Answer:
0.3222 = 32.22% probability that the mean weight of the sample babies would differ from the population mean by more than 45 grams.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation(which is the square root of the variance) [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.
Central Limit Theorem
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, we have that:
[tex]\mu = 3366, \sigma = \sqrt{244036} = 494, n = 118, s = \frac{494}{\sqrt{118}} = 45.48[/tex]
Probability if differs by more than 45 grams?
Less than 3366-45 = 3321 or more than 3366+45 = 3411. Since the normal distribution is symmetric, these probabilities are equal. So we find one of them, and multiply by them.
Less than 3321.
pvalue of Z when X = 3321. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{3321 - 3366}{45.48}[/tex]
[tex]Z = -0.99[/tex]
[tex]Z = -0.99[/tex] has a pvalue of 0.1611
2*0.1611 = 0.3222
0.3222 = 32.22% probability that the mean weight of the sample babies would differ from the population mean by more than 45 grams.
"A movie data base claims that the average length of movies is 117 minutes. A researcher collected a random sample of 160 movies released during 2010–2015. The mean length of those movies is 118.44 minutes and the standard deviation is 8.82. The researcher wonders if the actual mean length of movies released during 2010-2015 is more than the data base value and wants to carry out a hypothesis test. What are the null and alternative hypothesis?"
Answer:
We need to conduct a hypothesis in order to check if the mean the actual mean length of movies released during 2010-2015 is more than the data base value (a;ternative hypothesis) ,so then the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 117[/tex]
Alternative hypothesis:[tex]\mu > 117[/tex]
Step-by-step explanation:
Data given and notation
[tex]\bar X=118.44[/tex] represent the sample mean
[tex]s=8.82[/tex] represent the sample standard deviation
[tex]n=160[/tex] sample size
[tex]\mu_o =117[/tex] represent the value that we want to test
[tex]\alpha[/tex] represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean the actual mean length of movies released during 2010-2015 is more than the data base value (a;ternative hypothesis) ,so then the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 117[/tex]
Alternative hypothesis:[tex]\mu > 117[/tex]
Which are solutions of the linear equation?
Select all that apply.
3x + y = 10
(1, 6)
(2, 4)
(3, 1)
(4, –1)
(5, –5)
The solutions of the linear equation are; (2, 4), (3, 1) and (5, –5)
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.
The given linear equation is;
3x + y = 10
For (1, 6)
3x + y = 10
y = 10 - 3x
y = 10 - 3(1)
y = 10 -3 = 7
So, this is not the solution of the linear equation.
For (2, 4)
y = 10 - 3x
y = 10 - 3(2)
y = 10 -6 = 4
So, this is the solution of the linear equation.
For (3, 1)
y = 10 - 3x
y = 10 - 3(3)
y = 10 -9 = 1
So, this is the solution of the linear equation.
For (4, –1)
y = 10 - 3x
y = 10 - 3(4)
y = 10 -12 = -2
So, this is not the solution of the linear equation.
For (5, –5)
y = 10 - 3x
y = 10 - 3(5)
y = 10 -15 = -5
So, this is the solution of the linear equation.
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The moods of U.S. Marines following a month-long training exercise conducted at cold temperature and at high altitudes were assessed. Negative moods, including fatigue and anger, increased substantially during the training and lasted up to three month after the training ended. The scores for 5 of the Marines were 14, 10, 13, 10, 11. The mean mood score was compared to population norms for college men; the population mean anger score for college men is 8.90. a) Test the null hypothesis that the population mean is 8.90 against the alternative that the population mean is greater than 8.90 at α=.05. Show all 6 steps. b) Interpret the results. What did we learn about the Marines’ negative moods?
Answer:
Step-by-step explanation:
Sample mean = (14 + 10 + 13 + 10 + 11)/5 = 11.6
Sample standard deviation,s = √(summation(x - mean)/n
Summation(x - mean) = (14 - 11.6)^2 + (10 - 11.6)^2 + (13 - 11.6)^2 + (10 - 11.6)^2 + (11 - 11.6)^2 = 13.2
s = √(13.2/5) = 1.62
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
µ = 8.9
For the alternative hypothesis,
µ > 8.9
it is a right tailed test because of >.
Since the number of samples is 5 and no population standard deviation is given, the distribution is a student's t.
