Answer:
The absolute value is [tex]|z| = 1.92[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 20.1[/tex]
The standard deviation is [tex]\sigma = 1.4[/tex]
For the null hypothesis [tex]H_0[/tex]
The mean remains [tex]\mu = 20.1[/tex]
For the alternative hypothesis [tex]H_a[/tex]
The mean is [tex]\mu < 20[/tex]
This mean that the claim drops
The test statistic(the calculated value ) (z) is mathematically obtained with the following formula
[tex]z = \frac{\= x -\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]
Where [tex]\= x[/tex] is the mean for the the alternative hypothesis
substituting values
[tex]z = \frac{18.9 - 20.1}{\frac{1.4}{\sqrt{5} } }[/tex]
[tex]= -1.92[/tex]
the absolute value of the calculated value is
[tex]|z| = 1.92[/tex]
Answer:
[tex]\mid z \mid = 1.92[/tex]
Step-by-step explanation:
The null hypothesis is that the average number of complaints per week is 20.1
If H₀ = Null hypothesis
H₀: μ = 20.1
After the training, the complaints drop to 18.9 < 20.1. This means that the alternative hypothesis, [tex]H_{a} : \mu < 20.1[/tex]
[tex]\bar{x} = 18.9[/tex]
To know if the alternative hypothesis is true, we need to calculate the absolute z value using the test statistic
number of days, n = 5
Standard deviation, [tex]\sigma = 1.4[/tex]
[tex]z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n} } }[/tex]
[tex]z = \frac{18.9 - 20.1}{\frac{1.4}{\sqrt{5} } }[/tex]
z = -1.92
[tex]\mid z \mid = 1.92[/tex]
Suppose we want to assess the effect of a one-day SAT prep class at a 5% level of significance. Scores on the SAT writing exam can range from 200 to 800. A random sample of 50 students takes the SAT writing test before and after a prep class. We test the hypotheses: H 0: μ = 0 H a: μ > 0 where μ is the mean of the difference in SAT writing scores (after minus before) for all students who take the SAT prep class. The sample mean is 5 with a standard deviation of 18. Since the sample size is large, we are able to conduct the T-Test. The T-test statistic is approximately 1.96 with a P-value of approximately 0.028. What can we conclude? Group of answer choices The one-day SAT prep class is associated with statistically significant improvements in SAT writing performance. Students taking a one-day SAT prep class performed significantly better on the SAT writing exam than students who did not take the class. Students taking a one-day SAT prep class do not show statistically significant improvements in their SAT writing performance. Scores only increased by 5 points, which is not significant on an exam where scores can range from 200 to 800. The one-day SAT prep class produces statistically significant improvements in SAT writing performance.
Answer: The one-day SAT prep class is associated with statistically significant improvements in SAT writing performance.
Step-by-step explanation: just took the quiz
The correct conclusion about the situation is, the one-day SAT prep class produces statistically significant improvements in SAT writing performance, which is option (e).
Given that:
It is assessing the performance of the students in the SAT writing exam before and after SAT prep class.
The hypothesis is:
H₀: μ = 0
H₁: μ > 0
This is a one-tailed test.
Here, the T-test is used.
Now, the significance level is, α = 0.05
p-value = 0.028
Since, the p-value, 0.028 is less than the significance level 0.05, the null hypothesis is rejected.
So, the mean of the difference in SAT scores is greater than 0.
That is, there is a significant effect in SAT exam by the prep class.
Hence, the correct conclusion is, The one-day SAT prep class produces statistically significant improvements in SAT writing performance, which is option (e).
Learn more about T-test here :
https://brainly.com/question/26462012
#SPJ12
Last month, Bethany sent 5,450 texts. This month she sent 7,085 texts. What was the percent increase in her texting from last month to this month?
Answer:
Hello
The answer is 30% increase in texts since last month.
IF you feel any problem in understanding , do comment pls.
