Answer:
a) 0.5.
b) 0.8413
c) 0.8413
d) 0.6826
e) 0.9332
f) 1
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 6, \sigma = 0.2[/tex]
(a) P(x > 6) =
This is 1 subtracted by the pvalue of Z when X = 6. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{6-6}{0.2}[/tex]
[tex]Z = 0[/tex]
[tex]Z = 0[/tex] has a pvalue of 0.5.
1 - 0.5 = 0.5.
(b) P(x < 6.2)=
This is the pvalue of Z when X = 6.2. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{6.2-6}{0.2}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a pvalue of 0.8413
(c) P(x ≤ 6.2) =
In the normal distribution, the probability of an exact value, for example, P(X = 6.2), is always zero, which means that P(x ≤ 6.2) = P(x < 6.2) = 0.8413.
(d) P(5.8 < x < 6.2) =
This is the pvalue of Z when X = 6.2 subtracted by the pvalue of Z when X 5.8.
X = 6.2
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{6.2-6}{0.2}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a pvalue of 0.8413
X = 5.8
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{5.8-6}{0.2}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a pvalue of 0.1587
0.8413 - 0.1587 = 0.6826
(e) P(x > 5.7) =
This is 1 subtracted by the pvalue of Z when X = 5.7.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{5.8-6}{0.2}[/tex]
[tex]Z = -1.5[/tex]
[tex]Z = -1.5[/tex] has a pvalue of 0.0668
1 - 0.0668 = 0.9332
(f) P(x > 5) =
This is 1 subtracted by the pvalue of Z when X = 5.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{5-6}{0.2}[/tex]
[tex]Z = -5[/tex]
[tex]Z = -5[/tex] has a pvalue of 0.
1 - 0 = 1
Summary of probabilities
[tex](a)\ P(x > 6) = 0.5\\(b)\ P(x < 6.2) = 0.8413\\(c)\ P(x \leq 6.2) = 0.8413\\(d)\ P(5.8 < x < 6.2) = 0.6826\\(e)\ P(x > 5.7) = 0.9332\\(f)\ P(x > 5) \approx 1\\[/tex]
(a) [tex]\(P(x > 6)\)\\[/tex]
1. Calculate the z-score for [tex]\(x = 6\)[/tex] :
[tex]\[ z = \frac{6 - 6}{0.2} = \frac{0}{0.2} = 0 \][/tex]2. Find [tex]\(P(Z > 0)\)[/tex] :
Since the standard normal distribution is symmetric, [tex]\(P(Z > 0) = 0.5\)[/tex]So, [tex]\(P(x > 6) = 0.5\)[/tex](b) [tex]\(P(x < 6.2)\)[/tex]
1. Calculate the z-score for [tex]\(x = 6.2\)[/tex] :
[tex]\[ z = \frac{6.2 - 6}{0.2} = \frac{0.2}{0.2} = 1 \][/tex]2. Find [tex]\(P(Z < 1)\)[/tex]:
Using the Z-table, [tex]\(P(Z < 1) = 0.8413\)[/tex]So, [tex]\(P(x < 6.2) = 0.8413\)[/tex](c) [tex]\(P(x \leq 6.2)\)[/tex]
For continuous distributions, [tex]\(P(x \leq 6.2) = P(x < 6.2)\)[/tex]So, [tex]\(P(x \leq 6.2) = 0.8413\)[/tex](d) [tex]\(P(5.8 < x < 6.2)\)[/tex]
1. Calculate the [tex]\(z\)[/tex]-score for [tex]\(x = 5.8\):[/tex]
[tex]\[ z = \frac{5.8 - 6}{0.2} = \frac{-0.2}{0.2} = -1 \][/tex]2. Calculate the [tex]\(z\)[/tex]-score for [tex]\(x = 6.2\):[/tex]
[tex]\[ z = \frac{6.2 - 6}{0.2} = \frac{0.2}{0.2} = 1 \][/tex]3. Find [tex]\(P(Z < 1)\)[/tex] and [tex]\(P(Z < -1)\):[/tex]
[tex]\[ P(Z < 1) = 0.8413 \][/tex][tex]\[ P(Z < -1) = 0.1587 \][/tex]4. Calculate [tex]\(P(-1 < Z < 1)\):[/tex]
[tex]\[ P(-1 < Z < 1) = P(Z < 1) - P(Z < -1) = 0.8413 - 0.1587 = 0.6826 \][/tex]So, [tex]\(P(5.8 < x < 6.2) = 0.6826\)[/tex](e) [tex]\(P(x > 5.7)\)[/tex]
1. Calculate the [tex]\(z\)[/tex]-score for [tex]\(x = 5.7\):[/tex]
[tex]\[ z = \frac{5.7 - 6}{0.2} = \frac{-0.3}{0.2} = -1.5 \][/tex]2. Find [tex]\(P(Z > -1.5)\):[/tex]