Since n = 5,
Degrees of freedom, df = n - 1 = 5 - 1 = 4
t = (x - µ)/(s/√n)
Where
x = sample mean = 11.6
µ = population mean = 8.9
s = samples standard deviation = 1.62
t = (11.6 - 8.9)/(1.62/√5) = 3.73
We would determine the p value using the t test calculator. It becomes
p = 0.01
Since alpha, 0.05 > than the p value, 0.01, then we would reject the null hypothesis. Therefore, At a 5% level of significance, the sample data showed significant evidence that mean anger score of the marines is greater than that of college men.
Therefore, the marines's negative moods increased and it is higher than that of college men.
Graph the line with slope 1 passing through the point (1,1)
Answer:
start at (0,0) and go up 1, right 1, and mark a point and keep doing that
Step-by-step explanation:
Factor 16p^4 - 24p^3.
Answer:
8p^3(2p - 3) is the factor
Step-by-step explanation:
Two numbers have a sum of 23 and a difference of 9. Find the two numbers
Answer:
The numbers are 16 and 7
Step-by-step explanation:
Let the numbers be x and y
x+y = 23
x-y = 9
Add the two equations together
x+y = 23
x-y = 9
-------------------
2x = 32
Divide each side by 2
2x/2 = 32/2
x = 16
Now subtract the two equations
x+y = 23
-x +y = -9
-------------------
2y = 14
Divide by 2
2y/2 = 14/2
y = 7
Final answer:
The two numbers with a sum of 23 and a difference of 9 are 16 and 7. Solved by setting up equations for the sum and difference, then solving for the two unknowns.
Explanation:
To find the two numbers with a sum of 23 and a difference of 9, we can set up two equations based on the given information:
x + y = 23 (Equation for sum)x - y = 9 (Equation for difference)Adding the two equations together, we get:
2x = 32
Dividing both sides by 2:
x = 16
Now, substituting x back into one of the original equations, for example, x + y = 23:
16 + y = 23
y = 23 - 16
y = 7
Therefore, the two numbers are 16 and 7.
The mean weight of an adult is 6060 kilograms with a variance of 100100. If 118118 adults are randomly selected, what is the probability that the sample mean would differ from the population mean by greater than 0.80.8 kilograms? Round your answer to four decimal places.
Answer:
The probability that the sample mean would differ from the population mean by greater than 0.8 kg is P=0.3843.
Step-by-step explanation:
We have a population with mean 60 kg and a variance of 100 kg.
We take a sample of n=118 individuals and we want to calculate the probability that the sample mean will differ more than 0.8 from the population mean.
This can be calculated using the properties of the sampling distribution, and calculating the z-score taking into account the sample size.
The sampling distribution mean is equal to the population mean.
[tex]\mu_s=\mu=60[/tex]
The standard deviation of the sampling distribution is equal to:
[tex]\sigma_s=\sigma/\sqrt{n}=\sqrt{100}/\sqrt{118}=10/10.86=0.92[/tex]
We have to calculate the probability P(|Xs|>0.8). The z-scores for this can be calculated as:
[tex]z=(X-\mu_s)/\sigma_s=\pm0.8/0.92=\pm0.87[/tex]
Then, we have:
[tex]P(|X_s|>0.8)=P(|z|>0.87)=2*(P(z>0.87)=2*0.19215=0.3843[/tex]
Use Euler’s formula for exp(ix) and exp(-ix) to write cos(x) as a combination of exp(ix) and exp(-ix)
Answer = (cos(x) = (exp(ix)+exp(-ix))/2)
For real a and b, use the previous answer to find write both cos(a+b) and cos(a)cos(b) in terms of exp. Throughout the rest you will probably use exp(x+y)=exp(x)exp(y).
Answer:
[tex]cos(a+b)=\frac{e^{i(a-b)}+e^{i(-a+b)}}{2}[/tex]
Step-by-step explanation:
[tex]cos(x)=\frac{e^{ix}+e^{-ix}}{2}[/tex]
[tex]cos(a+b)[/tex]
We need to expand cos(a+b) using the cos addition formula.