Step-by-step explanation:
Let
X = last month sent texts
y = this month sent texts
First of all find the no. of increased texts,
by subtracting x from y
=> y-x= 7085- 5450
= 1635
We want to find these 15 texts % with respect to 5450 texts
i.e. 1635/X
=0.30
for answer in % multiply with 100
i.e. 30%
Hi please help I keep getting the anwser wrong and really need to get at least 1/2 the two right or I’ll get a zero!!!pls
Answer:
x = [tex]14\frac{7}{9}[/tex] or 14.78
Step-by-step explanation:
The lines are parallel, therefore, k(18) acts same as g(x)
That means that:
k(18) = g(x)
- 14 = [tex]-\frac{18}{7}x[/tex] + 24
- 14 - 24 = [tex]-\frac{18}{7}x[/tex]
- 38 = [tex]-\frac{18}{7}x[/tex]
38(7) = 18x
266 = 18x
266 / 18 = x
133 / 9 = x
x = [tex]14\frac{7}{9}[/tex] or 14.78
A softball pitcher has a 0.487 probability of throwing a strike for each pitch. If the softball pitcher throws 29 pitches, what is the probability that no more than 14 of them are strikes?
Answer:
0.4801
Step-by-step explanation:
This is a binomial distribution question.
It can be approximated using normal distribution if the following conditions are met:
np > 10
n(1-p) > 10
Here,
n = 29
p = 0.487
So,
np = 14.12
n(1-p) = 14.88
So, we can use normal approximation here:
Binomial: X ~ B(n,p) becomes
Normal Approx: X~ N([tex]np,\sqrt{np(1-p)}[/tex])
Mean is:
[tex]\mu=np=14.123[/tex]
Standard Deviation is:
[tex]\sigma=\sqrt{np(1-p)} =2.69[/tex]
We need probability of less than or equal to 14, so we can say:
P(x ≤ 14)
Using [tex]z=\frac{x-\mu}{\sigma}[/tex], we have:
P(x ≤ 14) = [tex]P(\frac{x-\mu}{\sigma} \leq \frac{14-14.123}{2.69})\\=P(z \leq -0.05)\\=0.4801[/tex]
Note: We used z table in the last line
So the probability is 0.4801
The bumper car ride at the state fair has 2 red cars, 4 green cars, an for the ride and is assigned a the probability that both events A and B occur. Express your answer your answer to the nearest tenth d 2 blue cars. Garth is first in line car at random. Patty is next in line and is randomly assigned a car. Find as a percent. If necessary, round
Event A: Garth will drive a red bumper car.
Event B: Patty will drive a red bumper car.
a. 6.3%
b. 25%
c. 96.4%
d. 3.6%.
Answer:
a) 3.6%
Step-by-step explanation:
The given question mixed up, below is the correct question:
The bumper car ride at the state fair has 2 red cars, 4 green cars, and 2 blue cars. Garth is first in line for the ride and is assigned a car at random. Patty is next in line and is randomly assigned a car. Find the probability that both events A and B occur. Express your answer as a percent. If necessary, round your answer to the nearest tenth.
Calculation:
Given that the state fair has 2 red cars, 4 green cars and 2 blue cars.
There are therefore 2+4+2 = 8 cars in total.
Probability that Events A occurs P(A) = [tex]\frac{2}{8}[/tex] = 4
Probability that Events B occurs P(B) = [tex]\frac{1}{7}[/tex]
Probability that Events A and B occur P(A ∩ B) = [tex]\frac{2}{8}[/tex] × [tex]\frac{1}{7}[/tex] = [tex]\frac{2}{56}[/tex] = 0.0357 = 3.57% ≈ 3.6%
Therefore, the probability that both events A and B occur is 3.6%
Final answer:
The probability that both Garth and Patty will drive a red bumper car is found by multiplying the probability of Garth picking a red car (1/4) by the probability of Patty picking a red car after Garth (1/7), resulting in 1/28 or approximately 3.6%.
Explanation:
To solve the problem, we need to calculate the probability that both events A and B happen, which involves Garth and Patty both getting a red bumper car. Initially, there are 2 red cars, 4 green cars, and 2 blue cars, totaling 8 cars.
Event A: Garth picks a red car. The probability of this happening is the number of red cars over the total number of cars. So P(A) = 2/8 = 1/4.
After Garth picks a red car, there is 1 red car, 4 green cars, and 2 blue cars left, totaling 7 cars.
Event B: Patty picks a red car after Garth has already picked one. The probability of this happening is the number of remaining red cars over the total number of remaining cars. So P(B after A) = 1/7.
The probability that both A and B occur is the product of the probability of A and the probability of B given A has occurred. So P(A and B) = P(A) × P(B after A) = (1/4) × (1/7).
P(A and B) = 1/28. To express this as a percent, we multiply by 100%: (1/28) × 100% ≈ 3.6%.
Therefore, the probability that both Garth and Patty will drive a red bumper car is approximately 3.6%, which corresponds to option d.
