Answer:
When conducting an analysis of variance analysis on a set of samples and the null hypothesis is rejected, we can test for the difference between treatment can be tested with the aid of a t-test. This is employed when 2 related groups are involved. Independent sample, paired sample or one-sample t-test can be conducted.
Step-by-step explanation:
A t-test is a test statistic used to make inferences that determine the differences that exist statistically between 2 related groups. It tells us if the 2 groups tested are from the same population. There are 3 types of t-test namely independent sample t-test, paired-sample t-test and one-sample t-test
Evaluate the expression.........
Answer:
9
Step-by-step explanation:
p^2 -4p +4
Let p = -1
(-1)^1 -4(-1) +4
1 +4+4
9
PLEASE HELP ITS DUE SOON ALL HELP NEEDED!!
Answer:
12345678901234567890
Answer:
[tex]95ft^2[/tex]
Step-by-step explanation:
First, note the surfaces we have. We have four triangles and one square base. Thus, we can find the surface area of each of them and them add them all up.
First, recall the area of a triangle is [tex]\frac{1}{2} bh[/tex]. We have four of them so:
[tex]4(\frac{1}{2} bh)=2bh[/tex]
The base is 5 while the height is 7. Thus, the total surface area of the four triangles are:
[tex]2(7)(5)=70 ft^2[/tex]
We have one more square base. The area of a square is [tex]b^2[/tex]. The base is 5 so the area is [tex]25ft^2[/tex].
The total surface area is 70+25=95.
simpifly (-5x2 - 3x - 7) + (-2x3 + 6x2 - 8)
Answer:
-2x³ + x² - 3x - 15
Step-by-step explanation:
Simply combine like terms together:
-5x² - 3x - 7 - 2x³ + 6x² - 8
-2x³ + (-5x² + 6x²) - 3x + (-7 - 8)
-2x³ + x² - 3x + (-7 - 8)
-2x³ + x² - 3x - 15
Answer: -2x^3+x^2-3x-15
Step-by-step explanation:
As there is only addition and subtraction here, and the two groups of parenthesis are added, you can ignore the parenthesis.
Thus, simply combine like terms to get.
-2x^3+x^2-3x-15
Hope it helps <3
4. Find the total area of the four walls of a room 10 m long, 8 m wide
and 3 m
high.
Answer:
268m²
Step-by-step explanation:
given,
l= 10m
b= 8m
h= 3m
A = ?
we know,
A = 2 (lb + bh + lh)
= 2 (10m×8m + 8m×3m + 10m×3m)
= 2 ( 80m² + 24m² + 30m² )
= 2 ( 134m² )
= 268m²
Given that f(x) =2x-3 and g(x) =1-x^2 calculate f(g(0)) and f(g(0))
Answer:
f(g(0)) = -1
g(f(0)) = -8
using substitution
help help help pls pls
Answer:
C. {2.4, 4.8, 6.3, 8.8}
Step-by-step explanation:
You only need to find the first domain value to make the appropriate answer selection.
14.1 = 7x -2.7
16.8 = 7x . . . . . . add 2.7
2.4 = x . . . . . . . . divide by 7
The appropriate choice is ...
C. {2.4, 4.8, 6.3, 8.8}
_____
In the attachment, we have applied the same "solve for x" steps to each of the range values, confirming our answer choice.
Researchers often enter a lot of data into statistical software programs. The probability of making zero to two errors per 1,000 keystrokes is 0.41, and the probability of making three to five errors per 1,000 keystrokes is 0.22. Find the probabilities (per 1,000 keystrokes) associated with each of the following.(a) at most two errors(b) at least three errors(c) at most five errors(d) more than five errors
Answer:
(a) P(0≤x≤2) = 0.41
(b) P(x≥3) = 0.59
(c) P(x≤5) = 0.63
(d) P(x≥6) = 0.37
Step-by-step explanation:
(a) The probability to have at most two errors is the probability to have 0, 1 or 2 errors or the probability of making zero to two errors. So, the probability to have at most two error is:
P(0≤x≤2) = 0.41
(b) The probability to have at least three errors is the probability to have 3 or more errors. So, it can be calculated as:
P(x≥3) = 1 - P(x≤2)
P(x≥3) = 1 - 0.41
P(x≥3) = 0.59
(c) The probability to have at most five error is the probability to have 0, 1, 2, 3, 4 or 5 errors. This can be calculated as the sum of the probability to have zero to two errors and the probability to have three to five errors as:
P(x≤5) = P(0≤x≤2) + P(3≤x≤5)
P(x≤5) = 0.41 + 0.22
P(x≤5) = 0.63
(d) The probability to have more than five errors is the probability to have 6 or more errors. So, it can be calculated as:
P(x≥6) = 1 - P(x≤5)
P(x≥6) = 1 - 0.63
P(x≥6) = 0.37
Brian can lay a slab of concrete in 6 hours, while Greg can do it in 4 hours. If Brian and Greg work together, how long will it take?