[tex]cos(a+b)=cos(a)cos(b)-sin(a)sin(b)[/tex]
We know that we also need to use Euler's formula for sin, which is:
[tex]sin(x)=\frac{e^{ix}-e^{-ix}}{2}[/tex] (you can get this from a similar way of getting the first result, of simply just expanding [tex]e^{ix}=cosx+isinx[/tex] and seeing the necessary result)
We can now substitute our cos's and sin's for e's
[tex]cos(a+b)=(\frac{e^{ia}+e^{-ia}}{2})(\frac{e^{ib}+e^{-ib}}{2})-(\frac{e^{ia}-e^{-ia}}{2})(\frac{e^{ib}-e^{-ib}}{2})[/tex]
Now lets multiply out both of our terms, I'm using the exponent multiplication identity here ([tex]e^{x+y}=e^xe^y[/tex])
[tex]cos(a+b)=\frac{e^{i(a+b)} + e^{i(a-b)}+e^{i(-a+b)} + e^{i(-a-b)}}{4}-\frac{e^{i(a+b)} - e^{i(a-b)}-e^{i(-a+b)}+e^{i(-a-b)}}{4}[/tex]
Now we can subtract these two terms.
[tex]cos(a+b)=\frac{2e^{i(a-b)}+2e^{i(-a+b)}}{4}[/tex]
This is starting to look a lot tidier, let's cancel the 2
[tex]cos(a+b)=\frac{e^{i(a-b)}+e^{i(-a+b)}}{2}[/tex]
Using Euler's formula, we can write cos(x) as the average of exp(ix) and exp(-ix). Further, we demonstrated how to express cos(a+b) and cos(a)cos(b) in terms of exponential functions, utilizing the properties of Euler's formula and complex exponentials.
Using Euler's formula, exp(ix) = cos(x) + i sin(x) and exp(-ix) = cos(x) - i sin(x), we can represent cos(x) as a combination of exp(ix) and exp(-ix). By adding these two equations, we eliminate the sin(x) terms due to their opposite signs, leading us to the formula for cos(x):
cos(x) = (exp(ix) + exp(-ix)) / 2
To express cos(a+b), use the expansion:
cos(a+b) = cos(a)cos(b) - sin(a)sin(b)
Using Euler's formula, this expands to:
cos(a+b) = [exp(ia) + exp(-ia)]/2 * [exp(ib) + exp(-ib)]/2 - [exp(ia) - exp(-ia)]/2i * [exp(ib) - exp(-ib)]/2i
Similarly, to express cos(a)cos(b), we again use the representation of cos(x) in terms of exp:
cos(a)cos(b) = [exp(ia) + exp(-ia)]/2 * [exp(ib) + exp(-ib)]/2
Determine the value of so that the area under the standard normal curve a. in the right tail is Round your answer to two decimal places. b. in the left tail is Round your answer to two decimal places. c. in the left tail is Round your answer to two decimal places. d. in the right tail is Round your answer to two decimal places. Click if you would like to Show Work for this ques
Answer:
a) 2.81 b)-2.33 c) -2.88 d)3.09
Step-by-step explanation:
The complete question is:
Determine the value of z so that the area under the standard normal curve
a. in the right tail is 0.025 Round your answer to two decimal places.
b. in the left tail is 0.01 Round your answer to two decimal places.
c. in the left tail is 0.002 Round your answer to two decimal places.
d. in the right tail is 0.01 Round your answer to two decimal places.
a)P( Z> ???)= 0.0025
P(Z> ???)= 1-P(Z<???)
P(Z<???)= 1-0.0025
P(Z<??)= 0.9975
From Z distribution table,
Z = 2.81
b) P(Z<???)= 0.01
From Z distribution table
Z= -2.33
c) P(Z< ??? ) = 0.002
From Z distribution table
Z= -2.88
d) P( Z> ???)= 0.001
P(Z> ???)= 1-P(Z<???)
P(Z<???)= 1-0.001
P(Z<??)= 0.999
From Z distribution table,
Z=3.09
The value of a gold coin picturing the head of the Roman Emperor Vespasian is increasing at the rate of 5% per year. If the coin is worth $105 now, what will it be worth in 11 years?
Answer:
255.75
Step-by-step explanation:
Answer:
$179.59
Step-by-step explanation:
Step 1 Write the exponential growth function for this situation.
y = a(1 + r)t Write the formula.
= 105(1 + 0.05)t Substitute 105 for a and 0.05 for r.
= 105(1.05)t Simplify.
Step 2 Find the value in 11 years.
y = 105(1.05)t Write the formula.
= 105(1.05)11 Substitute 11 for t.
≈ 179.59 Use a calculator and round to the nearest hundredth.