Using the Z-table, [tex]\(P(Z < -1.5) = 0.0668\)[/tex]Thus, [tex]\(P(Z > -1.5) = 1 - 0.0668 = 0.9332\)[/tex]So, [tex]\(P(x > 5.7) = 0.9332\)[/tex](f) [tex]\(P(x > 5)\)[/tex]
1. Calculate the [tex]\(z\)[/tex]-score for [tex]\(x = 5\):[/tex]
[tex]\[ z = \frac{5 - 6}{0.2} = \frac{-1}{0.2} = -5 \][/tex]2. Find [tex]\(P(Z > -5)\):[/tex]
Since [tex]\(z = -5\)[/tex] is far in the tail of the standard normal distribution, [tex]\(P(Z < -5)\)[/tex] is almost 0.Thus, [tex]\(P(Z > -5) \approx 1\)[/tex]So, [tex]\(P(x > 5) \approx 1\)[/tex]The range of Fx) = 7*4^x is all positive real numbers.
A. True
B. False
Answer:
The answer is A. True
Step-by-step explanation:
The range of Fx) = 7*4^x is all positive real numbers.
hope this helps : )
what is the difference between distrust and distake .
Answer:
The difference between mistrust and distrust comes down to nuances in meaning. Distrust is a withholding of trust based on evidence or informed opinion. Many people distrust salespeople working on commission, for instance, knowing that these salespeople personally benefit from their purchases.
Step-by-step explanation:
T(t)T, models the daily high temperature (in Celsius) in Santiago, Chile, t days after the hottest day of the year. Here, t is entered in radians.
T(t)=7.5cos(2π/365t)+21.5
What is the second time after the hottest day of the year that the daily high temperature is 20 degrees celsius?
Round your final answer to the nearest whole day.
Answer:
the answer is 262 days
Step-by-step explanation:
To find the second time after the hottest day of the year that the daily high temperature is 20 degrees Celsius, you need to solve the equation T(t) = 20. This involves finding the inverse cosine of a specific value, setting up an equation, and adding one year to the solution. After performing these steps, you can find the value of t that corresponds to the second time.
Explanation:To find the second time after the hottest day of the year that the daily high temperature is 20 degrees Celsius, we need to solve the equation T(t) = 20. We can rewrite this equation as 7.5cos(2π/365t) + 21.5 = 20. Subtracting 21.5 from both sides gives us 7.5cos(2π/365t) = -1.5. Dividing both sides by 7.5 and simplifying further, we have cos(2π/365t) = -0.2. To find the second time, we need to find the value of t that satisfies this equation.
To find the value of t, we need to use the inverse cosine function (also known as arccosine). The inverse cosine function (cos^(-1)) gives us the angle whose cosine is a specific value. In this case, we want to find t such that cos(2π/365t) = -0.2. We can use a calculator or math software to find the inverse cosine of -0.2. Let's assume the inverse cosine of -0.2 is x.
Now we can set up an equation: 2π/365t = x. Solving for t, we get t = (365x)/(2π). However, we need to find the second time after the hottest day, so we need to find the value of t that satisfies the equation after adding one year (365 days) to the original value. Therefore, the second time after the hottest day of the year that the daily high temperature is 20 degrees Celsius is t = (365x)/(2π) + 365.
Underwood Grocery Store had seven bunches of bananas, and each bunch had six bananas. A customer buys four bananas. Complete and solve the number sentence below to find how many bananas the grocery store has left.
