6000 kilograms per square centimeter
(c) Measurements of the diameter of forged pistons that conform to engineering specifications.
(d) Cholesterol levels that measure less than 180 and greater than 220.
Step-by-step explanation:
The complement of a set refers to elements that does not exist in that set. It means what does not exist in the set but exist in the universal set.
(a) Engineers with greater than 36 months of full-time employment.
In this case, the Universal set is a set of engineers in full-time employment. The given set is for engineers with less than 36 months of full-time employment. The complement is engineers with greater than 36 months of full-time employment.
(b) Samples of cement blocks with compressive strength greater than 6000 kilograms per square centimeter
In this case, the universal set is a set of samples of cement block having compressive strength. The given set is a set of cement block having compressive strength less than 6000 kilograms per square centimeter. The complement is samples of cement blocks with compressive strength greater than 6000 kilograms per square centimeter.
(c) Measurements of the diameter of forged pistons that conform to engineering specifications.
In this case, the universal set is a set of measurements of the diameter of forged pistons. The given set is a set of measurements of the diameter of forged pistons that do not conform to engineering specifications. The complement is a set of measurements of the diameter of forged pistons that conforms to engineering specification.
(d) Cholesterol levels that measure less than 180 and greater than 220.
In this case, the universal set is a set of Cholesterol levels. The given set is Cholesterol levels that measure greater than 180 and less than 220. The complement is Cholesterol levels that measure less than 180 and greater than 220.
the complement sets are engineers with 36 months or more of full-time employment, samples of cement blocks with compressive strength of 6000 kilograms per square centimeter or more, measurements of the diameter of forged pistons that do conform to engineering specifications and cholesterol levels that measure 180 or less, or 220 or more.
Complement sets are those that are not a part of collection of set. For example, if a set contains the numbers from 1 to 5 and set a = {1, 3, 5} then complement of set A will have {2, 4}. Now applying this concept we get:
Engineers with less than 36 months of full-time employment: The complement set would be engineers with 36 months or more of full-time employment.Samples of cement blocks with compressive strength less than 6000 kilograms per square centimeter: The complement is samples of cement blocks with compressive strength of 6000 kilograms per square centimeter or more.Measurements of the diameter of forged pistons that do not conform to engineering specifications: The complement would be measurements of the diameter of forged pistons that do conform to engineering specifications.Cholesterol levels that measure greater than 180 and less than 220: The complement set would be cholesterol levels that measure 180 or less, or 220 or more.Thus, the complement sets are engineers with 36 months or more of full-time employment, samples of cement blocks with compressive strength of 6000 kilograms per square centimeter or more, measurements of the diameter of forged pistons that do conform to engineering specifications and cholesterol levels that measure 180 or less, or 220 or more.
Evaluate the following expression
[10×2+(30-15)÷7+3×8
Answer:
46.142857143
Step-by-step explanation:
10×2+(30-15)÷7+3×8
=10×2+15÷7+3×8
=20+15÷7+3×8
=20+2.142857143+3×8
=20+2.142857143+24
=46.142857143
A school sold tickets to a musical.
The school received
$6.50
$6.50
per ticket sold.
Write an equation that represents the relationship between the number of tickets sold and the total amount of money the school received from selling tickets.
Let
m=the money collected and
t= tickets sold.
m=6.50t
6.50 per ticket so you multiply 6.50 by t. The money collected is the answer to the equation. Hope this helps!
Eric spent $21.85, including sales tax, on 2 jerseys and 3 pairs of socks. The jerseys cost $6.75 each and the total sales tax was $1.03. Fill in the table with the correct prices.