Answer:
2 2/5 hours
Step-by-step explanation:
In 6 hours Brian can lay 1 slab of concrete
dividing both side by 6
in 6/6 hours Brian can lay 1/6 slab of concrete
Thus, in 1 hour Brian can lay 1/6 slab of concrete
In 4 hours Greg can lay 1 slab of concrete
dividing both side by 4
in 4/4 hours Greg can lay 1/4 slab of concrete
Thus, in 1 hour Greg can lay 1/4 slab of concrete
Thus, total part of slab laid by both in 1 hour when they work together
1/6 + 1/4 = 4+6/(6*4) = 10/24 = 5/12
5/12 of slab of concrete is laid by both of them in 1 hour
time taken to lay 5/12 of slab = 1 hour
dividing both side by 5/12
time taken to 5/12/ 5/12 of slab = 1/5/12 hour = 12/5 hours
time taken to 1/1 of slab = 12/5 hours = 2 2/5 hours
Thus,
it takes 2 2/5 hours to lay the full slab of concrete when Brian and Greg work together,
if p+4/p-4, what is the value of p
Answer:
p = 2
Step-by-step explanation:
p + 4/p - 4
multiplying through by p,
p×p + 4/p ×p - 4×p
p² + 4 - 4p = 0
p² - 4p + 4 = 0
factorizing,
p(p - 2) -2(p - 2) =0
(p -2)(p -2) =0
p-2 =0
p=2
PLEASE ANSWER ASAP! please
Answer:
3 ÷ 0.5
Step-by-step explanation:
Since each large square is 1 whole, and theirs five out of 10 columns that are distinctivly a different orange, it'd be 3 divided by 0.5.
A rectangular solid with a square base has a volume of 5832 cubic inches. (Let x represent the length of the sides of the square base and let y represent the height.)
(a) Determine the dimensions that yield the minimum surface area.
(b) Find the minimum surface area.
Answer:
a) 18 in x 18 in x 18 in
b) [tex]S = 1944\ in2[/tex]
Step-by-step explanation:
a) Let's call 's' the side of the square base and 'h' the height of the solid.
The surface area is given by the equation:
[tex]S = 2s^2 + 4sh[/tex]
The volume of the solid is given by the equation:
[tex]V = s^2h = 5832[/tex]
From the volume equation, we have that:
[tex]h = 5832/s^2[/tex]
Then, using this value of h in the surface area equation, we have:
[tex]S = 2s^2 + 4s(5832/s^2)[/tex]
[tex]S = 2s^2 + 23328/s[/tex]
To find the side length that gives the minimum surface area, we can find where the derivative of S in relation to s is zero:
[tex]dS/ds = 4s - 23328/s^2 = 0[/tex]
[tex]4s = 23328/s^2[/tex]
[tex]4s^3 = 23328[/tex]
[tex]s^3 = 23328/4 = 5832[/tex]
[tex]s = 18\ inches[/tex]
The height of the solid is:
[tex]h = 5832/(18)^2 = 18\ inches[/tex]
b) The minimum surface area is:
[tex]S = 2(18)^2 + 4(18)(18)[/tex]
[tex]S = 1944\ in2[/tex]
Which of the following statements about the backward elimination procedure is false? a. It does not permit an independent variable to be reentered once it has been removed. b. It is a one-variable-at-a-time procedure. c. It does not guarantee that the best regression model will be found. d. It begins with the regression model found using the forward selection procedure.
Answer:
c. It does not guarantee that the best regression model will be found.
Step-by-step explanation:
Backward elimination (or deletion) procedure requires a subsequent removal of individual independent variables in an equation to derive an appropriate regression equation. It is a step-wise operation which make use of a predefined criterion for essential variables.