Answer:
38 bananas
Step-by-step explanation:
6(7)=42 bananas 42-4=38 bananas
A red die and a blue die are thrown. Both dice are loaded (that is, not all sides are equally likely). Rolling a 1 with the red die is twice as likely as rolling each of the other five numbers and rolling a 3 with the blue die is twice as likely as rolling each of the other five numbers. a. (2.5 pt.) What is the probability of each outcome of the red die
Answer:
P(1) = 0.2857
P(2) = 0.1428
P(3) = 0.1428
P(4) = 0.1428
P(5) = 0.1428
P(6) = 0.1428
Step-by-step explanation:
From the question, we know that Rolling a 1 with the red die is twice as likely as rolling each of the other five numbers, so we can write the following equation:
P(1) = 2X
Where X is the probability of rolling each of the other five numbers or:
P(2) = P(3) = P(4) = P(5) = P(6) = X
Additionally, the sum of all the probabilities is 1, so:
P(1) + P(2) + P(3) + P(4) + P(5) + P(6) = 1
Now, we can replace P(1) by 2X and P(2), P(3), P(4), P(5) and P(6) by X, as:
P(1) + P(2) + P(3) + P(4) + P(5) + P(6) = 1
2X + X + X + X + X + X = 1
Finally, solving for X, we get:
7X = 1
X = 1/7
X = 0.1428
So, the probability of rolling a 1 is equal to:
P(1) = 2X = 2*(0.1428) = 0.2857
And the probability of rolling each of the other five numbers is:
P(2) = P(3) = P(4) = P(5) = P(6) = X
P(2) = P(3) = P(4) = P(5) = P(6) = 0.1428
Use the interactive to graph the line with a y-intercept of –2 and slope of –1/3.
What is the x-intercept of the line?
Answer:
The x-intercept is -6.
Step-by-step explanation:
You could use a graphing calculator, which would make it so much easier to find, but under the circumstances you aren't allowed to do so, you should:
1) Start from the y-intercept. In your case, it is -2. Since the y-intercept is negative, you want to apply the slope in a certain way.
The line will remain the same if your slope is -1/3 or if it is 1/-3. In your case, since your y-intercept is -2, you want to apply the slope 1/-3.
2) Move the point (0,-2) up 1, then left 3. This will get you the point (-3,-1). Your final answer should be in the format (x,0).
3) Now, move the point (-3,-1) up 1, then left 3. This will result in your point being (-6,0). Notice how the y-value is 0, so this is your final answer.
Keep in mind that this technique will not always be so easy to use. This particular problem is fine, though.
Of the students that took a survey about after school activities,33 1/3 % said they watch television, 1/2 said they go to sports practice and the remaining said they do homework. What fraction represents the students that go homework.
Answer:
The fraction that represents the proportion of students that go make their homework is 1/6
Step-by-step explanation:
The sum of the percentage of students is 100% = 1.
In this problem, we have that:
1/3 said they watch television
1/2 said they go to sports practice
x said they do homework.
This is a sum of fractions, and the lesser common multiple of 3 and 2 is 6.
So
[tex]\frac{1}{3} + \frac{1}{2} + x = 1[/tex]
[tex]\frac{2 + 3 + 6x}{6} = 1[/tex]
[tex]5 + 6x = 6[/tex]
[tex]6x = 1[/tex]
[tex]x = \frac{1}{6}[/tex]
The fraction that represents the proportion of students that go make their homework is 1/6
Find the measure of the supplement of the angle.Find the supplement of 7°.
Answer:
173
Step-by-step explanation:
Same thing as last time, just instead of 90, it's 180.
Need help on this question.
The Rivera family is taking a cruise that costs $3,082.24 for a family of four. How much does it cost per person?
Please answer this correctly correctly
Answer:
Step-by-step explanation:
+ You click on -15 for a point.
+ Then you move the mouse to the left.
+ Because x<-15, that means you do not take -15, you click on the -15 one more.
That is all.
Hope you understand.
Answer:
1.) You click on -15 for a point.
2.) Then you move the mouse to the left.
3.) Because x<-15, that means you do not take -15, you click on the -15 one more.
A man claims to have extrasensory perception (ESP). As a test, a fair coin is flipped 20 times, and the man is asked to predict the outcome in advance. He gets 17 out of 20 correct. What is the probability that he would have done at least this well if he had no ESP? Hint: If he has no ESP, then he's just randomly guessing, right? If he is randomly guessing, what should you use as p, the chance of success for each individual trial? Probability of doing at least this well =
Answer:
[tex]P(x\geq 17)=0.00128[/tex]
Step-by-step explanation:
The probability that the man gets x out of 20 correct follows a Binomial distribution, so the probability is calculated as:
[tex]P(x)=\frac{n!}{x!(n-x)!}*p^{x}*(1-p)^{n-x}[/tex]
Where n is the number of identical experiments and p is the probability of success. In this case n is 20.
