Answer:
[tex]28-2.064\frac{10}{\sqrt{25}}=23.872[/tex]
[tex]28+2.064\frac{10}{\sqrt{25}}=32.128[/tex]
So on this case the 95% confidence interval would be given by (23.9;32.1)
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".
[tex]\bar X=28[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
s=10 represent the sample standard deviation
n=25 represent the sample size
Solution to the problem
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
In order to calculate the critical value [tex]t_{\alpha/2}[/tex] we need to find first the degrees of freedom, given by:
[tex]df=n-1=25-1=24[/tex]
Since the Confidence is 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,24)".And we see that [tex]t_{\alpha/2}=2.064[/tex]
Now we have everything in order to replace into formula (1):
[tex]28-2.064\frac{10}{\sqrt{25}}=23.872[/tex]
[tex]28+2.064\frac{10}{\sqrt{25}}=32.128[/tex]
So on this case the 95% confidence interval would be given by (23.9;32.1)
The 95% confidence interval for the average age of the boutique's customers is from 24.1 to 31.9 years, calculated using the sample mean of 28 years, a standard deviation of 10 years, and a sample size of 25.
To calculate a 95% confidence interval for the average age of all customers in the boutique, we will use the sample mean, standard deviation, and the size of the sample along with the z-score corresponding to a 95% confidence level.
The formula for a confidence interval when the population standard deviation is known is:
Confidence interval = {x} (Z {Σ}/√{n}})
In this case, we have:
Sample mean ({x}): 28 years
Standard deviation (Σ): 10 years
Sample size (n): 25
Z-score for 95% confidence: 1.96 (from z-tables)
First, we calculate the margin of error:
The margin of error = Z{Σ}/{√{n}} = 1.96 {10}/{√{25}} = 1.96 × 2 = 3.92
Then, the confidence interval is:
Lower limit = {x} - Margin of error = 28 - 3.92 = 24.08
Upper limit = {x} + Margin of error = 28 + 3.92 = 31.92
Therefore, the 95% confidence interval for the average age of the boutique's customers is from 24.1 to 31.9 years.
The function R(x)equals108 StartRoot x EndRoot gives the total revenue per year in thousands of dollars generated by a small business having x employees. Use this function to evaluate R(12)minusR(11). If the salary for the twelfth employee is $ 26 comma 000, is it a good decision to hire the twelfth employee?
Answer:
Step-by-step explanation:
We are given that [tex] R(x) = 108\sqrt[]{x}[/tex] is the revenue for having x employees.
Let us calculate the following
[tex]R(12)-R(11) = 108\sqrt[]{12}-108\sqrt[]{11} = 15.93[/tex] REcall that is amount represents the revenue that having one extra employee would have.
We have that the salary of the 12th employee would be 26000. One criteria to define if it's a good idea to hire the 12th employee is to check if the profit for having an extra employee is positive. We will take the revenue of the extra employee minus the cost and check if it is positiv. Then,
[tex](108\sqrt[]{12}-108\sqrt[]{11})\text{(revenue for 12 employees)}-26000\text{(cost for the 12th employee} =-25984<0[/tex]
Since it is a negative amount, this means that it would be more expensive to have one extra employee than the revenue it would generate. Therefore, it won't be suitable to hire the 12th employee
Jon drives a total of 47 miles each day to take his children to and from school. The children go to school 5 days a week. Jon's vehicle gets 21 miles per gallon of gas. About how many gallons of gas does Jon need to take his children to and from school each week?
Answer:
The correct answer is that Jon needs approximately 11.19 gallons of gas to take his children to and from school each week.
Step-by-step explanation:
To solve this problem, we first need to figure out how many miles Jon drives per week. To do this, we need to multiply the number of miles Jon drives per day (47 miles) by the number of days Jon drives per week (5).
47 * 5 = 235
This means that Jon drives 235 miles per week. Now, to figure out how many gallons of gas Jon uses, we need to divide the number of miles Jon drives (235) by the number of miles per gallon Jon's vehicle gets (21).
235/21 = 11.19
Therefore, the answer is that Jon needs about 11 gallons of gas to take his children to and from school each week.