One of its main importance is that it ensure that the best regression model is found by removal of inconsequential variables.
Therefore, the appropriate answer to the given question is option C.
Answer:
c. It does not guarantee that the best regression model will be found.
Step-by-step explanation:
Anna spends $4.65 each weekday (20 weekdays/month) on coffee and buys a bag of coffee for $8.99 that lasts 6 months. Her monthly income is $2,350. What percent of her monthly income does she spend on coffee? 1) 0.58% 2)4.34% 3) 4.02% 4) 4.65%
Answer:
C. 4.02%
Step-by-step explanation:
Anna spends $4.65 each weekday (20 weekdays/month) on coffee and buys a bag of coffee for $8.99 that lasts 6 months. Her monthly income is $2,350. What percent of her monthly income does she spend on coffee? 1) 0.58% 2)4.34% 3) 4.02% 4) 4.65%
She spends $4.65/weekday, and there are 20 weekdays/month
In 1 month, she spends:
$4.65/weekday * 20 weekdays/month = $93/month
In 6 months, she spends 6 * $93 = $558
She buys a bag of coffee for $8.99 that lasts 6 months.
The total cost of all coffee in 6 months is:
$558 + $8.99 = $566.99
Her income in 1 month is $2,350
Her income in 6 months is 6 * $2,350 = $14,100
The percent is:
566.99/14,100 * 100% = 4.02%
Answer: 3) 4.02%
The working lifetime, in years, of a particular model of bread maker is normally distributed with mean 10 and variance 4. Calculate the 12th percentile of the working lifetime, in years.
Answer:
The 12th percentile of the working lifetime is 7.65 years.
Step-by-step explanation:
When the distribution is normal, we use 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.
In this question, we have that:
[tex]\mu = 10, \sigma = \sqrt{4} = 2[/tex]
12th percentile:
X when Z has a pvalue of 0.12. So X when Z = -1.175.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.175 = \frac{X - 10}{2}[/tex]
[tex]X - 10 = -1.175*2[/tex]
[tex]X = 7.65[/tex]
The 12th percentile of the working lifetime is 7.65 years.
What is the solution to the system of equations x+y=10 and x+2y=4 using the linear combination method?
Answer:
The solution:
X = 16 and Y = -6
Step-by-step explanation:
The equations to be solved are:
x+y = 10 ------- equation 1
x+2y = 4 ----------- equation 2
we can multiply equation 1 by -1 to make the value of x and y negative.
This will give us
-x- y = - 10 ------- equation 3
x+2y = 4 ----------- equation 2
We will now add equations 3 and 2 together so that x will cancel itself out.
this will give us
y = -10 +4 = -6
hence, we have the value of y as -6.
To get the value of x, we can put this value of y into any of the equations above. (I will use equation 1)
x - 6 = 10
from this, we have that x = 4
Therefore, we have our answer as
X = 16 and Y = -6
According to the Vivino website, suppose the mean price for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is $32.48. A New England-based lifestyle magazine wants to determine if red wines of the same quality are less expensive in Providence, and it has collected prices for 65 randomly selected red wines of similar quality from wine stores throughout Providence. The mean and standard deviation for this sample are $30.15 and $12, respectively.
(a) Develop appropriate hypotheses for a test to determine whether the sample data support the conclusion that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48. (Enter != for ≠ as needed.)
H0:
Ha:
(b) Using the sample from the 60 bottles, what is the test statistic? (Round your answer to three decimal places.)
Using the sample from the 60 bottles, what is the p-value? (Round your answer to four decimal places.)
p-value =
(c) At α = 0.05, what is your conclusion?
Do not reject H0. We can conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.
Reject H0. We can conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.
Do not reject H0. We cannot conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.
Reject H0. We cannot conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.
(d) Repeat the preceding hypothesis test using the critical value approach.
State the null and alternative hypotheses. (Enter != for ≠ as needed.)
H0:
Ha:
Find the value of the test statistic. (Round your answer to three decimal places.)
State the critical values for the rejection rule. Use
α = 0.05.
(Round your answers to three decimal places. If the test is one-tailed, enter NONE for the unused tail.)
test statistic ≤
test statistic ≥
State your conclusion.
Do not reject H0. We can conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.
Reject H0. We can conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.