5. Oscar needs to fill a sphere-shaped balloon with
helium. If the balloon has a diameter of 8 inches, what is
the total amount of helium that the balloon will hold to
the nearest tenth?
A. 2,143.6 in.3
B. 714.5 in.
C. 268.1 in.3
D. 150.7 in.
Final answer:
Oscar's balloon, which has an 8-inch diameter, will hold approximately 268.1 cubic inches of helium, calculated using the volume formula for a sphere.
Explanation:
Oscar needs to calculate the volume of a sphere-shaped balloon to determine how much helium it can hold. To find the balloon's volume, we use the formula for the volume of a sphere, which is V = ⅓πd³, where V is the volume, π is approximately 3.14159, and d is the diameter of the sphere. Since the balloon has a diameter of 8 inches, its radius r is 4 inches (which is half of the diameter).
Plugging the radius into the formula, we get: V = ⅓π(4 inches)³ = ⅓π(64 inches³) = 268.0826 inches³. Therefore, Oscar's balloon will hold approximately 268.1 cubic inches of helium to the nearest tenth, making the correct answer C. 268.1 in.³
ΔWXY, the measure of ∠Y=90°, WY = 8, YX = 15, and XW = 17. What ratio represents the tangent of ∠X?
In a right triangle, the tangent of an angle is defined as the ratio of the opposite side to the adjacent side. Therefore, for triangle ΔWXY, the tangent of ∠X is the ratio of side WY to YX, which is 8/15.
Explanation:To understand this question, we need to know that in the context of a right triangle, the tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side. In ΔWXY, where the measure of ∠Y=90°, ∠X is the angle we are considering. The side opposite to ∠X is WY and the side adjacent to ∠X is YX. Therefore, the tangent of ∠X can be calculated using the formula: tan(X) = WY / YX.
In this scenario, we know that WY = 8 and YX = 15. So, the tangent of ∠X is given by: tan(X) = WY / YX = 8 / 15. Hence, the ratio that represents the tangent of ∠X is 8 / 15.
Learn more about Tangent in a Triangle here:https://brainly.com/question/39327278
#SPJ2
Evaluate the function
Given f(x) = x^2-3x+2, find f(-2)
Answer:
f( - 2) =12
Step-by-step explanation:
[tex]f(x) = x^2-3x+2 \\ plugging \: x = - 2 \\ f( - 2) = ( - 2)^2-3( - 2)+2 \\ f( - 2) =4 + 6+2 \\ f( - 2) =12 \\ [/tex]
A toolbox has 10 screwdrivers Sid 6 wrenches.
Bella puts 8 more wrenches in the toolbox.
*) How many more wrenches are in the toolbox
than screwdrivers?
Answer: There are 4 more wrenches in the toolbox then the screwdrivers.
Step-by-step explanation: Add the 6 wrenches Sid put in the toolbox with the 8 wrenches Bella added to get 14 wrenches in total. Then, subtract the 10 screwdrivers from the 14 wrenches to get 4 wrenches.
Final answer:
Bella added 8 wrenches to the toolbox, making a total of 14 wrenches. There were initially 10 screwdrivers, so there are now 4 more wrenches than screwdrivers.
Explanation:
Calculating the Difference Between Wrenches and Screwdrivers in a Toolbox
Initially, there are 10 screwdrivers and 6 wrenches in the toolbox. Bella adds 8 more wrenches, which brings the total number of wrenches to 6 + 8, which equals 14 wrenches. The question asks how many more wrenches there are than screwdrivers. To find this, we subtract the number of screwdrivers from the number of wrenches:
14 wrenches - 10 screwdrivers = 4 more wrenches than screwdrivers in the toolbox.
Over 10 minutes ,how far on a clock does the tip of a 12 inch minute hand move ?
A: 2.09inches
B: 6.28 inches
C: 12.56 inches
D: 75.36 inches
Need help please anyone
Answer:
C: 12.56 inches
Step-by-step explanation:
We know that the minute hand can move an equivalent of 60 minutes in any one revolution.
-10 minutes movement is equal to 1/6 the total distance and the circumference covered in that time is calculated as:
[tex]C=\pi D\\\\=\frac{1}{6}\pi \times (12\times 2)\\\\\\=12.56\ in[/tex]
Hence, over 10 minutes the minutes hand moves 12.56 inches away.