Hope this helps!
If the annual coupon rate is 7 percent on a $1000 face value bond with market price equal to $ 985. Find current yield
Answer:
7.1%
Step-by-step explanation:
Current yield is the ratio of coupon payment of a bond to its current market price. It is calculated by using coupon payment and the current market value of the bond.
As per given data
Coupon rate = 7%
Face value = $1,000
Market Value = $985
Coupon Payment = $1,000 x 7% = $70
Formula for Current yield is as follow
Current Yield = Annual Coupon Payment / Current Market Price
Current Yield = $70 / $985
Current Yield = 7.11%
A.(-3,0)
B.(1,0)
C.(-4,-1)
D.(-1,-4)
draw a rectangle that is 28 units by 12 units
Answer:
Attached
Step-by-step explanation:
On a cartessian plane, we take four points as shown. Point A has coordinates as (4, 0) while point B is (32, 0). Since the y cordinates are zero, don't change, only x change. Change in x coordinates is 32-4=28 units.
Point C is (32, 12) where x has not changed when compared to point B but y changes by 12-0=12 units
Therefore, the diagram is triangle whose length is 28 units while width is 12 units.
A new manager of a small convenience store randomly samples 20 purchases from yesterday’s sales. The mean was $45.26 and the standard deviation was $20.67. We wish to test for evidence that the overall mean purchase amount is at least $40? What is the value of the t-statistic for this test (three decimal places)?
Answer:
The value of the t-statistic for this test is 1.138.
Step-by-step explanation:
We are given that a new manager of a small convenience store randomly samples 20 purchases from yesterday’s sales. The mean was $45.26 and the standard deviation was $20.67.
We wish to test for evidence that the overall mean purchase amount is at least $40
Let [tex]\mu[/tex] = overall mean purchase amount
SO, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\geq[/tex] $40 {means that the overall mean purchase amount is at least $40}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < $40 {means that the overall mean purchase amount is less than $40}
The test statistics that will be used here is One-sample t test statistics because we don't know about the population standard deviation;
T.S. = [tex]\frac{\bar X -\mu}{{\frac{s}{\sqrt{n} } } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean sale = $45.26
s = sample standard deviation = $20.67
n = sample of purchases = 20
So, test statistics = [tex]\frac{45.26-40}{{\frac{20.67}{\sqrt{20} } } }[/tex] ~ [tex]t_1_9[/tex]
= 1.138
Hence, the value of the t-statistic for this test is 1.138.
25 points!!!!!!!!!!!!!!!!!!!!!!!!!
3.5 in to fraction with 5 repeating
plz help ill rate 5 star
Answer:
32/9 or 3 5/9
Step-by-step explanation:
3.5555
3 5/9
(3×9 + 5)/9
32/9
Answer:
x = 32/9
Step-by-step explanation:
Let x = 3.55555555repeating
Multiply by 10
10x = 35.555555 repeating
Subtract the first equation
10x = 35.555555 repeating
-x = 3.55555555repeating
-------------------------------------
9x = 32
Divide each side by 9
9x/9 = 32/9
x = 32/9
The graph shows the solution for which inequalities?
Answer:
The answer is c
Step-by-step explanation:
the graph shows the equations y=3x-2 and y=1/2+3 and if y is greater than the otherside you shade above and if it's less than the otherside you shade below. y=3x-2 is sahded above the line and y=1/2+3 is shaded below the line.
Answer:
see below
Step-by-step explanation:
The line with the shallow slope has a slope of 1 unit of rise for each 2 units of run, so a slope of 1/2. It has a y-intercept of 3. The shading is below it, so you're looking for an inequality that looks like ...
y ≤ 1/2x + 3
Only one answer choice matches.
A rectangle has a height of 7 and a width of 2x^2-3 express the area of the entire rectangle
Six people, named Anna, Bob, Chandra, Darlene, Ed, and Frank, will be interviewed for a job. The interviewer will choose two at random to interview on the first day. What is the probability that Darlene is interviewed first and Bob is interviewed second? Express your answer as a fraction or a decimal, rounded to four decimal places.