Find the surface area of a triangular prism with measurements 8 cm 6 cm 5 cm and 3 cm
Answer:
86.96
Step-by-step explanation:
not sure what is height or base.
Answer:
86.96
Step-by-step explanation:
Which of these statements is best? The errors in a regression model are assumed to have an increasing mean. The regression model assumes the error terms are dependent. The errors in a regression model are assumed to have zero variance. The regression model assumes the errors are normally distributed.
Answer:
[tex] \epsilon = Y -X\beta[/tex]
And the expected value for [tex] E(\epsilon) = 0[/tex] a vector of zeros and the covariance matrix is given by:
[tex] Cov (\epsilon) = \sigma^2 I[/tex]
So we can see that the error terms not have a variance of 0. We can't assume that the errors are assumed to have an increasing mean, and we other property is that the errors are assumed independent and following a normal distribution so then the best option for this case would be:
The regression model assumes the errors are normally distributed.
Step-by-step explanation:
Assuming that we have n observations from a dependent variable Y , given by [tex] Y_1, Y_2,....,Y_n[/tex]
And for each observation of Y we have an independent variable X, given by [tex] X_1, X_2,...,X_n[/tex]
We can write a linear model on this way:
[tex] Y = X \beta +\epsilon [/tex]
Where [tex]\epsilon_{nx1}[/tex] i a matrix for the error random variables, and for this case we can find the error ter like this:
[tex] \epsilon = Y -X\beta[/tex]
And the expected value for [tex] E(\epsilon) = 0[/tex] a vector of zeros and the covariance matrix is given by:
[tex] Cov (\epsilon) = \sigma^2 I[/tex]
So we can see that the error terms not have a variance of 0. We can't assume that the errors are assumed to have an increasing mean, and we other property is that the errors are assumed independent and following a normal distribution so then the best option for this case would be:
The regression model assumes the errors are normally distributed.
Final answer:
The best statement is that the regression model assumes the errors are normally distributed. In regression analysis, it is essential that the errors are independent, normally distributed, and have constant variance, which supports the validity of the model's predictions.
Explanation:
The correct statement among the provided options is that the regression model assumes the errors are normally distributed. This is a fundamental assumption of linear regression analysis, where it's assumed that the residuals or errors of the regression model are randomly distributed about an average of zero. These error terms must be independent, normal, and have constant variance (homoscedasticity) across all levels of the independent variables.
According to the theoretical foundation of regression, it is not assumed that errors have an increasing mean, nor that they have zero variance, as some diversity in errors is expected. Additionally, the assumption that errors are indeed dependent would violate the principles of ordinary least squares (OLS) regression, making the model invalid.
Normality, independence, and equal variance are key premises in regression analysis to ensure the validity of the model's inferences. Indeterminate errors that affect the dependent variable 'y' are assumed to be normally distributed and independent of the independent variable 'x'. This maintains the integrity of the regression model.
Min's mother spent $3.96 on ground coffee that costs $0.45 per ounce. How many ounces of ground coffee did she buy?
Answer:
8.8 ounces
Step-by-step explanation:
3.96/0.45=8.8
Evaluate the expression. 23 [ 14 + 4(36 ÷ 12)]
Answer:
598
Step-by-step explanation:
Answer:
598
Step-by-step explanation:
[tex]23[14 + 4(36 \div 12)] \\ = 23[14 + 4(3)] \\ = 23[14 + 12] \\ = 23 \times 26 \\ = 598 \\ [/tex]
The Price of kiwis can be deterrent by the equation P=1.15n where p is the price and n is the number of kiwis. What is the constant of proportionality (unit rate)?
Answer:
1.15
Step-by-step explanation:
The required constant of proportionality of equation P = 1.15 n is k = 1.15.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
Given that,
The equation for the price of the kiwis is,
P = 1.15 n
Here, P, shows the price and n shows the number of kiwis.
The ratio that establishes a proportionate link between any two given values is referred to as the constant of proportionality.
Let a proportionality equation is,
y = k x,
k is the constant of proportionality here,
To find the constant of proportionality,
Compare the given equation P = 1.15 n with standard proportionality equation,
k = 1.15
The constant of proportionality is 1.15 unit.
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How many times larger is 4 x 10^8 than 2 x 10^-5
Answer:The answer is 8x10^7
Step-by-step explanationi took the thing
Owen has completed his education and is looking for a job. He received three different offers. He researched each job, and what he learned is shown in the table.