Additionally, if he has no ESP the probability that he predict correctly is 0.5, because he is only guessing.
Then, the probability that he gets x out of 20 correct is equal to:
[tex]P(x)=\frac{20!}{x!(20-x)!}*0.5^{x}*(1-0.5)^{20-x}[/tex]
Therefore the probability that he would have done at least 17 out of 20 well if he had no ESP is:
[tex]P(x\geq 17)=P(17)+P(18)+P(19)+P(20)\\[/tex]
Where:
[tex]P(17)=\frac{20!}{17!(20-17)!}*0.5^{17}*(1-0.5)^{20-17}=0.00108719\\P(18)=\frac{20!}{18!(20-18)!}*0.5^{18}*(1-0.5)^{20-18}=0.00018119\\P(19)=\frac{20!}{19!(20-19)!}*0.5^{19}*(1-0.5)^{20-19}=0.00001907\\P(20)=\frac{20!}{20!(20-20)!}*0.5^{20}*(1-0.5)^{20-20}=0.00000095[/tex]
So, [tex]P(x\geq 17)[/tex] is equal to:
[tex]P(x\geq 17)=0.00108719+0.00018119+0.00001907+0.00000095\\P(x\geq 17)=0.00128[/tex]
The probability that he would have done at least 17 out of 20 if he had no ESP is 0.00128 and this can be determined by using the binomial distribution formula.
Given :
A man claims to have extrasensory perception (ESP). As a test, a fair coin is flipped 20 times, and the man is asked to predict the outcome in advance. He gets 17 out of 20 correct.
The formula of the binomial distribution is given by:
[tex]\rm P(x)=\dfrac{n!}{x!(n-x)!}\times p^x \times (1-p)^{n-x}[/tex]
Now, put all the known terms in the above formula.
[tex]\rm P(x)=\dfrac{20!}{x!(20-x)!}\times 0.5^x \times (1-05)^{20-x}[/tex]
Now, the probability that he would have done at least 17 out of 20 if he had no ESP:
[tex]\rm P(x\geq 17) = P(17)+P(18)+P(19)+P(20)[/tex]
where:
[tex]\rm P(17)=\dfrac{20!}{(20-17!)}\times 0.5^{17}\times 0.5^{20-17}=0.00108719[/tex]
[tex]\rm P(18)=\dfrac{20!}{(20-18!)}\times 0.5^{18}\times 0.5^{20-18}=0.00018119[/tex]
[tex]\rm P(19)=\dfrac{20!}{(20-19!)}\times 0.5^{19}\times 0.5^{20-19}=0.00001907[/tex]
[tex]\rm P(20)=\dfrac{20!}{(20-20!)}\times 0.5^{20}\times 0.5^{20-20}=0.00000095[/tex]
So, the value of P(x [tex]\geq[/tex] 17) is:
[tex]\rm P(x\geq 17)= 0.00108719+0.00018119+0.00001907+0.00000095[/tex]
[tex]\rm P(x\geq 17)= 0.00128[/tex]
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Evaluate the following integral in spherical coordinates. ModifyingBelow Integral from nothing to nothing Integral from nothing to nothing Integral from nothing to nothing With Upper D (x squared plus y squared plus z squared )Superscript 3 divided by 2 Baseline font size decreased by 4 dV; D is the unit ball centered at the origin Set up the triple integral using spherical coordinates that should be used to evaluate the given integral as efficiently as possible. Use increasing limits of integration.
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached image below for the full explanation to the above question.
The final expression for the triple integral in spherical coordinates is:
[tex]\int\limits^{2\pi}_0\int\limits^{\pi /2}_0 \int\limits^1_0[/tex]ρ⁴ sin(φ) dρ dφ dθ
To evaluate the given integral efficiently in spherical coordinates, we'll set up the triple integral over the unit ball centered at the origin. The integral represents the volume element for a sphere, which we can express in spherical coordinates as follows:
∭D (x² + y² + z²)^(3/2) dV
In spherical coordinates, the volume element dV is given by:
dV = ρ² sin(φ) dρ dφ dθ
Here, ρ represents the radial distance from the origin, φ represents the polar angle (measured from the positive z-axis), and θ represents the azimuthal angle (measured from the positive x-axis in the xy-plane).