Do not reject H0. We cannot conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.
Reject H0. We cannot conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.
Answer:
a) Null and alternative hypothesis
[tex]H_0: \mu=32.48\\\\H_a:\mu< 32.48[/tex]
b) Test statistic t=-1.565
P-value = 0.0612
NOTE: the sample size is n=65.
c) Do not reject H0. We cannot conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.
d) Null and alternative hypothesis
[tex]H_0: \mu=32.48\\\\H_a:\mu< 32.48[/tex]
Test statistic t=-1.565
Critical value tc=-1.669
t>tc --> Do not reject H0
Do not reject H0. We cannot conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=32.48\\\\H_a:\mu< 32.48[/tex]
The significance level is 0.05.
The sample has a size n=65.
The sample mean is M=30.15.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=12.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{12}{\sqrt{65}}=1.4884[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{30.15-32.48}{1.4884}=\dfrac{-2.33}{1.4884}=-1.565[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=65-1=64[/tex]
This test is a left-tailed test, with 64 degrees of freedom and t=-1.565, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t<-1.565)=0.0612[/tex]
As the P-value (0.0612) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
At a significance level of 0.05, there is not enough evidence to support the claim that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.
Critical value approach
At a significance level of 0.05, for a left-tailed test, with 64 degrees of freedom, the critical value is t=-1.669.
As the test statistic is greater than the critical value, it falls in the acceptance region.
The null hypothesis failed to be rejected.
Merry Soy, married, earns a weekly salary of $830 and claims one withholding allowance. By the percentage method, how much income tax will be withheld? (Use tables in the text or the Handbook.)
Answer:
Hello!
_____________________
The total amount of income tax to withhold is: 35.70 + 34.67 = 70.37$
Step-by-step explanation: Subtract this amount from the salary: 830 - 77.90 = 752.1 $. This is the amount subject to withholding.
The amount subject to withholding is between 521 and 1613$, which means that the income tax to withhold is: 35.70$ + 15% of excess over $521
Therefore, calculate the excess: 752.1 - 521 = 231.1$
Now, calculate the percentage: 231.1 × 15 ÷ 100 = 34.67$
Hope this helped you!
What is the arithmetic mean between 27 and -3
HELP PLEASE!!What method can you use to find the area of the composite figure. Check ALL that apply.
Answer:
C
Step-by-step explanation:
The reason we can use this method is because we are given a composite figure with a house shape with one triangle on top. We can use the guidance of the dotted lines to make out that a rectangle can be used to find the figure. We can see that apart from the figure, there are two congruent triangles. To find the area we would do -
First find the missing height of the smaller triangles. We would use the pythagorean theorem to find that the missing height is√5
We could do 8(4) = 32 to find the area of the rectangle.
Then, we could do 2√5/2 to find one missing triangle. We could then add the triangles to find the measures of the combined triangles as 2√5. Then, we could do 32 - 2√5 to find the area as 27.5.
Hope this helps :)
Answer:
it is A,B,D
Step-by-step explanation:
i got it right on edge
Yvette exercises 14 days out of 30 in one month. What is the ratio of the number of days she exercises to the number of days in the month? Simplify the ratio.
Answer:
7 to 15, 7:15, 7/15
Step-by-step explanation:
Ratios can be written as:
a to b
a:b
a/b
We want to find the ratio of exercise days to days in the month. She exercises 14 days out of 30 days in the month. Therefore,
a= 14
b= 30
14 to 30
14:30
14/30
The ratios can be simplified. Both numbers can be evenly divided by 2.
(14/2) to (30/2)
7 to 15
(14/2) : (30/2)
7:15
(14/2) / (30/2)
7/15
Answer:
divide both numbers by 14.. the ans is 1: 2
There is a bag with 50 popsicles inside. 5
are red, 15 are orange, 12 are blue, 8 are
yellow and 10 are purple. If you were to
grab one popsicle from the bag, what is
the probability that it is red or not orange?
P(red or not orange)
Answer: [tex]\frac{6}{25}[/tex]
In this case, we're asked to pick one of 12 blue popsicles out of a bag of 50 – from this, we can just write that the probability of picking a blue popsicle is 12/50. Simplifying this, we can divide both the numerator and denominator by 2 to get our final answer of [tex]\frac{6}{25}[/tex]
Hope this helped you!