A 4-column table with 3 rows. Column 1 has entries Salary, benefits, average monthly rent at job location. Column 2 is labeled Job A with entries 46,650 dollars, 14,000 bonus and health insurance and 401 k, 850 dollars. Column 3 is labeled Job B with entries 38,750 dollars, 15,000 dollar bonus and health insurance and 401 k, 790 dollars. Column 4 is labeled Job C with entries 52,880 dollars, 8,000 dollar bonus and health insurance and 401 k, 950 dollars.
Based on the information in the table, which job should Owen take?
Job
Job A is the correct answer! :)
Based on the information in the table, Owen should take Job A with total earnings of $50,400 before tax.
What determines job acceptance?The factors that should determine if a job should be accepted or not include:
Base salaryBenefits (e.g. 401(K)Working hoursResidential /transportation costsCareer advancement.Data and Calculations:Job A Job B Job C
Salary $46,650 $38,750 $52,880
Benefits 14,000 15,000 8,000
Average monthly rent 850 790 950
Annual rent $10,200 $9,480 $11,400 ($950 x 12)
Earnings before tax $50,400 $44,270 $49,480
Thus, based on the information in the table, Owen should take Job A with total earnings of $50,400 before tax.
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Confidence interval precision: We know that narrower confidence intervals give us a more precise estimate of the true population proportion. Which of the following could we do to produce higher precision in our estimates of the population proportion? Group of answer choices We can select a higher confidence level and increase the sample size. We can select a higher confidence level and decrease the sample size. We can select a lower confidence level and increase the sample size. We can select a lower confidence level and decrease the sample size.
Answer:
We can select a lower confidence level and increase the sample size.
Step-by-step explanation:
The precision of the confidence interval depends on the margin of error ME = Zcritical * Sqrt[(p(1-p)/n]
In this Zcritical value is in the numerator. Z critical decreases as Confidence level decreases. (Zc for 99% = 2.576, Zc for 95% is 1.96, Zc for 90% = 1.645). Therefore decreasing the Confidence level decreases ME.
Also we see that sample size n is in the denominator. So the ME decreases as sample size increases.
Therefore, We can select a lower confidence level and increase the sample size.
The best option that could be used to produce higher precision in our estimates of the population proportion is;
Option C; We can select a lower confidence level and increase the sample size.
Formula for confidence interval is given as;
CI = p^ ± z√(p^(1 - p^)/n)
Where;
p^ is the sample proportion
z is the critical value at given confidence level
n is the sample size
Now, the margin of error from the CI formula is:
MOE = z√(p^(1 - p^)/n)
Now, the lesser the margin of error, the narrower the confidence interval and thus the more precise is the estimate of the population proportion.
Now, looking at the formula for MOE, two things that could change aside the proportion is;
z and n.
Now, the possible values of z are;
At CL of 99%; z = 2.576
At CL of 95%; z = 1.96
At CL of 90%; z = 1.645
We can see that the higher the confidence level, the higher the critical value and Invariably the higher the MOE.
Thus, to have a narrow CI, we need to use a lower value of CL and increase the sample size.
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The speed S of blood that is r centimeters from the center of an artery is given below, where C is a constant, R is a radius of the artery, and S is measured in centimeters per second. Suppose a drug is administered and the artery begins to dilate at a rate of dR/dt. At a constant distance r, find the rate at which s changes with respect to t for C = 1.32 times 10^5, R = 1.3 times 10^-2, and dR/dt = 1.0 times 10^-5. (Round your answer to 4 decimal places.) S = C(R^2 - r^2) dS/dt =
Answer:
dS/dt ≈ 0.0343
Step-by-step explanation:
We are given;
C = 1.32 x 10^(5)
R = 1.3 x 10^(-2)
dR/dt = 1.0 x 10^(-5)
The function is: S = C(R² - r²)
We want to find dS/dt when r is constant.