The limits of integration for the triple integral in spherical coordinates can be set as follows:
ρ: 0 to 1 (since D is the unit ball, ρ ranges from 0 to the radius of the sphere, which is 1)
φ: 0 to π/2 (since we only need to consider the upper half of the sphere)
θ: 0 to 2π (covering a full revolution around the z-axis)
Now, we can express the integral using these limits and the volume element:
∭D (x² + y² + z²)[tex]^{(3/2)[/tex] dV
= ∫[0 to 2π] ∫[0 to π/2] ∫[0 to 1] (ρ²)[tex]^{(3/2)[/tex] (ρ² sin(φ)) dρ dφ dθ
Simplifying the integrand:
(ρ²)[tex]^{(3/2)[/tex] (ρ² sin(φ)) = ρ³ ρ sin(φ) = ρ⁴ sin(φ)
Therefore, the final expression for the triple integral in spherical coordinates is:
[tex]\int\limits^{2\pi}_0\int\limits^{\pi /2}_0 \int\limits^1_0[/tex]ρ⁴ sin(φ) dρ dφ dθ
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Which answer is the largest? * 10 points -16 • 8 = -16 ÷ 8 = -16 + 8 = -16 - 8 =
Answer:
The largest value is -2 from -16/ 8
The largest absolute value is -108 from -16*8
Step-by-step explanation:
Are you asking for the greatest value?
The largest number?
-16 * 8 = - 108
-16 / 8 = -2
-16 + 8 = -8
-16 - 8 = -24
The largest value is -2 from -16/ 8
The largest absolute value is -108 from -16*8
I need help with #12 please!
Answer:
125/512 in³125 smaller cubesStep-by-step explanation:
The volume of a cube is the cube of the edge dimension. Here, that dimension is 5/8 in, so the volume is ...
V = s³ = (5/8 in)³ = 125/512 in³ . . . volume of the cube
The volume of a cube 1/8 inch on a side is ...
V = (1/8 in)³ = 1/512 in³
Clearly, a volume that is 125/512 in³ will require 125 of the cubes of size 1/512 in³ to fill it.
125 of the smaller cubes will fit inside.
_____
Alternate solution
You can also determine the number of smaller cubes by considering it takes 5 of them in each direction to make 5/8 inch. Then the volume is 5³ = 125 of the smaller cubes.
Gwen, a friend of Mary from the previous question, is also practicing free throws. However, she is trying to score 3 points in a single set. She will keep shooting sets until she has three successful shots in a single set. Gwen is more confident in her abilities, and believes that she can successfully make any single shot with a probability of 0.8.
Give your answer as a decimal to 4 decimal places.
a) Given the information above, how many sets does Gwen expect to make?
b)b) Given the information above, what is the variance for the number of sets Gwen will make?
c) Given the information above, how many shots does Gwen expect to make?
Answer:
a. Gwen expect to make 3.75 sets
b. The variance for the number of sets Gwen will make is 0.9375
c. Gwen expect to make 2 shots
Step-by-step explanation:
a. According to the given data we have the following:
Here this follows negative binomial distribution with parameter r =3 and p=0.8
To calculate how many sets does Gwen expect to make we have to calculate the following formula:
expected number of sets =r/p
expected number of sets =3/0.8=3.75
Gwen expect to make 3.75 sets.
b. In order to calculate the variance for the number of sets Gwen will make we have to use the following formula:
variance for the number of sets=σ∧2=r(1-p)/p∧2
variance for the number of sets=3*(1-0.8)/0.8^2
variance for the number of sets=0.9375
The variance for the number of sets Gwen will make is 0.9375
c. To calculate how many shots does Gwen expect to make, we have to calculate first the probability she shoots all the three in the set as follows:
probability she shoots all the three in the set=0.8∧3=0.512
if E(X)=1/p, therefore, 1/p=1/0.512=1.95
Gwen expect to make 2 shots
a scatter plot has a negative, linear correlation. which statement is true about the relationship between the x-and y-values
Answer: as the x values increase the y values decrease
Step-by-step explanation:
Took the teat
PLEASE HELP!! Find the sixth term of the sequence 14,9,4,..
Answer:
39
Step-by-step explanation:
We notice this is an arithmetic sequence.