Step-by-step explanation:
Use technology to find the P-value for the hypothesis test described below.
The claim is that for a smartphone carrier's data speeds at airports, the mean is μ = 10.00Mbps. The sample size is n = 32 and the test statistic is z = - 2.816.
What is the p-value?
(Round to three decimal places as needed.)
Answer:
P-value = 0.002
Step-by-step explanation:
The claim is that for a smartphone carrier's data speeds at airports, the mean is μ = 10.00 Mbps. This is the null hypothesis that is tested.
Then, the alternative hypothesis will represent the claim that the mean data speed is less than 10.00 Mbps.
We can write this as:
[tex]H_0: \mu=10\\\\H_a:\mu< 10[/tex]
We have a sample size n=32. As the test statistic is z, and not t, we don't need to calculate the degrees of freedom.
The test statistic is z=-2.816. This test is a left-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z<-2.816)=0.002[/tex]
What is the complete factorization of x^2+4x-45?
Answer:(x-5)(x+9)
Step-by-step explanation:
You want two numbers that can give you -45 in multiplication and two numbers that can add to 4 and that is -5 and 9.
Answer: (x - 5)(x + 9)
If you have to solve, x=5 or x= -9
Step-by-step explanation: You need two numbers that multiply to be 45.
(could be 3 × 15 or 5 × 9) . The difference between the two factors needs to be 4, the coefficient of the middle term.
9 - 5 =4, so use those. -45 has a negative sign, so one of the factors must be + and the other - Since the 4 has the + sign, the larger factor has to be + so the difference will be positive.
So (x -5)(x + 9) are your factors. You can FOIL to be sure
x × x += x² . x × 9 = 9x . -5 × x = -5x . -5 × 9 = -45 .
Combine the x terms: 9x -5x = +4x
If a baseball player has a batting average of 0.375, what is the probability that the player will get the following number of hits in the next four times at bat?
A. Exactly 2 hits(Round to 3 decimal places as needed)
B. At least 2 hits (Round to 3 decimal places as needed)
Answer:
a) [tex]P(X=2)=(4C2)(0.375)^2 (1-0.375)^{4-2}=0.330[/tex]
b) [tex]P(X\geq 2)=1-P(X< 2)=1-[P(X=0)+P(X=1)][/tex]
[tex]P(X=0)=(4C0)(0.375)^0 (1-0.375)^{4-0}=0.153[/tex]
[tex]P(X=1)=(4C1)(0.375)^1 (1-0.375)^{4-1}=0.366[/tex]
And replacing we got:
[tex]P(X\geq 2)=1-P(X< 2)=1-[0.153+0.366]=0.481[/tex]
Step-by-step explanation:
Let X the random variable of interest, on this case we now that:
[tex]X \sim Binom(n=4, p=0.375)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
Part a
[tex]P(X=2)=(4C2)(0.375)^2 (1-0.375)^{4-2}=0.330[/tex]
Part b
[tex]P(X\geq 2)=1-P(X< 2)=1-[P(X=0)+P(X=1)][/tex]
[tex]P(X=0)=(4C0)(0.375)^0 (1-0.375)^{4-0}=0.153[/tex]
[tex]P(X=1)=(4C1)(0.375)^1 (1-0.375)^{4-1}=0.366[/tex]
And replacing we got:
[tex]P(X\geq 2)=1-P(X< 2)=1-[0.153+0.366]=0.481[/tex]
The amount of pollutants that are found in waterways near large cities is normally distributed with mean 8.6 ppm and standard deviation 1.3 ppm. 38 randomly selected large cities are studied. Round all answers to 4 decimal places where possible
a. What is the distribution of X?
b. What is the distribution of a?
c. What is the probability that one randomly selected city's waterway will have more than 8.5 ppm pollutants?
d. For the 38 cities, find the probability that the average amount of pollutants is more than 8.5 ppm.
e. For part d), is the assumption that the distribution is normal necessary?
f. Find the IQR for the average of 38 cities.
Q1=__________ ppm
Q3 =_________ ppm
IQR=_________ ppm
We assume that question b is asking for the distribution of [tex] \\ \overline{x}[/tex], that is, the distribution for the average amount of pollutants.