The tip of a 12 inch minute hand will move approximately 12.56 inches over the course of 10 minutes, which aligns with option C in your given choices.
Explanation:The subject of this question is Mathematics, specifically geometry and involves calculating the length of an arc within a circle. The minute hand of a clock can be thought of as the radius of a circle, with a full rotation of the hand representing a complete circle. The minute hand moves 360 degrees in 60 minutes (or 6 degrees per minute), so over 10 minutes, the minute hand will move 60 degrees.
Now, the length of that portion of the circle (the arc length) is calculated using the formula: (2πr)(θ/360), where r is the radius (half of the diameter, or 12 inches in this case), and θ is the angle in degrees. When you plug in the respective values, you will find that the minute hand of the clock moves an approximate distance of 12.56 inches, which corresponds to option C in your given choices.
Learn more about geometry here:https://brainly.com/question/31408211
#SPJ3
Figure ABCD is a square. Prove BD ≅ AC. Square A B C D with diagonals is shown. Statements Reasons 1. ABCD is a square 1. given 2. ∠DAB, ∠ABC, ∠BCD, and ∠CDA are right angles 2. definition of a square 3. ∠DAB ≅ ∠ABC ≅ ∠BCD ≅ ∠CDA 3. right angles are congruent 4. AB ≅ BC ≅ CD ≅ DA 4. ? 5. △BAD ≅ △ABC 5. SAS 6. BD ≅ AC 6. CPCTC What is the missing reason in the proof?
all sides of a square are congruent
all right angles measure 90°
definition of diagonal
definition of perpendicular
Answer:
all sides are congruent
Step-by-step explanation:
its talking about sides
I believe A is correct
Good luck!
Find the slope of the line that passes through the pair of points.
(5,-4) AND (9,-4)
USE THE SLOPE FORMULA
Answer:
0
Step-by-step explanation:
The slope formula is ...
m = (y2 -y1)/(x2 -x1)
Filling in the given point values, we find the slope to be ...
m = (-4 -(-4))/(9 -5) = 0/4 = 0
The slope is 0.
_____
The y-values are the same at -4, the equation of the line is y = -4. It is a horizontal line with zero slope.
Need to solve
15,000,000 = 4700e 0.154t
Answer:
[tex]t=52.39[/tex]
Step-by-step explanation:
An important problem in thermodynamics is to find the work done by an ideal Carnot engine. A cycle consists of alternating expansion and compression of gas in a piston. The work done by the engine is euqal to the area of the region R enclosed by two isothermal curves xy=a, xy=b and two adiabatic curves xy^1.4=c, xy^1.4=d, where 0
Answer:
The work done is 2.5(b-a)* ln(d/c).
Step-by-step explanation:
Steps are in the following attachments
The work done by an ideal Carnot engine is equal to the area enclosed by the region in the pV diagram.
Explanation:The work done by an ideal Carnot engine is equal to the area enclosed by the region in the pV diagram. This region is bounded by two isothermal curves and two adiabatic curves. The work done by the engine can be calculated by finding the area under the isothermal curves and subtracting the area under the adiabatic curves.
To find the work done, you can divide the region into smaller shapes, such as rectangles or triangles, and calculate the area of each shape. Then, sum up the areas of all the shapes to get the total work done by the engine.
Remember to use the equations for the isothermal and adiabatic processes to relate the pressure and volume of the gas at different points in the cycle.
Learn more about Work done by a Carnot engine here:https://brainly.com/question/34820223
#SPJ11
Help Fast Which transformations could have occurred to map △ABC to △A"B"C"? a rotation and a dilation a rotation and a reflection a reflection and a dilation a translation and a dilation
Answer:
its A
Step-by-step explanation:
If 10 pounds of ice cream are separated into 15 bowls, how much ice cream would be in each bowl?
Answer:
2/3 of a pound.
Step-by-step explanation:
10 pounds per 15 bowls = 2 pounds per 3 bowls, this is equal to 2/3 of ice cream a pound in a single bowl.