14, 9, 4.
common difference = d = 14 - 9 = 5
first term a_1 = 14
Find 6th term a_6
a_n = (n -1)*d + a_1
a_6 = (6 -1)*5 + 14
a_6 = 5*5 + 14 = 25 + 14 = 39
You are thinking of employing a t procedure to test hypotheses about the mean of a population using a significance level of 0.05. You suspect the distribution of the population is not Normal and may be moderately skewed. Which of the following statements is correct?A) You may use the t procedure, but you should probably claim the significance level is only 0.10.B) You may use the t procedure, provided your sample size is large, say, at least 30.C) You should not use the t procedure because the population does not have a Normal distribution.D) You may not use the t procedure because t procedures are robust to non-Normality for confidence intervals but not for tests of hypotheses.
Answer: B. You may use the t procedure, provided your sample size is large, say, at least 30.
Step-by-step explanation: To use a T test hypothesis, the following steps is considered;
1. Add the test hypothesis when using a T test module in the experiment
2. Add the date set that contains the columns that is to be analyzed
3. Decide which kind of T test is appropriated for the data
4. If single sample is been used, the adequate parameters should be used.
The correct statement in this case is "You may use the t procedure, provided your sample size is large, say, at least 30."
One True Love? A survey that asked whether people agree or disagree with the statement ‘‘There is only one true love for each person." has been conducted. The result is that 735 of the 2625 respondents agreed, 1812 disagreed, and 78 answered ‘‘don’t know." (a) Find a 99% confidence interval for the proportion of people who disagree with the statement. Round your answers to three decimal places. The 99% confidence interval is
Answer:
99% confidence interval for the proportion of people who disagree with the statement is [0.667 , 0.713].
Step-by-step explanation:
We are given that a survey that asked whether people agree or disagree with the statement ‘‘There is only one true love for each person." has been conducted. The result is that 735 of the 2625 respondents agreed, 1812 disagreed, and 78 answered ‘‘don’t know."
Firstly, the pivotal quantity for 99% confidence interval for the population proportion is given by;
P.Q. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of people who disagree with the statement = [tex]\frac{1812}{2625}[/tex] = 0.69
n = sample of respondents = 2625
p = population proportion of people who disagree with statement
Here for constructing 99% confidence interval we have used One-sample z proportion statistics.
So, 99% confidence interval for the population proportion, p is ;
P(-2.58 < N(0,1) < 2.58) = 0.99 {As the critical value of z at 0.5% level
of significance are -2.58 & 2.58}
P(-2.58 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 2.58) = 0.99
P( [tex]-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]{\hat p-p}[/tex] < [tex]2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.99
P( [tex]\hat p-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.99
99% confidence interval for p = [ [tex]\hat p-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] , [tex]\hat p+2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ]
= [ [tex]0.69-2.58 \times {\sqrt{\frac{0.69(1-0.69)}{2625} } }[/tex] , [tex]0.69+2.58 \times {\sqrt{\frac{0.69(1-0.69)}{2625} } }[/tex] ]
= [0.667 , 0.713]
Therefore, 99% confidence interval for the proportion of people who disagree with the statement is [0.667 , 0.713].
PLEASEE HELPPP MEEEE
solve for x
ANSWER CHOICES
a= 7
b= 6
c= 2
d= 4
Answer:
x = 2
Step-by-step explanation:
the 2 given angles are vertical angles, meaning they are equal.
38x-1 = 75
solve the above equation, and x = 2
Answer:
2
Step-by-step explanation:
Those two angles are equal:
75 = 38x - 1
so, add 1 to both
76 = 38x
divide by 38
2 = x
Giving brainliest for CORRECT awnser.
Answer:
It's D.
Step-by-step explanation:
Answer:
3(x - 2)(x - 5)
Step-by-step explanation:
Factor 3 from all terms within the trinomial:
(3x² - 21x + 30)/3 = x² - 7x + 10
3(x² - 7x + 10)
Simplify.
(x² - 7x + 10)
x -5
x -2
3(x - 2)(x - 5)* is your answer.
* remember to bring the 3 that you factored out in the beginning and stick it to the front.
~
Calculate the perimeter of this shape.