Thus, let's differentiate since we have dR/dt;
dS/dR = 2CR
So, dS = 2CR.dR
Let's accommodate dt. Thus, divide both sides by dt to obtain;
dS/dt = 2CR•dR/dt
Plugging in the relevant values to get;
dS/dt = 2(1.32 x 10^(5))x 1.3 x 10^(-2) x 1.0 x 10^(-5)
dS/dt = 3.432 x 10^(-2)
dS/dt ≈ 0.0343
Ice-cream palace has received an order for 3 gallons of ice cream the shop packages its ice cream in 1 quart containers
Suppose we conduct a hypothesis test to determine if an exercise program helps people lose weight. We measure the weight of a random sample of participants before and after they complete the exercise program. The mean number of pounds lost for the sample turns out to be 7.9 lbs. The hypotheses for the test are: H0: The program is not effective for weight loss. Ha: The program is effective for weight loss. The P-value for the test turns out to be 0.012. Which of the following is the appropriate conclusion, assuming that all conditions for inference are met and the level of significance is 0.05? (i) We reject H0---this sample does not provide significant evidence that the program is effective. (ii) We reject H0---this sample provides significant evidence that the program is effective. (iii) We fail to reject H0---this sample provides significant evidence that the program is not effective. (iv) We fail to reject H0---this sample does not provide significant evidence that the program is effective.
Answer: (ii) We reject H0---this sample provides significant evidence that the program is effective.
Step-by-step explanation:
The null hypothesis is
The program is not effective for weight loss.
The alternative hypothesis is
The program is effective for weight loss.
If the P-value for the test turns out to be 0.012, and the level of significance is 0.05, then
Alpha, 0.05 > p value, 0.012
Therefore, there is enough evidence to reject the null hypothesis. We then accept the alternative hypothesis.
The correct option is
(ii) We reject H0---this sample provides significant evidence that the program is effective.
The dot plot shows how many hours this week students in the band practiced their instruments.
A dot plot titled Hours of Band Practice going from 0 to 4. 0 has 1 dot, 1 has 2 dots, 2 has 3 dots, 3 has 4 dots, 4 has 3 dots.
How many observations were used for the dot plot?
Hope you get it right so you can get brainlest
Answer:
the answer is 13!
Step-by-step explanation:
hope this helps
Answer:
the answer is 13
Step-by-step explanation:
What is the value for x 2x+3=x-4
Answer:
x = -7
Step-by-step explanation:
2x + 3 = x - 4
→ Minus x from both sides to isolate -4
x + 3 = -4
→ Minus 3 from both sides to isolate x and henceforth find the value of x
x = -7
A big ship drops its anchor.
E represents the anchor's elevation relative to the water's surface (in meters) as a function of time t (in seconds).
E=−2.4t+75
How far does the anchor drop every 5 seconds?
The anchor drops 63 meters in the first 5 seconds.
The given function E(t) = -2.4t + 75 represents the elevation of the ship's anchor relative to the water's surface at any given time t. To find how far the anchor drops every 5 seconds, substitute t = 5 into the function:
E(5) = -2.4(5) + 75
E(5) = -12 + 75
E(5) = 63
Therefore, after 5 seconds, the anchor has dropped 63 meters relative to the water's surface. This indicates the change in elevation during this time period. The negative coefficient of t in the function implies a downward motion, and the constant term (75) represents the initial height of the anchor above the water. So, the anchor drops 63 meters in the first 5 seconds.
The amount in milligrams of a drug in the body t hours after taking a pill is given by A(t) = 25(0.85)t a. What is the initial dose given? b. What percent of the drug leaves the body each hour? c. What is the amount of drug left after 10 hours? (Write answer using function notation)
Answer:
(a)25 Milligrams
(b)15%
(c)[tex]A(10) = 25(0.85)^{10}[/tex]
Step-by-step explanation:
The amount in milligrams of a drug in the body t hours after taking a pill is given by the model:
[tex]A(t) = 25(0.85)^t[/tex]
(a)Comparing this with the exponential decay model, [tex]A(t)=A_0(\frac{1}{2})^{\frac{t}{t_{1/2}} }[/tex], the initial dose given is 25 milligrams.
(b)From the model,
[tex]A(t) = 25(0.85)^t\\A(t) = 25(1-0.15)^t[/tex]
We can also use this method:
[tex]r = a - 1 = 0.85 - 1 = -0.15=-15\%[/tex]
We can see that for every hour, 15% of the drug leaves the body.
(c)After 10 hours
When t=10
[tex]A(10) = 25(0.85)^{10}[/tex]
The amount of drug left after 10 hours is given above in function notation.
a. The initial dose given is 25 milligrams. b. 85(0.85)^t percent of the drug leaves the body each hour. c. The amount of drug left after 10 hours is 0.2147 milligrams.