(1 point) Let pp be the quartic (degree 4) polynomial that satisfies p(i)=2i,i=0,1,2,3,4. p(i)=2i,i=0,1,2,3,4. Then p(x)=p(x)= . Hint: You may have a better idea, but a brute force approach is to write p(x)=ax4+bx3+cx2+dx+e p(x)=ax4+bx3+cx2+dx+e where aa, bb, cc, dd, and ee, are the unknown coefficients, and then solve the linear system p(0)=1p(0)=1, p(1)=2p(1)=2, p(2)=4p(2)=4, p(3)=8p(3)=8, and p(4)=16p(4)=16 for aa, bb, cc, dd, and ee. Preview My AnswersSubmit Answers
Answer:
a = 1/3
b = -3
c = 26/3
d = -6
e = 0
Step-by-step explanation:
Given the quartic polynomial
p(x)=ax⁴+bx³+cx²+dx+e and
p(i) =2i when i=0,1,2,3,4
If i = 0:
p(0) = 2(0)
p(0) = 0
0 = 0+0+0+0+0++e
e = 0
When i = 1
p(1) = 2(1) = 2
2 = a(1)⁴+b(1)³+c(1)²+d(1)+e
2 = a+b+c+d+0
a+b+c+d = 0... (1)
When i = 2, p(2) = 2(2)
p(2) = 4
4 = a(2)⁴+b(2)³+c(2)²+d(2)+e
4 = 16a+8b+4c+2d+0
16a+8b+4c+2d = 4
8a+4b+2c+d = 2... (2)
When i = 3
p(3) = 8
8 = a(3)⁴+b(3)³+c(3)²+d(3)+0
8 = 81a+27b+9c+3d..(3)
When i = 4
p(4) =16
16 = a(4)⁴+b(4)³+c(4)²+d(4)+0
16 = 256a+64b+16c+4d
64a+16b+4c+d = 4...(4)
Solving equation 1 to 4 simultaneously.
Check the attachment for solution.
The problem here is to determine the coefficients of a quartic polynomial to match the given conditions. This results in a system of linear equations which can be solved to find the desired coefficients.
Explanation:This question is a
polynomial problem
and involves finding the coefficients of a
quartic polynomial
, and for that we form a system of linear equations. Using the given conditions, we get the following equations:
For p(0), we get e = 2*0 = 0 For p(1), we get a + b + c + d + e = 2 For p(2), we get 16a + 8b + 4c + 2d + e = 4 For p(3), we get 81a + 27b + 9c + 3d + e = 6 For p(4), we get 256a + 64b + 16c + 4d + e = 8By solving the above system of equations, we can find the values of a, b, c, d and e that satisfy those equations simultaneously.
Learn more about Quartic Polynomial here:https://brainly.com/question/32490490
#SPJ3
In repeated samples, approximately 99% of all differences in sample means will fall within the bounds of the interval already computed.
a. True
b. False
Answer:
a) True
Step-by-step explanation:
Repeated samples are a type of samples that are used to determine the features or characteristics or a given set of data.
In repeated samples, statistical techniques are applied whereby two samples that have similar characteristics are tested or analysed under different conditions.
Repeated samples can also be called matched or paired samples.
In repeated samples , we have what we refer to as confidence intervals. These are intervals whereby the true and correct value of certain parameters such as mean, the standard deviation of a given data or distribution is determined. We have confidence interval levels of 90%, 95% and 99%.
In repeated samples, approximately 99% of all differences in sample means will fall within the bounds of the interval already computed.
Use the confidence level and sample data to find a confidence interval for estimating the population muμ. Round your answer to the same number of decimal places as the sample mean. A random sample of 9595 light bulbs had a mean life of x overbar equals 510x=510 hours with a standard deviation of sigma equals 37 hours.σ=37 hours. Construct a 90% confidence interval for the mean life, muμ, of all light bulbs of this type.
Answer:= (504, 516)
Therefore, the 90% confidence interval (a,b) = ( 504, 516)
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean gain x = 510
Standard deviation r = 37
Number of samples n = 95
Confidence interval = 90%
z(at 90% confidence) = 1.645
Substituting the values we have;
510+/-1.645(37/√95)
510+/-1.645(3.796)
510+/-6.24
510+/-6
= (504, 516)
Therefore at 90% confidence interval (a,b) = ( 504, 516)
A scatterplot shows a strong, positive, linear relationship between the number of rebounds a basketball team averages and the number of wins that team records in a season. Which conclusion is most appropriate?
Answer:
The correct answer is wins and rebounds are correlated positively ,but we cannot decided that having more rebounds leads to more wins,on average.
Step-by-step explanation:
From the example given, the most appropriate conclusion is that, because causation is not the same as correlation, If two variables are compared,this does not mean that one leads to the other.
An observed data is based on correlation,but for description of causation ,we need to make experiments,as we update the variable treatment regarding to the changes in response variable.