Answer:
The socks cost $2.44 per pair
Step-by-step explanation:
Everything costs $21.85 in total. The given values are $6.75 for each jersey (which adds to make both jerseys together make $13.50). There is also a given value of $1.03 for total sales tax. If you add the jerseys and tax, you get $14.53. Subtract that from $21.85 to get $7.2. That is the total for all three pairs of socks, so divide that by three and you get $2.44 for each pair of socks :)
A random sample of 25 college males was obtained and each was asked to report their actual height and what they wished as their ideal height. A 95% confidence interval for µd = average difference between their ideal and actual heights was 0.8" to 2.2". Based on this interval, which one of the null hypothesis below (versus a two-sided alternative) can be rejected?
A. H0: μd= 0.5B. H0: μd= 1.0C. H0: μd= 1.5D. H0: μd= 2.0
Answer:
Correct option is (A). H₀: [tex]\mu_{d}[/tex] = 0.5
Step-by-step explanation:
The (1 - α)% confidence interval for a population parameter can be used to determine whether to reject a null hypothesis or not.
The decision rule is:
If the (1 - α)% confidence interval for a population parameter consists of the null value of the parameter then the null hypothesis will be accepted or else it will be rejected.
A hypothesis test is performed to determine the difference between the ideal and actual heights of college males.
The 95% confidence interval for the mean difference, [tex]\mu_{d}[/tex] is:
CI = (0.8, 2.2)
The four null hypothesis provided are:
H₀: [tex]\mu_{d}[/tex] = 0.5H₀: [tex]\mu_{d}[/tex] = 1.0H₀: [tex]\mu_{d}[/tex] = 1.5H₀: [tex]\mu_{d}[/tex] = 2.0The 95% confidence interval for the mean difference consists of the value, 1.0, 1.5 and 2.0.
But it does not consist the value 0.5.
So, the null hypothesis that can be rejected is:
H₀: [tex]\mu_{d}[/tex] = 0.5
Thus, the correct option is (A).
Based on the 95% confidence interval given, we can only reject null hypothesis H0: μd= 0.5. The rest of the null hypotheses fall within the interval and therefore, cannot be rejected.
Explanation:Based on the 95% confidence interval, which ranges from 0.8" to 2.2", we are interested in whether 0 falls within this range. When it falls within this range, we cannot reject the null hypothesis. Going through the provided null hypotheses, we can reject the null hypothesis which falls outside the confidence interval.
Considering:
A. H0: μd= 0.5
B. H0: μd= 1.0
C. H0: μd= 1.5
D. H0: μd= 2.0
Only hypothesis A falls outside the confidence interval, thus we can reject null hypothesis H0: μd= 0.5. The null hypotheses stating μd= 1.0, μd= 1.5, and μd= 2.0 fall within this range and therefore, cannot be rejected based on this confidence interval.
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A marketing firm would like to test-market the name of a new energy drink targeted at 18- to 29-year-olds via social media. A study by the Pew Research Center found that 35% of U.S. adults (18 and older) do not use social media (Pew Research Center website, October 2015). The percentage of U.S. young adults age 30 and older is 78%. Suppose that the percentage of the U.S. adult population that is either age 18–29 or uses social media is 67.2%. a. What is the probability that a randomly selected U.S. adult uses social media? b. What is the probability that a randomly selected U.S. adult is aged 18–29? c. What is the probability that a randomly selected U.S. adult is 18–29 and a user of social media? Anderson, David R.. Essentials of Statistics for Business and Economics (p. 198). Cengage Learning. Kindle Edition.
To find the probabilities of a randomly selected U.S. adult using social media and being aged 18-29, we can use probability concepts and the given information.
Explanation:To solve this problem, we can use the concept of probability. Let's define the following events:
A: randomly selected U.S. adult uses social mediaB: randomly selected U.S. adult is aged 18-29From the information given, we have P(A' ∩ B') = 35%, P(A' ∩ B) = 0, P(A ∩ B') = 67.2%. We need to find the probabilities P(A) and P(B).