Explanation:a. The initial dose given can be found by substituting t = 0 into the function A(t) = 25(0.85)^t. This gives A(0) = 25(0.85)^0 = 25(1) = 25 milligrams.
b. To find the percent of the drug that leaves the body each hour, we need to find the rate of change of A(t) with respect to time. Taking the derivative of A(t) gives dA/dt = 25(0.85)^t * ln(0.85) = 21.25(0.85)^t. This represents the rate of change of A(t) with respect to time. To find the percent, we can divide this rate by the initial dose and multiply by 100: (21.25(0.85)^t / 25) * 100 = 85(0.85)^t percent.
c. To find the amount of drug left after 10 hours, we substitute t = 10 into the function A(t) = 25(0.85)^t: A(10) = 25(0.85)^10 = 25(0.0859) = 0.2147 milligrams.
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A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:
Also SSR (X1 ∣ X2) = 36400.6326 and SSR (X2 ∣ X1) = 3297.7917
What fraction of the variability in house size is explained by income and size of family?
A. 84.79%
B. 71.89%
C. 17.56%
D. 70.69%
Answer:
Correct option: (B) 71.89%.
Step-by-step explanation:
R-squared is a statistical quantity that measures, just how near the values are to the fitted regression line. It is also known as the coefficient of determination.
The coefficient of determination R² specifies the percentage of the variance in the dependent variable (Y) that is forecasted or explained by linear regression and the forecaster variable (X, also recognized as the independent variable).
The coefficient of determination R² can be computed by the formula,
[tex]R^{2}=\frac{SSR}{SST}[/tex]
Here,
SSR = sum of squares of regression
SST = sum of squares of total
From the output attached below the value of SSR and SST are:
SSR = 37043.3236
SST = 51531.0863
Compute the value of R² as follows:
[tex]R^{2}=\frac{SSR}{SST}[/tex]
[tex]=\frac{37043.3236 }{51531.0863}[/tex]
[tex]=0.7188539\\\approx 0.7189[/tex]
Thus, the fraction of the variability in house size is explained by income and size of family is 71.89%.
The correct option is (B).
To find the fraction of the variability in house size that is explained by family income and size, we sum the two SSR values and express this as a fraction or percentage of the total variability in house size. The actual value could not be determined from the provided information as it appears to be missing.
Explanation:The question focuses on understanding the impact of family income and family size (the independent variables) on the house size (the dependent variable). The builder calculated the Sum of Squares for Regression (SSR) considering each independent variable given other independent variables constant. These calculations provide crucial insights into the contribution made by each independent variable to the variation in the dependent variable.
The total SSR (from both variables) can be calculated by summing the SSRs given: SSR(X1 ∣ X2) = 36400.6326 and SSR(X2 ∣ X1) = 3297.7917, which gives 39698.4243. This total variability is a representation of the entire variability in house size that is accounted for by both family income and family size. Express this as a fraction or percentage of total variability in house size to determine the proportion of variability explained by the two predictors.
Note: The Excel output and the options (A. 84.79%, B. 71.89%, C. 17.56%, D. 70.69%) should contain the exact proportion but in the provided information, these values are missing.
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figure out what 100 times 1000 equals?
Answer:
100,000 lol
Step-by-step explanation:
The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took these 100 customers to check out was 4.0 minutes. It is known that the standard deviation of the checkout time is one minute. The 98% confidence interval for the average checkout time of all customers is Group of answer choices 3.02 to 4.98 3.00 to 5.00 3.795 to 4.205 3.767 to 4.233
Answer:
[tex]4-2.326\frac{1}{\sqrt{100}}=3.767[/tex]
[tex]4+2.326\frac{1}{\sqrt{100}}=4.233[/tex]
So on this case the 98% confidence interval would be given by (3.767;4.233)
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=4[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
[tex]\sigma=1[/tex] represent the population standard deviation
n=100 represent the sample size
Solution to the problem
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (1)
Since the Confidence is 0.98 or 98%, the value of [tex]\alpha=0.02[/tex] and [tex]\alpha/2 =0.01[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.01,0,1)".And we see that [tex]z_{\alpha/2}=2.326[/tex]
Now we have everything in order to replace into formula (1):
[tex]4-2.326\frac{1}{\sqrt{100}}=3.767[/tex]
[tex]4+2.326\frac{1}{\sqrt{100}}=4.233[/tex]
So on this case the 98% confidence interval would be given by (3.767;4.233)
Use StatKey or other technology to generate a bootstrap distribution of sample proportions and find the standard error for that distribution. Compare the result to the standard error given by the Central Limit Theorem, using the sample proportion as an estimate of the population proportion p.