Researchers are studying two populations of sea turtles. In population D, 30 percent of the turtles have a shell length greater than 2 feet. In population E, 20 percent of the turtles have a shell length greater than 2 feet. From a random sample of 40 turtles selected from D, 15 had a shell length greater than 2 feet. From a random sample of 60 turtles selected from E, 11 had a shell length greater than 2 feet. Let pˆD represent the sample proportion for D, and let pˆE represent the sample proportion for E.
Complete question:
Researchers are studying two populations of sea turtles. In population D, 30 percent of the turtles have a shell length greater than 2 feet. In population E, 20 percent of the turtles have a shell length greater than 2 feet. From a random sample of 40 turtles selected from D, 15 had a shell length greater than 2 feet. From a random sample of 60 turtles selected from E, 11 had a shell length greater than 2 feet. Let pˆD represent the sample proportion for D, and let pˆE represent the sample proportion for E.
(a) What is the value of the difference pˆD−pˆE? Show your work.
(b) What are the mean and standard deviation of the sampling distribution of the difference in sample proportions pˆD−pˆE? Show your work and label each value.
(c) Can it be assumed that the sampling distribution of the difference of the sample proportions pˆD−pˆE is approximately normal? Justify your answer.
(d) Consider your answer in part (a). What is the probability that pˆD−pˆE is greater than the value found in part (a)?
Answer:
a) 0.1917
b) The mean is 0.1917 and the standard deviation is 0.0914.
c)Yes, the sampling distribution of the difference of the sample proportions pˆD−pˆE is approximately normal
d) 0.1580
Step-by-step explanation:
a) for p`D we have:
[tex] \frac{15}{40} [/tex]
= 0.375
For p`E we have:
[tex] \frac{11}{60} [/tex]
= 0.1833
Therefore, p`D - p`E, we have:
0.375 - 0.1833
=0.1917
b) The Mean can be calculated as p`D - p`E =
0.375 - 0.1833
=0.1917
For standard deviation:
[tex] s.d = \sqrt{\frac{p`D (1-p`D)}{N_D} + \frac{p`E(1-p`E)}{N_E}}[/tex]
[tex] s.d = \sqrt{\frac{0.375(1 - 0.375)}{40} + \frac{0.1833(1 - 0.1833)}{60}}= 0.0914[/tex]
The mean is 0.1917 and the standard deviation is 0.0914.
c) Yes, the sampling distribution of the difference of the sample proportions pˆD−pˆE is approximately normal, because for normal condition, we have:
i) np ≥ 10
ii) n(1-p) ≥ 10.
From the expressions, we can see the samples satisfy the condition for normality.
d) To get the probability, wen need to find the Z score.
The Z score can be calculated using the formula:
[tex] Z = \frac{(p`D - p`E) -(pD - pE)}{s.d}[/tex]
[tex] = \frac{(0.1917) -(0.1)}{0.0914}[/tex]
= 1.0029
Therefore,
P(Z > 1.0029) = 1 - P(Z ≤ 1.0029)
From the z distribution table, we have:
P (Z > 1.0029) = 1 - 0.8420 = 0.1580
The probability is 0.1580
The value of the difference pˆD−pˆE is 0.1917. The mean and standard deviation is 0.1917 and 0.0914 respectively and the probability that pˆD−pˆE is greater than the 0.1917 is 0.1580.
Given :
In population D, 30 percent of the turtles have a shell length greater than 2 feet.In population E, 20 percent of the turtles have a shell length greater than 2 feet.From a random sample of 40 turtles selected from D, 15 had a shell length greater than 2 feet.From a random sample of 60 turtles selected from E, 11 had a shell length greater than 2 feet.a) The value of pˆD is:
[tex]=\dfrac{15}{40}[/tex]
The value of pˆE is:
[tex]=\dfrac{11}{60}[/tex]
So, the value of (pˆD - pˆE) is:
[tex]=\dfrac{15}{40}-\dfrac{11}{60}[/tex]
= 0.375 - 0.1833
= 0.1917
b) Mean is given by the formula:
pˆD - pˆE = 0.1917
For standard deviation using the formula:
[tex]\rm SD =\sqrt{ \dfrac{p\hat{}D(1-p\hat{}D)}{N_D}+\dfrac{p\hat{}E(1-p\hat{}E)}{N_E}}[/tex]
[tex]\rm SD = \sqrt{\dfrac{0.375(1-0.375)}{40}+\dfrac{0.1833(1-0.1833)}{60}}[/tex]
SD = 0.0914
c). Yes, the sampling distribution of the difference of the sample proportions pˆD−pˆE is approximately normal.
d). To determine the probability, first evaluate the z-score.