Using the formula for the probability of the complement of an event, we have P(A') = 35%.Using the given value of the percentage of U.S. young adults age 30 and older (78%), we have P(B') = 100% - 78% = 22%.Using the formula P(A ∩ B') = P(A) - P(A ∩ B), we have P(A) = P(A ∩ B') + P(A' ∩ B') = 67.2% + 35% = 102.2%.Using the formula P(B) = P(B') - P(A' ∩ B'), we have P(B) = 22% - 0% = 22%.Therefore, the probability that a randomly selected U.S. adult uses social media is 102.2%, the probability that a randomly selected U.S. adult is aged 18-29 is 22%, and the probability that a randomly selected U.S. adult is 18-29 and a user of social media is 67.2%.
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a. Probability of a randomly selected U.S. adult using social media is 45.2%.
b. Probability of a randomly selected U.S. adult being aged 18-29 is 65%.
c. Probability of a randomly selected U.S. adult being 18-29 and a user of social media is approximately 29.38%.
a. Probability a randomly selected U.S. adult uses social media:
Probability of being 18-29 or use social media = 67.2%
Percentage of US adults aged 30 and older = 78%
Thus, percentage of US adults aged 18-29 = 100% - 78% = 22%
Probability of using social media = 67.2% - 22% = 45.2%
b. Probability of a randomly selected U.S. adult being aged 18-29:
Percentage of adults not using social media = 35%
Thus, percentage of adults aged 18-29 = 100% - 35% = 65%
c. Probability of a randomly selected U.S. adult being 18-29 and a user of social media:
Probability of using social media = 45.2%
Probability of being 18-29 = 65%
Probability of being 18-29 and using social media = 0.452 * 0.65 = 29.38%
If you deposit $10,000 at 3.85% interest, compounded daily, what would your ending balance be after three years?
Answer: $11,155
Step-by-step explanation: For this problem, first we will use the "Simple Interest" equation to find the total interest earned after three years.
First, convert 3.85% to a decimal, 0.0385.
I, interest = 10,000 x 0.0385 x 3
I = 1,155
Now add the total interest $1,155 to the total deposit $10,000.
1,155 + 10,000 = $11,155
By using the formula for amount of Compound Interest the result is
Ending balance after 3 years = $11224.29
What is compound Interest?
If the interest on a certain principal increases exponentially rather than linearly on a certain rate over a certain period of time, then the interest obtained is known as compound interest.
If the principal be P, rate is r%, time is n years,
Amount = [tex]P(1 + \frac{r}{100})^n[/tex]
CI = Amount - Principal
Here,
Principal = $10000
Rate = 3.85%
Time = 3years
Amount =
[tex]10000(1+\frac{3.85}{36500})^{3\times 365}\\10000(1 + \frac{385}{3650000})^{1095}\\[/tex]
11224.29
Ending balance after 3 years = $11224.29
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Find the sample size required to estimate the percentage of college students who use student loans to help fund their tuition. Assume that we want 95% confidence that the proportion from the sample is within two percentage points of the true population percentage. Record your answer as a whole number.
Answer:
We need a sample of size at least 2401.
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].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/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].
Assume that we want 95% confidence that the proportion from the sample is within two percentage points of the true population percentage.
We need a sample of size at least n.
n is found when [tex]M = 0.02[/tex]
We don't know the exact proportion, so we use [tex]\pi = 0.5[/tex], which is the case for which we are going to need the largest sample size.
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.02 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.02\sqrt{n} = 1.96*0.5[/tex]
[tex]\sqrt{n} = \frac{1.96*0.5}{0.02}[/tex]
[tex](\sqrt{n})^{2} = (\frac{1.96*0.5}{0.02})^{2}[/tex]
[tex]n = 2401[/tex]
We need a sample of size at least 2401.