Proportion of peanuts in mixed nuts, with n=94 and P =0.52
Round your answer for the bootstrap SE to two decimal places, and your answer for the formula SE to three decimal places.
Answer:
0.0515
Step-by-step explanation:
By the central limit theorem
when n increase distribution when data follows normal
Standard Error, SE of P is
[tex]SE = \sqrt{\frac{p(1-p)}{n} }[/tex]
Bootstrap Standard Error = [tex]\sqrt{\frac{p(1-p)}{n} }[/tex]
where n = 94 and p = 0.52
hence,
SE of Bootstrap = [tex]\sqrt{\frac{0.52(1-0.52)}{94} }[/tex]
[tex]=\sqrt{\frac{0.2496}{94} }\\\\=0.0515[/tex]
SE and the SE of Bootstrap are the same
Consider a hypothesis test to decide whether the mean annual consumption of beer in the nation's capital is less than the national mean. Answer the following questions.
1. "The mean annual consumption of beer in the nation's captial is less than the national mean and the result of the hypothesis test does not lead to the conclusion that the mean annual consumption of beer in the nation's capital is less than the national mean" is a:________
a. Correct decision
b. Type II error
c. Type I error
2. "The mean annual consumption of beer in the nation's captial is less than the national mean and the result of the sampling leads to the conclusion that the mean annul consumption of beer in the nation's capital is less than the national mean" is a:_________
a. Correct decision
b. Type II error
c. Type I error
3. "The mean annual consumption of beer in the nation's captial is less than the national mean but the result of the sampling does not lead to the conclusion that the mean annual consumption of beer in the nation's capital is less than the national mean" is a:________
4. Correct decision
b. Type II error
c. Type I error
d. "The mean annual consumption of beer in the nation's captial is not less than the national mean and the result of the sampling does not lead to the conclusion that the mean annual consumption of beer in the nation's capital is less than the national mean" is a:________
a. Correct decision
b. Type II error
c. Type I error
Answer:
Step-by-step explanation:
Type I error occurs when the null hypothesis is rejected even when it is true.
Type II error occurs when the null hypothesis is not rejected even when it is false.
The null hypothesis is
The mean annual consumption = the national mean
The alternative hypothesis is
The mean annual consumption < the national mean
1) it is a type II error because the null hypothesis was not rejected even when it is false
2) it is a correct decision because the decision corresponds to the outcome
3) it is also a type II error
d) it is a correct decision because the null hypothesis is accepted when it is true
By interpreting the various scenarios related to hypothesis testing, it is determined that scenarios 1 and 3 represent Type II errors, while scenarios 2 and 4 represent correct decisions. This shows an understanding of statistical hypothesis tests.
Explanation:This problem falls within the discipline of statistical hypothesis testing, a method used to make statistical decisions using data. In the context of this problem, the null hypothesis states that the mean annual consumption of beer in the nation's capital is not less than the national mean.
'The mean annual consumption of beer in the nation's capital is less than the national mean and the result of the hypothesis test does not lead to the conclusion that the mean annual consumption of beer in the nation's capital is less than the national mean' is a Type II error. This is because the reality is that the consumption in the nation's capital is indeed less, but the test results failed to conclude this.'The mean annual consumption of beer in the nation's capital is less than the national mean and the result of the sampling leads to the conclusion that the mean annul consumption of beer in the nation's capital is less than the national mean' is a correct decision. This is because the reality and the test conclusion are in agreement.'The mean annual consumption of beer in the nation's capital is less than the national mean but the result of the sampling does not lead to the conclusion that the mean annual consumption of beer in the nation's capital is less than the national mean' is a Type II error. Even though in reality the consumption in the nation's capital is less, the test results failed to detect it.'The mean annual consumption of beer in the nation's capital is not less than the national mean and the result of the sampling does not lead to the conclusion that the mean annual consumption of beer in the nation's capital is less than the national mean' is a correct decision. This is because both reality and test results agree that the nation's capital's consumption is not below the national mean.Learn more about statistical hypothesis testing here:https://brainly.com/question/34698067
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