12 cm
18 cm
Answer:
[tex] 12 +18 + x+y + z +w[/tex]
In this special case we know that [tex] x+y =12[/tex] and [tex] z+w =18[/tex] and for this case we can add all the values 12+18 +12+18=60 and that represent the perimeter
Step-by-step explanation:
For this case we know that the perimeter is given by:
[tex] 12 +18 + x+y + z +w[/tex]
In this special case we know that [tex] x+y =12[/tex] and [tex] z+w =18[/tex] and for this case we can add all the values 12+18 +12+18=60 and that represent the perimeter
A test engineer wants to estimate the mean gas mileage (in miles per gallon) for a particular model of automobile. Eleven of these cars are subjected to a road test, and the gas mileage is computed for each car. A dot plot of the 11 gas-mileage values is roughly symmetrical and has no outliers. The mean and standard deviation of these values are 25.5 and 3.01, respectively. Assuming that these 11 automobiles can be considered a simple random sample of cars of this model, which of the following is a correct statement?
a. A 95% confidence interval for μ is 25.5 ±2.2284 3.01
b. A 95% confidence interval for μ is 25.5±2.201 3.01
c. A 95% confidence interval for μ is 25.5±2.228 10 3.01
d. A 95% confidence interval for μ is 25.5±2.201 10
e.The results cannot be trusted; the sample is too small.
Answer:
a) A 95% confidence interval for μ is 25.5 ±2.2284 3.01
The 95% of confidence intervals for mean μ is determined by
(23.478 , 27.522)
Step-by-step explanation:
Step( i ) :-
Given sample size 'n' =11
The mean of the sample x⁻ = 25.5
The standard deviation of the sample 'S' = 3.01
95% of confidence intervals:
The 95% of confidence intervals for mean μ is determined by
[tex]( x^{-} - t_{\frac{\alpha }{2} } \frac{S}{\sqrt{n} } , x^{-} + t_{\frac{\alpha }{2} } \frac{S}{\sqrt{n} } )[/tex]
Step(ii):-
The critical value ∝ =0.05
[tex]t_{\frac{\alpha }{2} } = 2.228[/tex]
The degrees of freedom ν=n-1 = 11-1 =10
[tex]( 25.5 - 2.228 \frac{3.01}{\sqrt{11} } , 25.5 + 2.228 \frac{3.01}{\sqrt{11} } )[/tex]
(25.5-2.0220, 25.5 + 2.0220)
(23.478 , 27.522)
Final answer:-
The 95% of confidence intervals for mean μ is determined by
(23.478 , 27.522)
Final answer:
The correct statement is: a. A 95% confidence interval for μ is 25.5 ±2.2284 3.01. To calculate the confidence interval for the population mean, we use the formula: sample mean ± (critical value) × (standard deviation / square root of sample size).
Explanation:
The correct statement is:
a. A 95% confidence interval for μ is 25.5 ±2.2284 3.01
To calculate the confidence interval for the population mean, we use the formula: sample mean ± (critical value) × (standard deviation / square root of sample size).
In this case, with a sample mean of 25.5, standard deviation of 3.01, and a sample size of 11, the critical value for a 95% confidence level is 2.2284. Therefore, the correct confidence interval is 25.5 ± 2.2284 × 3.01.
In a completely randomized experimental design, three brands of paper towels were tested for their ability to absorb water. Equal-size towels were used, with four sections of towels tested per brand. The absorbency rating data follow. At a level of significance, does there appear to be a difference in the ability of the brands to absorb water?
Answer:
Yes. At this significance level, there is evidence to support the claim that there is a difference in the ability of the brands to absorb water.
Step-by-step explanation:
The question is incomplete:
The significance level is 0.05.
The data is:
Brand X: 91, 100, 88, 89
Brand Y: 99, 96, 94, 99
Brand Z: 83, 88, 89, 76
We have to check if there is a significant difference between the absorbency rating of each brand.