Answer:
[tex]n=\frac{0.5(1-0.5)}{(\frac{0.02}{1.96})^2}=2401[/tex]
And rounded up we have that n=2401
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
Solution to the problem
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. And the critical value would be given by:
[tex]z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96[/tex]
The margin of error for the proportion interval is given by this formula:
[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex] (a)
And on this case we have that [tex]ME =\pm 0.02[/tex] or 2% points and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex] (b)
We can use an prior estimation for p [tex]\hat p=0.5[/tex]. And replacing into equation (b) the values from part a we got:
[tex]n=\frac{0.5(1-0.5)}{(\frac{0.02}{1.96})^2}=2401[/tex]
And rounded up we have that n=2401
how many times does 100 go into 540
Answer:
100 goes into 540 5 times
Step-by-step explanation:
which leaves a remainder of 40
hi and hope this helps!!
Answer:
5 remainder: 40 or 5.4
Step-by-step explanation:
when dividing 540 to 100, you need to know how many times 540 can go into 100. 100 can go into 540 5 times, so, you'll multiply 100 by 5. That should give you 500, then, you'll subtract 540 to 500, and that should give you a remainder of 40.
If you want to divide it to a decimal, you need to add an additional zero . to 40. That should give you 400. Then, 100 can go into 400, 4 times. So, you'll subtract 400 to 400, and that should give you 0. Now, you're done!
A manufacturer has determined that a model of its washing machine has an expected life that is Exponential with a mean of four years to failure and irrelevant board burn-in period. He wants to testthe system and complete data collection. Find the probability that one of these washing machines will have a life that ends: (Note you can find the reliability of the washing machine life)
Complete question:
A manufacturer has determined that a model of its washing machine has an expected life that is Exponential with a mean of four years to failure and irrelevant board burn-in period. He wants to testthe system and complete data collection. Find the probability that one of these washing machines will have a life that ends: (Note you can find the reliability of the washing machine life)
a) After an initial four years of washing machine service
b) Before four years of washing machine service are completed
c) Not before six years of washing machine service.
Answer:
a) 0.3679
b) 0.6321
c) 0.2231
Step-by-step explanation:
Given:
Mean, u= 4
/\ = 1/u
= 1/4 = 0.25
The cummulative distribution function, will be:
For x≥0,
[tex] F(x) = 1 - e^-^0^.^2^5^X[/tex]
[tex]P(x<X) = F(X)[/tex]
a) After an intial four years:
[tex]P(x>4) = 1-(1-e^-^0^.^2^5^*^4^.^0)[/tex]
P(x>4) = 0.3679
b) Before four years:
[tex]P(x<4) = 1-(e^-^0^.^2^5^*^4^.^0)[/tex]
P(x<4) = 0.6321
c) Not before 6 years:
[tex]P(x>6) = 1-(1-e^-^0^.^2^5^*^4^.^0)[/tex]
P(x>6) = 0.2231
What is the median of this set of data 100,102,103,106,109
Step-by-step explanation:
In ascending order
100 , 102 , 103 , 106, 109
No of data (N) = 5
Now
Position of median
= ( N + 1) /2 th item
=( 5+1 )/2 th item
= 6 / 2 th item
= 3rd item
Therefore exact median = 103
Hope it will help you :)
Answer:
103
Step-by-step explanation:
100,102,103,106,109
Median position: (n+1)/2
(5+1)/2 = 3rd value
Median = 103
What is the result of subtracting the second equation from the first?
- 2x + 7y = 10
3x+ 7y = 2
"D" size batteries produced by MNM Corporation have had a life expectancy of 85.8 hours. Because of an improved production process, the company believes that there has been an INCREASE in the life expectancy of its D size batteries. A sample of 54 batteries showed an average life of 88.7 hours with a standard deviation of 3.8 hours. Conduct an appropriate hypothesis test. Find the t-statistic and the appropriate conclusion at the 0.1 level of significance.
Answer:
The calculated value t = 5.608 > 2.3988 at 0.1 level of significance with 53 degrees of freedom.