Answer:
there is a 1/18th percent chance Darlene and bob will go in that order
Step-by-step explanation:
Electric charge is distributed over the disk x2 + y2 ≤ 16 so that the charge density at (x, y) is rho(x, y) = 2x + 2y + 2x2 + 2y2 (measured in coulombs per square meter). Find the total charge on the disk.
Answer:
Required total charge is [tex]256\pi[/tex] coulombs per square meter.
Step-by-step explanation:
Given electric charge is dristributed over the disk,
[tex]x^2=y^2\leq 16[/tex] so that the charge density at (x,y) is,
[tex]\rho (x,y)=2x+2y+2x^2+2y^2[/tex]
To find total charge on the disk let Q be the total charge and [tex]x=r\cos\theta,y=r\sin\theta[/tex] so that,
[tex]Q={\int\int}_Q\rho(x,y) dA[/tex] where A is the surface of disk.
[tex]=\int_{0}^{2\pi}\int_{0}^{4}(2x+2y+2x^2+2y^2)dA[/tex]
[tex]=\int_{0}^{2\pi}\int_{0}^{4}(2r\cos\theta+2r\sin\theta+2r^2 \cos^{2}\theta+2r^2\sin^2\theta)rdrd\theta[/tex]
[tex]=2\int_{0}^{2\pi}\int_{0}^{4}r^2(\cos\theta+\sin\theta)drd\theta+2\int_{0}^{2\pi}\int_{0}^{4}r^3drd\theta[/tex]
[tex]=\frac{2}{3}\int_{0}^{2\pi}(\sin\theta+\cos\theta)\Big[r^3\Big]_{0}^{4}d\theta+2\int_{0}^{2\pi}\Big[\frac{r^4}{4}\Big]d\theta[/tex]
[tex]=\frac{128}{3}\int_{0}^{2\pi}(\sin\theta+\cos\theta)d\theta+128\int_{0}^{2\pi}d\theta[/tex]
[tex]=\frac{128}{3}\Big[\sin\theta-\cos\theta\Big]_{0}^{2\pi}+128\times 2\pi[/tex]
[tex]=\frac{128}{3}\Big[\sin 2\pi-\cos 2\pi-\sin 0+\cos 0\Big]+256\pi[/tex]
[tex]=256\pi[/tex]
Hence total charge is [tex]256\pi[/tex] coulombs per square meter.
To find the total charge on a disk with a given charge density, we need to integrate the charge density over the entire area of the disk. In this case, the charge density is not constant, so we convert the cartesian coordinates to polar coordinates which simplifies the integral. The final solution is obtained by performing a double integral over r and θ.
Explanation:The student is asking for the total electric charge on a disk with a given charge density. The disk being referred to is defined by the equation x² + y² ≤ 16, i.e., a disk of radius 4 units, and the charge density at any point (x, y) on the disk is given by rho(x, y) = 2x + 2y + 2x² + 2y².
In such problems, we find the total charge by integrating the charge density over the entire area of the disk. But in this case, we first need to convert the cartesian coordinates (x, y) to polar coordinates. which simplifies the integral. In polar coordinates, the area element is r dr dθ and the charge density funciton becomes rho(r, θ) = 2r cosθ + 2r sinθ + 2r². We perform a double integral of this function over r from 0 to 4 and θ from 0 to 2π.
This is a classic example of a problem in electrostatics, particularly involving the calculation of electric charge given a non-uniform charge density.
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According to a report in USAToday, more and more parents are helping their young adult children get homes. Suppose eight persons in a random sample of 40 young adults who recently purchased a home in Kentucky received help from their parents. You have been asked to construct a 95% confidence interval for the population proportion of all young adults in Kentucky who received help from their parents. What is the margin of error for a 95% confidence interval for the population proportion?
Answer:
a) 95% confidence interval for the population proportion of all young adults in Kentucky who received help from their parents.
( 0.0761 , 0.3239)
b) Margin of error = 0.1264.