[tex]\rm Z=\dfrac{(p\hat{}D-p\hat{}E)-(pD-pE)}{SD}[/tex]
[tex]\rm Z = \dfrac{0.1917-0.1}{0.0914}[/tex]
Z = 1.0029
Now, P(Z>1.0029) = 1 - P(Z [tex]\leq[/tex] 1.0029)
= 1 - 0.8420
= 0.1580
For more information, refer to the link given below:
https://brainly.com/question/2561151
When a car is first observed it has a speed of 20 ms-1. after a time of 10 S it is observed that the speed is 50 MS-1
Answer:
i need points.
Step-by-step explanation:
g Consider the following statement. For all sets A and B, (A − B) ∪ (A ∩ B) = A. Construct an algebraic proof for the statement. Cite a property from Theorem 6.2.2 for every step.
To prove the statement (A − B) ∪ (A ∩ B) = A, we can use the property of set difference, distribution, and identity from Theorem 6.2.2.
Explanation:To construct an algebraic proof for the statement (A − B) ∪ (A ∩ B) = A, we can use the property of set difference, distribution, and identity from Theorem 6.2.2.
Start with the left side of the equation: (A − B) ∪ (A ∩ B)Apply the property of set difference: (A − B) = A ∩ B'. Now the equation becomes (A ∩ B') ∪ (A ∩ B).Use the property of distribution: A ∩ (B' ∪ B) = A ∩ U = A, where U represents the universal set. Therefore, (A − B) ∪ (A ∩ B) = A. Learn more about Set theory here:https://brainly.com/question/27333813
#SPJ12
A coin is tossed and a number cube is rolled what is the probability that the coin shows heads and the number cube shows six
Answer:
There is a 1/2 chance the coin will land on heads and there is a 1/6 chance that the number cube will land on 6. hope this helps
what is the 20th shape the pattern is triangle,circle,circle
Answer:
Circle
Step-by-step explanation:
I don't know if there is a more "professional" way to solve this, but I wrote out the pattern until I got to the twentieth shape and it ended up being a circle :)
The 20th shape in the pattern is a circle.
Explanation:To determine the 20th shape in the pattern of triangle, circle, circle, we need to analyze the pattern. The pattern starts with a triangle and is followed by two circles. This sequence repeats - triangle, circle, circle. To find the 20th shape, we need to determine how many times this sequence repeats within the first 20 shapes. Each complete sequence consists of 3 shapes (triangle, circle, circle), so we divide 20 by 3 to get 6 complete sequences. The 6th complete sequence ends with a circle, so the 20th shape in the pattern is also a circle.
Learn more about Patterns here:https://brainly.com/question/36596313
#SPJ2
PLEASE CALCULUS HELP!!!!!!
Answer:
work and answer are shown in the picture
Step-by-step explanation:
if you have any questions about my work please let me know
The area of a triangle that is similar to the one below is the area of this triangle. What is the length of the base of the similar triangle? 2.3 ft 3.3 ft 7 ft 63 ft
The answer is 7 feet
Answer:
c. 7ft
good luck, i hope this helps :)
Suppose ACT Reading scores are normally distributed with a mean of 21.3 and a standard deviation of 5.9. A university plans to award scholarships to students whose scores are in the top 7%. What is the minimum score required for the scholarship? Round your answer to the nearest tenth, if necessary.
Answer:
30.0
Step-by-step explanation:
Given our data is normally distribute with [tex]\mu=21.3[/tex] and [tex]\sigma=5.9[/tex]
-Top 7% is given by find the z-value corresponding to p=(1-0.07)=0.93
-We substitute our values in the equation below;
[tex]z=\frac{\bar X-\mu}{\sigma}\\\\\\=\frac{X-21.3}{5.9}, z_{0.035}=1.476\\\\\therefore 1.476=\frac{X-21.3}{5.9}\\\\X=5.9\times 1.476+21.3\\\\=30.0084\approx30.0[/tex]
Hence, the minimum score required for the scholarship is 30.0
The minimum ACT Reading score required for a university scholarship awarded to the top 7% is approximately 30.0.