Answer:
a. The distribution of X is a normal distribution [tex] \\ X \sim N(8.6, 1.3)[/tex].
b. The distribution for the average amount of pollutants is [tex] \\ \overline{X} \sim N(8.6, \frac{1.3}{\sqrt{38}})[/tex].
c. [tex] \\ P(z>-0.08) = 0.5319[/tex].
d. [tex] \\ P(z>-0.47) = 0.6808[/tex].
e. We do not need to assume that the distribution from we take the sample is normal. We already know that the distribution for X is normally distributed. Moreover, the distribution for [tex] \\ \overline{X}[/tex] is also normal because the sample was taken from a normal distribution.
f. [tex] \\ IQR = 0.2868[/tex] ppm. [tex] \\ Q1 = 8.4566[/tex] ppm and [tex] \\ Q3 = 8.7434[/tex] ppm.
Step-by-step explanation:
First, we have all this information from the question:
The random variable here, X, is the number of pollutants that are found in waterways near large cities.This variable is normally distributed, with parameters:[tex] \\ \mu = 8.6[/tex] ppm.[tex] \\ \sigma = 1.3[/tex] ppm.There is a sample of size, [tex] \\ n = 38[/tex] taken from this normal distribution.a. What is the distribution of X?
The distribution of X is the normal (or Gaussian) distribution. X (uppercase) is the random variable, and follows a normal distribution with [tex] \\ \mu = 8.6[/tex] ppm and [tex] \\ \sigma =1.3[/tex] ppm or [tex] \\ X \sim N(8.6, 1.3)[/tex].
b. What is the distribution of [tex] \\ \overline{x}[/tex]?
The distribution for [tex] \\ \overline{x}[/tex] is [tex] \\ N(\mu, \frac{\sigma}{\sqrt{n}})[/tex], i.e., the distribution for the sampling distribution of the means follows a normal distribution:
[tex] \\ \overline{X} \sim N(8.6, \frac{1.3}{\sqrt{38}})[/tex].
c. What is the probability that one randomly selected city's waterway will have more than 8.5 ppm pollutants?
Notice that the question is asking for the random variable X (and not [tex] \\ \overline{x}[/tex]). Then, we can use a standardized value or z-score so that we can consult the standard normal table.
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]
x = 8.5 ppm and the question is about [tex] \\ P(x>8.5)[/tex]=?
Using [1]
[tex] \\ z = \frac{8.5 - 8.6}{1.3}[/tex]
[tex] \\ z = \frac{-0.1}{1.3}[/tex]
[tex] \\ z = -0.07692 \approx -0.08[/tex] (standard normal table has entries for two decimals places for z).
For [tex] \\ z = -0.08[/tex], is [tex] \\ P(z<-0.08) = 0.46812 \approx 0.4681[/tex].
But, we are asked for [tex] \\ P(z>-0.08) \approx P(x>8.5)[/tex].
[tex] \\ P(z<-0.08) + P(z>-0.08) = 1[/tex]
[tex] \\ P(z>-0.08) = 1 - P(z<-0.08)[/tex]
[tex] \\ P(z>-0.08) = 0.5319[/tex]
Thus, "the probability that one randomly selected city's waterway will have more than 8.5 ppm pollutants" is [tex] \\ P(z>-0.08) = 0.5319[/tex].
d. For the 38 cities, find the probability that the average amount of pollutants is more than 8.5 ppm.
Or [tex] \\ P(\overline{x} > 8.5)[/tex]ppm?
This random variable follows a standardized random variable normally distributed, i.e. [tex] \\ Z \sim N(0, 1)[/tex]:
[tex] \\ Z = \frac{\overline{X} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex] [2]
[tex] \\ z = \frac{\overline{8.5} - 8.6}{\frac{1.3}{\sqrt{38}}}[/tex]
[tex] \\ z = \frac{-0.1}{0.21088}[/tex]
[tex] \\ z = \frac{-0.1}{0.21088} \approx -0.47420 \approx -0.47[/tex]
[tex] \\ P(z<-0.47) = 0.31918 \approx 0.3192[/tex]
Again, we are asked for [tex] \\ P(z>-0.47)[/tex], then
[tex] \\ P(z>-0.47) = 1 - P(z<-0.47)[/tex]
[tex] \\ P(z>-0.47) = 1 - 0.3192[/tex]
[tex] \\ P(z>-0.47) = 0.6808[/tex]
Then, the probability that the average amount of pollutants is more than 8.5 ppm for the 38 cities is [tex] \\ P(z>-0.47) = 0.6808[/tex].
e. For part d), is the assumption that the distribution is normal necessary?