Step-by-step explanation:
Explanation:-
Given '8' persons in a random sample of 40 young adults who recently purchased a home in Kentucky received help from their parents.
sample proportion of success [tex]'p' = \frac{8}{40} = 0.2[/tex]
q = 1=p
q = 1-0.2 = 0.8
a)
95% confidence interval for the population proportion of all young adults in Kentucky who received help from their parents.
[tex](p-1.96\sqrt{\frac{pq}{n} } , p+1.96\sqrt{\frac{pq}{n} } )[/tex]
[tex](0.2-1.96\sqrt{\frac{0.2X0.8}{40} } , 0.2+1.96\sqrt{\frac{0.2X0.8}{40} } )[/tex]
(0.2 - 0.1239,0.2+0.1239)
( 0.0761 , 0.3239)
b) the margin of error for a 95% confidence interval for the population proportion.
For the 95% confidence interval ∝= 0.05 and zₐ = 1.96≅2.
[tex]Margin of error = \frac{2\sqrt{pq} }{\sqrt{n} }[/tex]
[tex]Margin of error = \frac{2\sqrt{0.2X0.8} }{\sqrt{40} }[/tex]
Margin of error for a 95% confidence interval for the population proportion.
Margin of error = 0.1264.
B. There are 7 red, 8 green, and 6 blue marbles in the bag. Kate is going to
select two marbles at random, replacing each marble after she selects it.
What is the probability, in simplest form, that she will select a green and
then a blue marble? Please show your work.
[4 points]
Answer:
Probability of event
0.34
Step-by-step explanation:
Customers at TAB are charged for the amount of salad the take. Sampling suggests that the
amount of salad taken is uniformly distributed between 5 ounces and 15 ounces. Let
Χ = Salad plate filling weight.
i. Find the probability density function of Χ
Answer:
The probability density function of X is:
[tex]f_{X}(x)=\frac{1}{15-5}=\frac{1}{10};\ 5<X<15[/tex]
Step-by-step explanation:
A continuous Uniform distribution is the probability distribution of a random outcome of an experiment that lies with certain specific bounds.
Consider that random variable X follows a continuous Uniform distribution and the value of X lies between a and b.
The probability density function of the random variable X is:
[tex]f_{X}(x)=\frac{1}{b-a};\ a<X<b,\ a<b[/tex]
Now, in this case it is provided that the amount of salad taken is uniformly distributed between 5 ounces and 15 ounces.
The random variable X is defined as:
Χ = Salad plate filling weight.
The probability density function of the salad plate filling weight is:
[tex]f_{X}(x)=\frac{1}{15-5}=\frac{1}{10};\ 5<X<15[/tex]
In mathematics at a college level, this answer explains how to find the probability density function of a uniformly distributed random variable representing the amount of salad taken by customers at TAB.
Given: Customers at TAB take salad that is uniformly distributed between 5 ounces and 15 ounces. Let X = Salad plate filling weight.
i. Find the probability density function of X: Since the salad amount is uniformly distributed, the probability density function is a horizontal line, given by f(x) = 1/(b-a), where a = 5 and b = 15, so f(x) = 1/10 for 5 ≤ x ≤ 15.
what is the value of z?
Simplify the product using the distributive property. (5h - 5)(5h - 6)
Which polynomials are prime? Check all of the boxes that apply.
x² +9
x²_9
x2 + 3x + 9
-2x² +8
Answer: x^2+9 and x^2+3x+9
Step-by-step explanation:
A polynomial is prime if it cannot be factored into polynomials of lower degree. In this case, x² +9 and x² + 3x + 9 are prime polynomials while x² -9 and -2x² +8 are not.
Explanation:In mathematics, a polynomial is said to be prime if it cannot be factored into polynomials of lower degree, at least one of which must be non-constant. To determine if a polynomial is prime, we try to factor it. In our case:
x² +9 is a prime polynomial because it is a sum of squares and cannot be factored into real polynomials of lower degree. x² -9 is not a prime polynomial because it can be factored into (x-3)(x+3). x² + 3x + 9 is a prime polynomial because it cannot be factored into real polynomials of lower degree. -2x² +8 is not a prime polynomial as it can be factored into -2(x²-4). Learn more about Prime Polynomials here:
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When faced with a problem or choice, humans can use two different strategies: "cognitive reflectivity," which results in slower responses and few mistakes, or "cognitive impulsivity," which results in quicker responses but also more mistakes. Depending on the individual, these two strategies are used differently.