To find the minimum ACT Reading score required for a scholarship awarded to students in the top 7%, we need to determine the z-score that corresponds to the top 7% of a normal distribution. We can then use this z-score to find the corresponding ACT score.
The z-score for the top 7% of a standard normal distribution is approximately 1.475. Since the ACT Reading scores have a mean (μ) of 21.3 and a standard deviation (σ) of 5.9, we can use the z-score formula to find the minimum score 'x' required for the scholarship: z = (x - μ) / σ.
Solving for 'x', we get: x = zσ + μ = 1.475(5.9) + 21.3 ≈ 30.0. Therefore, the minimum ACT Reading score required for the scholarship is approximately 30.0.
What is equivalent to 16 3/4x
Answer:
⁴ˣ√16³
Step-by-step explanation:
The equivalent to 16^(3/4x) is ⁴ˣ√16³. It reads, 4x root of 16 raised to the power of 3. 1/4x as an exponent means the 4x root of the base number. 3 as an exponent simply means that the base number is raised to the third power.
A certain flight arrives on time 8484 percent of the time. Suppose 143143 flights are randomly selected. Use the normal approximation to the binomial to approximate the probability that (a) exactly 108108 flights are on time. (b) at least 108108 flights are on time. (c) fewer than 124124 flights are on time. (d) between 124124 and 128128, inclusive are on time. (a) P(108108)equals=0.00200.0020 (Round to four decimal places as needed.) (b) P(Xgreater than or equals≥108108)equals=0.99800.9980 (Round to four decimal places as needed.) (c) P(Xless than<124124)equals=0.77960.7796 (Round to four decimal places as needed.) (d) P(124124less than or equals≤Xless than or equals≤128128)equals=0.19230.1923 (Round to four decimal places as needed.)
Answer:
a) P(x=108)=0.0020
b) P(x≥108)=0.9980
c) P(x<124)=0.7794
d) P(124≤x≤128)=0.1925
Step-by-step explanation:
We know the population proportion, that is p=0.84.
We take a sample of size n=143.
We will use the normal approximation to the binomial distribution to model this problem.
The mean and standard deviation of the normal approximation to the binomial distribution will be:
[tex]\mu=np=143*0.84=120.12\\\\\sigma=\sqrt{np(1-p)}=\sqrt{143*0.84*0.16}=\sqrt{19.22}=4.38[/tex]
a) We have to calculate the probability that exactly 108 flights are on time.
As the normal distribution considers the random variable to be continous, we have to apply the continuity correction factor.
In this case, the probability of 108 flights on time can be calculated as P(107.5<x<108.5):
[tex]P(x=108)=P(107.5<x<108.5)=P(x<108.5)-P(x<107.5)\\\\\\ z_1=(x_1-\mu)/\sigma=(107.5-120.12)/4.38=-12.62/4.38=-2.88\\\\z_2=(x_2-\mu)/\sigma=(108.5-120.12)/4.38=-11.62/4.38=-2.65\\\\\\P(x<108.5)-P(x<107.5)=P(z<-2.65)-P(z<-2.88)\\\\P(x<108.5)-P(x<107.5)=0.0040-0.0020=0.0020[/tex]
b) Now we have to calculate that at least 108 flights are on time.
As the probability includes 108, the continuity factor will indicates that we calculate P(x>107.5). The z-value for x=107.5 has been already calculated in point a:
[tex]P(x\geq108)=P(x>107.5)=P(z>-2.88)=0.9980[/tex]
c) We have to calculate the probability that fewer than 124 flights are on time. According to the continuity factor, we have to calculate the probability P(x<123.5), as the flight number 124 is not included in the interval.
[tex]P(x<124)=P(x<123.5)=P(z<0.77)=0.7794\\\\\\z=(x-\mu)/\sigma=(123.5-120.12)/4.38=0.77[/tex]
d) We have to calculate the probability that between 124 and 128 flights, inclusive, are on time.
This interval corresponds to the probability P(123.5<x<128.5)
[tex]P(123.5<x<128.5)=P(x<128.5)-P(x<123.5)\\\\\\ z_1=(x_1-\mu)/\sigma=(128.5-120.12)/4.38=8.38/4.38=1.91\\\\z_2=(x_2-\mu)/\sigma=(123.5-120.12)/4.38=0.77\\\\\\P(x<128.5)-P(x<123.5)=P(z<1.91)-P(z<0.77)\\\\P(x<128.5)-P(x<123.5)=0.9719-0.7794=0.1925[/tex]