For this question, we do not need to assume that the distribution from we take the sample is normal. We already know that the distribution for X is normally distributed. Moreover, the distribution for [tex] \\ \overline{X}[/tex] is also normal because the sample was taken from a normal distribution. Additionally, the sample size is large enough to show a bell-shaped distribution.
f. Find the IQR for the average of 38 cities.
We must find the first quartile (25th percentile), and the third quartile (75th percentile). For [tex]\\ P(z<0.25)[/tex], [tex] \\ z \approx -0.68[/tex], then, using [2]:
[tex] \\ -0.68 = \frac{\overline{X} - 8.6}{\frac{1.3}{\sqrt{38}}}[/tex]
[tex] \\ (-0.68 *0.21088) + 8.6 = \overline{X}[/tex]
[tex] \\ \overline{x} =8.4566[/tex]
[tex] \\ Q1 = 8.4566[/tex] ppm.
For Q3
[tex] \\ 0.68 = \frac{\overline{X} - 8.6}{\frac{1.3}{\sqrt{38}}}[/tex]
[tex] \\ (0.68 *0.21088) + 8.6 = \overline{X}[/tex]
[tex] \\ \overline{x} =8.7434[/tex]
[tex] \\ Q3 = 8.7434[/tex] ppm.
[tex] \\ IQR = Q3-Q1 = 8.7434 - 8.4566 = 0.2868[/tex] ppm
Therefore, the IQR for the average of 38 cities is [tex] \\ IQR = 0.2868[/tex] ppm. [tex] \\ Q1 = 8.4566[/tex] ppm and [tex] \\ Q3 = 8.7434[/tex] ppm.
Find the domain of the graphed function.
10
-10
10
10
O A. -45x39
B. -43x8
C. X2-4
0
D. x is all real numbers.
I got the answer but I really don’t know if it’s correct or not, please help this is due today
need help please asappppp!!!!
Answer:
40
Step-by-step explanation:
Angles in a circle add up to 360 degrees.
135 + 145 + x + x = 360
280 + 2x = 360
2x = 80
x = 40
Answer:
40
Step-by-step explanation:
The sum of the measures of the central angles of a circle is 360 deg.
145 + 135 + x + x = 360
280 + 2x = 360
2x = 80
x = 40
Solve the inequality and enter your solution as an inequality in the box below,
using "<=" for sor">=" for 2 if necessary.
-2(5x + 1) > 48
Answer here
Answer:
x < -5
Step-by-step explanation:
-2(5x + 1) > 48
Divide by -2, remembering to flip the inequality
-2/ -2(5x + 1) < 48/-2
5x +1 < -24
Subtract 1 from each side
5x+1-1 < -24-1
5x < -25
Divide by 5
5x/5 < -25/5
x < -5
Which of the following represents a coefficient from the expression given?
9x – 20 + x2
Answer:
1 or 9.
Step-by-step explanation:
A coefficient is "a numerical or constant quantity placed before and multiplying the variable in an algebraic expression (e.g. 4 in 4xy)".
So, in this case, the coefficient of 9x would be 9.
The coefficient of x^2 would be 1.
Hope this helps!
In the given quadratic expression 9x - 20 + x, 1, 9, and -20 are the coefficients.
What are coefficients in a quadratic expression?In a quadratic expression of the standard form ax² + bx + c, x is the variable and a, b, and c are the numeric coefficients.
How to solve the given question?In the question, we are asked to identify the coefficients from the given quadratic expression 9x - 20 + x².
First, we try to express the given quadratic expression, 9x - 20 + x², in the standard form of a quadratic expression, ax² + bx + c.
Therefore, 9x - 20 + x² = x² + 9x - 20.
Comparing the expression x² + 9x - 20 with the standard form of a quadratic expression ax² + bx + c, we get a = 1, b = 9, c = -20.
We know that in a quadratic expression ax² + bx + c, x is the variable and a, b, and c are the numeric coefficients.
Thus, we can say that in the given quadratic expression 9x - 20 + x², 1, 9, and -20 are the coefficients.
Learn more about quadratic expressions at
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