A pilot experiment was conducted on 22 right-handed individuals who were administered a cognitive reflectivity-impulsivity questionnaire, while recording voxel-based morphometry (regional gray matter density) in the ventral medial prefrontal cortex.1. Based on the experimental design and the kind of data collected, which statistical test(s) should be used to determine whether there is an association between the cognitive strategy, cognitive reflectivity and the gray matter density of the ventral medial prefrontal cortex?
Select all that apply!O t-test of zero linear correlationO One-way ANOVAO z-testO correlation coefficient (r)O two sample t-test
Based on the experimental design and the data collected the statistical test that should be used is the correlation coefficient.
What are statistical tests?The statistical tests are tests that are used by researchers to determine the progress of a set process and make a quantitative decision during analysis of test results.
Example of statistical tests include the following:
t-test of zero linear correlation,One-way ANOVA,z-test,correlation coefficient, and two sample t-test.The correlation coefficient which is a type of statistical test is used to assess the strength and direction of the linear relationships between pairs of variables.
Therefore, the relationship between cognitive reflectivity and cognitive impulsivity in human data can be statistically analysed using correlation coefficient.
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Thrush us a landscape architect. For his first public project he is asked a small scale drawing of a garden to be placed in the corner of a city park. The garden is a right triangle with base 10m and height 15m.
Answer:
Therefore, on the graph;
The height = 7.5 units
And base = 5.0 units
Attached is an image for further information;
Step-by-step explanation:
Given that;
1 unit on the grid represent 2m of the garden;
Ratio = 1/2 unit/m
For the height;
height h = 15m
On the graph;
h = 15m × 1/2 unit/m
h = 7.5 units
For the base;
Base b = 10m
On the graph;
b = 10m × 1/2 unit/m
b = 5 units
Therefore, on the graph;
The height = 7.5 units
And base = 5.0 units
In 2001, there were about 62.5 thousand golden retrievers registered in the United States. In 2002, the number was 56.1 thousand. 28. Write a linear equation to predict the number of golden retrievers G that will be registered in year t.
To predict the number of golden retrievers G that will be registered in year t, use the linear equation G = -6.4t + 12868.9.
Explanation:To predict the number of golden retrievers G that will be registered in year t, we can use a linear equation. We have two data points: (2001, 62.5) and (2002, 56.1). We can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.
Step 1: Determine the slope (m) using the formula m = (y2 - y1) / (x2 - x1) = (56.1 - 62.5) / (2002 - 2001) = -6.4
Step 2: Choose one of the data points and substitute the values into the equation to solve for b. Using (2001, 62.5), we can substitute x = 2001 and y = 62.5.
62.5 = -6.4 * 2001 + b
62.5 = -12806.4 + b
b = 12868.9
Step 3: The linear equation to predict the number of golden retrievers G is G = -6.4t + 12868.9.
A very large study showed that aspirin reduced the rate of first heart attacks by 44%. A pharmaceutical company thinks they have a drug that will be more effective than aspirin, and plans to do a randomized clinical trial to test the new drug. a) What is the null hypothesis the company will use? b) What is their alternative hypothesis?c) Is this question dealing with 1 mean or 1 proportion
Answer:
a) Null hypothesis: [tex]p \leq 0.44[/tex]
b) Alternative hypothesis: [tex]p > 0.44[/tex]
c) For this case our parameter of interest is a proportion "reduced rate of first heart attacks for a new drug". for this reason the answer would be 1 proportion and we can conduct the hypothesis with a 1 z proportion test
Step-by-step explanation:
For this case the pharmaceutical company thinks they have a drug that will be more effective than aspirin and on this case that means a better rate in order to reduce the heart attacks (that represent the alternative hypothesis since that;s what they want to proof), and the complement would be the null hypothesis.