The null hypothesis is rejected at 0.1 level of significance
The company do not believes that there has been an INCREASE in the life expectancy of its D size batteries
Step-by-step explanation:
Step(i):-
Given data the size of sample n=54
Given "D" size batteries produced by MNM Corporation have had a life expectancy of 85.8 hours
therefore mean of Population μ = 85.5 hours
Given a sample of 54 batteries showed an average life of 88.7 hours with a standard deviation of 3.8 hours
The mean of the sample x⁻ = 88.7 hours
The standard deviation of the sample (S) = 3.8 hours
Step(ii):-
Null hypothesis : H₀:μ > 85.5 hours
Alternative hypothesis: H₁:μ < 85.5 hours
Level of significance : ∝= 0.1
Degrees of freedom γ =n-1 = 54-1 =53
The test statistic
[tex]t= \frac{x^{-}-u }{\frac{S}{\sqrt{n} } }=\frac{88.7-85.8}{\frac{3.8}{\sqrt{54} } }[/tex]
t = 5.608
The tabulated value t = 2.3988 at 0.1 level of significance with 53 degrees of freedom.
Conclusion:-
The calculated value t = 5.608 > 2.3988at 0.1 level of significance with 53 degrees of freedom.
The null hypothesis is rejected at 0.1 level of significance
The company do not believes that there has been an INCREASE in the life expectancy of its D size batteries
A 4-column table with 4 rows. The first column has no label with entries C, D, E, total. The second column is labeled A with entries X, Y, Z, 1.0. The third column is labeled B with entries 0.25, 0.68, 0.07, 1.0. The fourth column is labeled total with entries G, H, J, 1.0. Which value for Y in the table would be least likely to indicate an association between the variables? 0.06 0.24 0.69 1.0
Answer:
.69 or c
Step-by-step explanation:
Which comparison is true?
38=36
38<36
38>36
Answer:
38 > 36
it is true it shows that 38 is greater than 36
There are 5 marbles in a bag: 4 are blue and 1 is red. What is the probability that a blue marble gets picked?
Answer:
the answer is 80%
Step-by-step explanation:
4/5 = 80%
Answer:
in fraction form that is 4/5 or .8 chance of getting a blue marble
Step-by-step explanation:
because you divide the number of possible winning out comes 4 marbles by the total event 5 marbles
Subtract 11 from n then divide by 5
Answer:
I think it's 55.
Step-by-step explanation:
11-n/5
n=11*5
n=55
Answer:
[tex]\frac{n-11}{5}[/tex]
Step-by-step explanation:
1) Subtract 11 from n to get [tex]n-11[/tex] You cannot find a solution for it because there is no value for n.
2) You divide that by 5 so you would just put n-11 over 5 to create a fraction that would look like [tex]\frac{n-11}{5}[/tex]
I am not sure if this is what you were asking but this is the most I can do for you with the information that you gave.
someone please help i’m very confused
(1) 132.67 square meters
(2) 379.94 square meters
Step-by-step explanation:
A barn is in the shape of a rectangle with each corner angle a right angle.
[tex] \therefore Central\: \angle \:(\theta) =90°[/tex]
Since, goat is tied at a corner of the barn, so she would be able to graze the grass of sector of circle with radius (r) = 13 m.
Area of field grazed by goat = area of sector of circle
[tex] = \frac{ \theta}{360 \degree} \times \pi {r}^{2} \\ \\ = \frac{90 \degree}{360 \degree} \times 3.14 \times {13}^{2} \\ \\ = \frac{1}{4} \times 3.14 \times 169\\ \\ = \frac{1}{4} \times530.66 \\ = 132.665 \\ = 132.67 \: {m}^{2} [/tex]
[tex] (2) \\ similarly \: for \: r \: = 22 \: m \\ area \: of \: sector = 379.94 \: {m}^{2} [/tex]
A bag contains 6 red marbles, 9 white marbles, and 8 blue marbles. You draw 5 marbles out at random, without replacement.
Round your answers to 4 decimal places as needed.