Null hypothesis: all means are equal
[tex]H_0:\mu_x=\mu_y=\mu_z[/tex]
Alternative hypothesis: the means are not equal
[tex]H_a: \mu_x\neq\mu_y\neq\mu_z[/tex]
We have to apply a one-way ANOVA
We start by calculating the standard deviation for each brand:
[tex]s_x^2=30,\,\,s_y^2=6,\,\,s_z^2=35.33[/tex]
Then, we calculate the mean standard error (MSE):
[tex]MSE=(\sum s_i^2)/a=(30+6+35.33)/3=71.33/3=23.78[/tex]
Now, we calculate the mean square between (MSB), but we previously have to know the sample means and the mean of the sample means:
[tex]M_x=92,\,\,M_y=97,\,\,M_z=84\\\\M=(92+97+84)/3=91[/tex]
The MSB is then:
[tex]s^2=\dfrac{\sum(M_i-M)^2}{N-1}\\\\\\s^2=\dfrac{(92-91)^2+(97-91)^2+(84-91)^2}{3-1}\\\\\\s^2=\dfrac{1+36+49}{2}=\dfrac{86}{2}=43\\\\\\\\MSB=ns^2=4*43=172[/tex]
Now we calculate the F statistic as:
[tex]F=MSB/MSE=172/23.78=7.23[/tex]
The degrees of freedom of the numerator are:
[tex]dfn=a-1=3-1=2[/tex]
The degrees of freedom of the denominator are:
[tex]dfd=N-a=3*4-3=12-3=9[/tex]
The P-value of F=7.23, dfn=2 and dfd=9 is:
[tex]P-value=P(F>7.23)=0.01342[/tex]
As the P-value (0.013) is smaller than the significance level (0.05), the null hypothesis is rejected.
There is evidence to support the claim that there is a difference in the ability of the brands to absorb water.
A history instructor has given the same pretest and the same final examination each semester. He is interested in determining if there is a relationship between the scores of the two tests. He computes the linear correlation coefficient and notes that it is 1.15. What does this correlation coefficient value tell the instructor?
A) The correlation is something other than linear.
B) There is a strong negative correlation between the tests.
C) The history instructor has made a computational error.
D) There is a strong positive correlation between the tests.
E) none of these
Answer:
5
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If y varies directly as x, and y is 6 when x is 72, what is the value of y when x is 82
Answer:
y = 41/6
Step-by-step explanation:
This means that y = kx. k is a constant.
6 = k*72
and.
y = k*82 ...
k = 6/72 = 1/12
y = 82/12
y = 41/6
Layana’s house is located at (2 and two-thirds, 7 and one-third) on a map. The store where she works is located at (–1 and one-third, 7 and one-third). What is the distance from Layana’s home to the store?
4 units
8 and two-thirds units
10 units
14 and two-thirds units
We have been given that Layana’s house is located at [tex](2\frac{2}{3}, 7\frac{1}{3})[/tex] on a map. The store where she works is located at [tex](-1\frac{1}{3}, 7\frac{1}{3})[/tex].
We are asked to find the distance from Layana’s home to the store
We will use distance formula to solve our given problem.
Let us convert our given coordinates in improper fractions.
[tex]2\frac{2}{3}\Rightarrow \frac{8}{3}[/tex]
[tex]7\frac{1}{3}\Rightarrow \frac{22}{3}[/tex]
[tex]-1\frac{1}{3}\Rightarrow -\frac{4}{3}[/tex]
Now we will use distance formula to solve our given problem.
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Upon substituting coordinates of our given point in above formula, we will get:
[tex]D=\sqrt{(\frac{22}{3}-\frac{22}{3})^2+(\frac{8}{3}-(-\frac{4}{3}))^2}[/tex]
[tex]D=\sqrt{(0)^2+(\frac{8}{3}+\frac{4}{3})^2}[/tex]
[tex]D=\sqrt{0+(\frac{8+4}{3})^2}[/tex]
[tex]D=\sqrt{(\frac{12}{3})^2}[/tex]
[tex]D=\sqrt{(4)^2}[/tex]
[tex]D=4[/tex]
Therefore, the distance from Layana's home to the store is 4 units and option A is the correct choice.
Answer:
its A ^3^
Step-by-step explanation:
2.
2x2 + 2x - 112 factor
Answer:
Use order of operation
Step-by-step explanation:
Answer:
2(x+8)(x-7)
Step-by-step explanation:
If the question is asking 2x^2+2x-112, then the answer is 2(x+8)(x-7).
First, you factor out the two: 2(x^2+x-56)
Next, you find something that adds to x and multiplies to -56: 8 and -7
After, you get 2(x+8)(x-7)
Expand to write an equivalent expression: -1/2(-2x + 4y)
Need help ASAP!
Answer:x-2y
Step-by-step explanation:
-1/2(-2x+4y)
Open the brackets
2x/2 - 4y/2
x - 2y