Part a
Null hypothesis: [tex]p \leq 0.44[/tex]
Part b
Alternative hypothesis: [tex]p > 0.44[/tex]
Part c
For this case our parameter of interest is a proportion "reduced rate of first heart attacks for a new drug". for this reason the answer would be 1 proportion and we can conduct the hypothesis with a 1 z proportion test
The amount of corn chips dispensed into a bag by the dispensing machine has been identified as possessing a normal distribution with a mean of μ=48.5 ounces and a standard deviation of σ=0.2 ounce. What chip amount represents the 67th percentile, p 67, for the bag weight distribution? Round to the nearest hundredth. Hint: the 67th percentile of the standard normal curve is z=0.44. Round your answer to to decimal places.
The chip amount that represents the 67th percentile is 48.588.and this can be determined by using the formula of z-score.
Given :
The amount of corn chips dispensed into a bag by the dispensing machine has been identified as possessing a normal distribution with a mean of μ = 48.5 ounces and a standard deviation of σ = 0.2 ounces.
To determine the chip amount that represents the 67th percentile, the below formula can be used:
[tex]\rm z = \dfrac{x-\mu}{\sigma}[/tex]
Now, substitute the values of known terms in the above formula:
[tex]\rm 0.44 = \dfrac{x - 48.5}{0.2}[/tex]
Cross multiply in the above equation.
[tex]\rm 0.44\times 0.2 = x - 48.5[/tex]
Now further, simplify the above equation.
0.088 = x - 48.5
x = 48.5 + 0.088
x = 48.588
So, the chip amount that represents the 67th percentile is 48.588.
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The weight that represents the 67th percentile of the corn chip bags, with a given mean of 48.5 ounces and a standard deviation of 0.2 ounce, is 48.59 ounces, calculated using the z-score provided.
To determine the amount of corn chips that represents the 67th percentile, p67, for a bag's weight distribution with a mean of μ = 48.5 ounces and a standard deviation of σ = 0.2 ounce. Given that the z-score for the 67th percentile is z = 0.44, we can use the percentile to z-score formula to find the corresponding weight.
To convert a z-score to a specific value within a normal distribution, we use the formula:
X = μ + zσ
For the 67th percentile:
X = 48.5 + (0.44 × 0.2)
X = 48.5 + 0.088
X ≈ 48.59 ounces (rounded to two decimal places)
This means that the weight that represents the 67th percentile of corn chip bag weights, to the nearest hundredth, is 48.59 ounces.
A survey reported that 5% of Americans are afraid of being alone in a house at night. If a random sample of 20 Americans is selected, what is the probability that exactly 3 people in the sample are afraid of being alone at night.
Final answer:
The probability that exactly 3 people out of a sample of 20 Americans are afraid of being alone in a house at night, given that 5% of Americans have this fear, is approximately 13.98%.
Explanation:
The question asks for the probability that exactly 3 people in a sample of 20 Americans are afraid of being alone in a house at night, given that 5% of Americans have this fear. This can be solved using the binomial probability formula, which is P(X = k) = C(n, k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successful trials, p is the probability of success on an individual trial, and C(n, k) is the number of combinations of n items taken k at a time.
Plugging in the values, we get P(X = 3) = C(20, 3) * 0.05³* 0.95¹⁷ First, calculate C(20, 3) = 20! / (3!(20-3)!) = 1140. Then calculate the probability: P(X = 3) = 1140 * 0.05³* 0.95¹⁷.
Doing the math, P(X = 3) ≈ 0.1398, or approximately 13.98%.
Final answer:
The probability that exactly 3 out of 20 Americans are afraid of being alone at night is found by using the binomial probability formula, which incorporates the number of people in the sample, the number who are afraid, and the overall chance of fear of being alone at night.
Explanation:
To find the probability that exactly 3 people out of a random sample of 20 Americans are afraid of being alone at night when it is known that 5% of Americans have this fear, we can use the binomial probability formula:
P(X = k) = C(n, k) * p^k * (1-p)^(n-k)
Where:
n is the number of trials (in this case, 20)
k is the number of successes (in this case, 3)
p is the probability of success on an individual trial (5% or 0.05)
C(n, k) is the number of combinations of n things taken k at a time
Let's calculate:
Compute C(20, 3): This is 20! / (3! * (20-3)!).