1. What is the probability that all the marbles are red?
2. What is the probability that exactly two of the marbles are red?
3. What is the probability that none of the marbles are red?
Problem 1
Answer: 0.0002----------------
Work Shown:
There are n = 6 red marbles and r = 5 ways to pick them (order does not matter). Use the combination formula to find that
n C r = (n!)/(r!(n-r)!)
6 C 5 = (6!)/(5!*(6-5)!)
6 C 5 = (6!)/(5!*1!)
6 C 5 = (6*5!)/(5!*1!)
6 C 5 = (6)/(1!)
6 C 5 = (6)/(1)
6 C 5 = (6)/(1)
6 C 5 = 6
Now repeat for n = 6+9+8 = 23 and r = 5
n C r = (n!)/(r!(n-r)!)
23 C 5 = (23!)/(5!*(23-5)!)
23 C 5 = (23!)/(5!*18!)
23 C 5 = (23*22*21*20*19*18!)/(5!*18!)
23 C 5 = (23*22*21*20*19)/(5!)
23 C 5 = (23*22*21*20*19)/(5*4*3*2*1)
23 C 5 = (4037880)/(120)
23 C 5 = 33649
We have 6 ways of getting what we want (picking five red marbles) out of 33649 ways total (to get five marbles of any color). Again order does not matter.
Divide: 6/33649 = 0.00017831139112
This rounds to 0.0002 when rounding to four decimal places.
=========================================
Problem 2
Answer: 0.3031----------------
Work Shown:
There are 6 C 2 = 15 ways to pick 2 red marbles
There are 17 C 3 = 680 ways to pick 3 non-red marbles.
There are 15*680 = 10,200 ways to pick 5 marbles such that 2 are red, the rest aren't.
There are 33649 ways to select 5 marbles where color doesn't matter
So,
10200/33649 = 0.30312936491427
which rounds to 0.3031
=========================================
Problem 3
Answer: 0.1839----------------
Work Shown:
There are 17 marbles that aren't red, so there are 17 C 5 = 6188 ways to pull out five of them
This is out of 33649 ways to pull out five marbles in general.
6188/33649 = 0.18389848138131
which rounds to 0.1839
The probability of drawing all marbles red is extremely low (0.0002), while the probability of drawing exactly two red marbles is much higher (0.2865). If no red marbles are drawn, the probability is 0.1839.
To solve these problems, we will use the basic principles of probability and combinations, since we are dealing with the probability of drawing marbles without replacement.
1. Probability that all marbles are red
We have a total of 23 marbles (6 red, 9 white, 8 blue). Since we're drawing 5 marbles without replacement, to get the probability that all marbles are red, we need to calculate the combinations of choosing 5 out of 6 red marbles and divide that by the combinations of choosing 5 out of all 23 marbles.
Probability = (⁶C₅) / (²³C₅) = 6/33649 = 0.0002
2. Probability that exactly two of the marbles are red
Here, we want two red marbles and the remaining three to be non-red (either white or blue). We calculate this by multiplying the combination of choosing 2 reds out of 6, 3 non-reds out of 17 (total marbles minus red marbles), and divide by the total combinations of choosing 5 out of 23.
Probability = (⁶C₂ × ¹⁷C₃) / (²³C₅) = (15 × 680) / 33649 = 0.2865
3. Probability that none of the marbles are red
To find the probability of drawing no red marbles, we only consider the white and blue ones, so we want all 5 to be from the 17 non-red marbles.
Probability = (¹⁷C₅) / (²³C₅) = 6188 / 33649 = 0.1839
The Polar Express movie is $12 and it will be on sale for $8.What is the percent of change
if the cost decreased $4?
please help
Answer:
33.333%.
Step-by-step explanation:
Take the cost changed ($4) and divide it by it's normal price ($12).
$4/$12 = .33333
Multiply that by 100 to get its percent. 33.333%
Answer:
- 33.3%
Step-by-step explanation:
You calculate percent change by dividing the change by the absolute value of the original. In this instance, it would be -4/12 which equals -0.3333. Multiply that by 100 and you get the percent.