Calculate p^k, which is 0.05^3.
Calculate (1-p)^(n-k), which is (1-0.05)^(20-3).
Multiply these together to get the probability.
After performing the calculations, we determine the probability of exactly 3 out of 20 Americans being afraid of being alone at night.
A random sample of 42 college graduates who worked during their program revealed that a student spent an average 5.5 years on the job before being promoted. The sample standard deviation was 1.1 years. Using the 0.99 degree of confidence, what is the confidence interval for the population mean?
a. 5.04 and 5.96b. 5.06 and 5.94c. 2.67 and 8.33d. 4.40 and 6.60
Answer:
[tex]5.5-2.701\frac{1.1}{\sqrt{42}}=5.04[/tex]
[tex]5.5+2.701\frac{1.1}{\sqrt{42}}=5.96[/tex]
So on this case the 99% confidence interval would be given by (5.04;5.96)
And the best option would be:
a. 5.04 and 5.96
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".
[tex]\bar X=5.5[/tex] represent the sample mean for the sample
[tex]\mu[/tex] population mean (variable of interest)
s=1.1 represent the sample standard deviation
n=42 represent the sample size
Solution to the problem
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
In order to calculate the critical value [tex]t_{\alpha/2}[/tex] we need to find first the degrees of freedom, given by:
[tex]df=n-1=42-1=41[/tex]
Since the Confidence is 0.99 or 99%, the value of [tex]\alpha=0.01[/tex] and [tex]\alpha/2 =0.005[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,41)".And we see that [tex]t_{\alpha/2}=2.701[/tex]
Now we have everything in order to replace into formula (1):
[tex]5.5-2.701\frac{1.1}{\sqrt{42}}=5.04[/tex]
[tex]5.5+2.701\frac{1.1}{\sqrt{42}}=5.96[/tex]
So on this case the 99% confidence interval would be given by (5.04;5.96)
And the best option would be:
a. 5.04 and 5.96
A publisher reports that 45% of their readers own a laptop. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 370 found that 40% of the readers owned a laptop. determine the p-value of the test statistic
Answer:
[tex]z=\frac{0.40 -0.45}{\sqrt{\frac{0.45(1-0.45)}{370}}}=-1.933[/tex]
[tex]p_v =2*P(z<-1.933)=0.0532[/tex]
Step-by-step explanation:
Information given
n=370 represent the sample selected
[tex]\hat p=0.4[/tex] estimated proportion of readers owned a laptop
[tex]p_o=0.45[/tex] is the value that we want to test
z would represent the statistic
[tex]p_v[/tex] represent the p value
Creating the hypothesis
We need to conduct a hypothesis in order to test if the true proportion of readers owned a laptop is different from 0.45, the system of hypothesis are:
Null hypothesis:[tex]p=0.45[/tex]
Alternative hypothesis:[tex]p \neq 0.45[/tex]
The statistic is:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing we got:
[tex]z=\frac{0.40 -0.45}{\sqrt{\frac{0.45(1-0.45)}{370}}}=-1.933[/tex]
Calculating the p value
We have a bilateral test so then the p value would be:
[tex]p_v =2*P(z<-1.933)=0.0532[/tex]
A toy car launched into the air has a height (h feet) at any given time (t second) as h= -16t + 160t until it hits the ground. At what times is it at a height of 9 feet above the ground?
Answer:
[tex]t_{1} \approx 9.943\,s[/tex] and [tex]t_{2} \approx 0.057\,s[/tex]
Step-by-step explanation:
The following polynomial is needed to be solved:
[tex]-16\cdot t^{2} + 160\cdot t - 9 = 0[/tex]
The roots are found by means of the General Equation for Second-Order Polynomials:
[tex]t_{1} \approx 9.943\,s[/tex] and [tex]t_{2} \approx 0.057\,s[/tex]
Physically speaking, both solutions are reasonable.
Answer:
t = 0.0625
Step-by-step explanation:
Given that,
Height, h = -16t + 160t
To obtain time,t at height,h = 9feet
We substitute h = 9 into the given equation to have:
9 = - 16t + 160t
: 9 = 144t
t = 9/ 144 = 0.0625
A face of a solid is
Answer:
In solid geometry, a face is a flat (planar) surface that forms part of the boundary of a solid object; a three-dimensional solid bounded exclusively by faces is a polyhedron. (OR) A face is a 2D shape that makes up one surface of a 3D shape, an edge is where two faces meet and a vertex is the point or corner of a geometric shape.
Step-by-step explanation:
A company is developing a new high-performance wax for cross country ski racing. In order to justify the price marketing wants, the wax needs to be very fast. Specifically, the mean time to finish their standard test course should be less than 55 seconds for a former Olympic champion. To test it, the champion will ski the course 8 times. The champion's time (selected at random) 57.9, 62.9, 50.6, 50.5, 48.2, 47.2, 50.2, and 43.1 seconds to complete the test course.1. Should they market the wax? Assume the assumptions and conditions for appropriate hypothesis testing are met for the sample. Assume (Sig=0.05). what is the null and alternative hypothesis? Choose the correct answer below.A) H0: u=55 vs. HA: u>55B) H0: u>55 vs. HA: u=55C) H0: u<55 vs. HA: u=55D) H0: u=55 vs. HA: u<552.What is the value of the test statistic?
A)Yes they should market the wax because it thaws before 55 seconds
C) Null hypothesis: mean <55 vs Alternative =55
D) The value is 51.33 moments
What is Hypothesis?
When The selected samples for the champion are: 57.9, 62.9, 50.6, 50.5,48.2,47.2,50.2 and 43.1
The mean is ;
Then, Sum =57.9 + 62.9 + 50.6 + 50.5+48.2+47.2+50.2+ 43.1 =410.6
After that, Mean is = 410.6/8 =51.33= mean
Considering Significant is =0.05, therefore, applying this level will give you 51.28-51.38
if particularly, the meantime to complete their standard test course should be less than 55 seconds for a former Olympic champion, then the nullified hypothesis is correct
After that; Null hypothesis: mean <55
Hence, Alternative hypothesis: mean =55
Find more information about Hypothesis here:
https://brainly.com/question/12721831
Find the area of the triangle 10cm 15 cm
Answer:
75 cm (if b=10 and h=15)
Step-by-step explanation:
The formula to calculate the area of a triangle is bh1/2. So you must do (10)(15)1/2, 10 multiplied by 15 equals 150. And 150 multiplied by 1/2 equals 75. Hope this helped!
Consider the reduction of the rectangle
Rounded to the nearest tenth, what is the value of x?.
A.0.1 feet
B.0.6 feet
C.1.6 feet
D.2.0 feet
The question is incomplete. The complete question is as follows.
Consider the reduction of the rectangle. A large rectangle has a length of 16.8 feet and width of 2.3 feet. A smaller rectangle has a length of 4.5 feet and width of x feet. Not drawn to scale (The drawing is in the attachment). Rounded to the nearest tenth.
What is the value of x?
A. 0.1 feet
B. 0.6 feet
C. 1.6 feet
D. 2.0 feet
Answer: B. 0.6 feet
Step-by-step explanation: Two quantity are proportional if the ratio of them is constant. From the drawing and the question, we have that the two rectangles are proportional between them.
[tex]\frac{x}{2.3} = \frac{4.5}{16.8}[/tex]
[tex]x = \frac{4.5*2.3}{16.8}[/tex]
x = [tex]\frac{10.35}{16.8}[/tex]
x = 0.6
The width of the smaller rectangle is 0.6 feet.
Answer: 0.6 ft.
Step-by-step explanation: 16.8/4.5= 3.733333333 repeating. The scale factor is 3.73333333333 repeating. 2.3/3.733333333333 Repeating equals .61607142857. We can shorten it to .61, and it says rounded to the nearest tenth, so .61 rounded is 0.6.