Solution :
Amounts spent on a trip : $31.11, $25.01, $18.53, $14.37, $24.16, $21.91
Confidence interval = 80%
Average amount spent = 8 to 9 years old
One sample T confidence interval
μ : Mean of variance
80% of confidence interval results :
Using statistical software,
Variable : data
Sample mean : 22.515
Std. Err. = 2.3479945
DF = 5
L. limit : 19.049632
U. Limit : 25.980368
SD = 5.75
Critical value = 1.476
Among various ethnic groups, the standard deviation of heights is known to be approximately three inches. We wish to construct a 95% confidence interval for the mean height of male Swedes. Forty-eight mile Swedes are surveyed. The sample mean is 71 inches. The sample standard deviation is 2.8 inches.
Required:
a. Calculate the error bound.
b. What will happen to the level of confidence obtained if 1,000 male Swedes are surveyed instead of 48? Why?
Answer:
a) The error bound of the confidence interval is of 0.66.
b) The confidence interval will be narrower.
Step-by-step explanation:
Question a:
We have to find the margin of error. Considering that we have the standard deviation for the sample, the t-distribution is used.
The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So
df = 71 - 1 = 70
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 70 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 1.9944
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}}[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
For this problem, [tex]s = 2.8, n = 71[/tex]. So
[tex]M = T\frac{s}{\sqrt{n}} = 1.9944\frac{2.8}{\sqrt{71}} = 0.66[/tex]
The error bound of the confidence interval is of 0.66.
b. What will happen to the level of confidence obtained if 1,000 male Swedes are surveyed instead of 48? Why?
The margin of error is inversely proportional to the square root of the sample size, so increasing the sample size leads to a smaller margin of error and a narrower confidence interval.
Extraneous solutions are answers that don't work and/or produce division by zero.
True
False
Hi friends,
Please assist with my question below.
In a right angle triangle, an angle of 30 degrees has an adjacent side which measures 17 cm. what is the length of its hypotenuse?
Answer : 19.6cm
I hope this helps you! Have a good day!
the ages of two students are in the ratio of 3:5,if the older is 40yrs. How old is the younger student
The ratio/proportion is young / old = young / old.
We know that one ratio is 3 / 5, so we need to complete the other.
3 / 5 = young / 40
5 goes into 40, 8 times, therefore we need to multiply the numerator by 8 also.
3 x 8 = 24
The younger student is 24 years old.
Hope this helps!
Answer:
24
Step-by-step explanation:
younger : older
3 :5
The older is 40
40/5 = 8
Multiply each by 8
younger : older
3 *8 :5 *8
24 : 40
The younger is 24
Tìm vi phân toàn phần của các hàm số sau:
ln(x+√(x^2+y^2 ) ) ln(sin(y/x))
Let f = ln(x + √(x ² + y ²)) ln(sin(y/x)).
Then the total differential is
[tex]\mathrm df = \dfrac{\mathrm d\left(x+\sqrt{x^2+y^2}\right)}{x+\sqrt{x^2+y^2}}\ln\left(\sin\left(\dfrac yx\right)\right) + \ln\left(x+\sqrt{x^2+y^2}\right)\dfrac{\mathrm d\left(\sin\left(\frac yx\right)\right)}{\sin\left(\frac yx\right)}[/tex]
[tex]\mathrm df = \dfrac{\mathrm dx + \frac{\mathrm d(x^2+y^2)}{\sqrt{x^2+y^2}}}{x+\sqrt{x^2+y^2}}\ln\left(\sin\left(\dfrac yx\right)\right) + \ln\left(x+\sqrt{x^2+y^2}\right)\dfrac{\cos\left(\frac yx\right)\,\mathrm d\left(\frac yx\right)}{\sin\left(\frac yx\right)}[/tex]
[tex]\mathrm df = \dfrac{\mathrm dx + \frac{2x\,\mathrm dx+2y\,\mathrm dy}{\sqrt{x^2+y^2}}}{x+\sqrt{x^2+y^2}\right)\ln\left(\sin\left(\dfrac yx\right)\right) + \ln\left(x+\sqrt{x^2+y^2}}\right)\dfrac{\cos\left(\frac yx\right)\frac{x\,\mathrm dy-y\,\mathrm dx}{x^2}}{\sin\left(\frac yx\right)}[/tex]
[tex]\mathrm df = \dfrac{\left(2x+\sqrt{x^2+y^2}\right)\,\mathrm dx +2y\,\mathrm dy}{x\sqrt{x^2+y^2}+x^2+y^2\right)\ln\left(\sin\left(\dfrac yx\right)\right) \\\\ \indent + \dfrac1{x^2}\cot\left(\dfrac yx\right)\ln\left(x+\sqrt{x^2+y^2}}\right)(x\,\mathrm dy-y\,\mathrm dx)[/tex]
[tex]\mathrm df = \left(\left(\dfrac{2x+\sqrt{x^2+y^2}}{x\sqrt{x^2+y^2}+x^2+y^2}\right)\ln\left(\sin\left(\dfrac yx\right)\right) - \dfrac y{x^2}\cot\left(\dfrac yx\right)\ln\left(x+\sqrt{x^2+y^2}\right)\right)\,\mathrm dx \\\\ \indent + \left(\dfrac{2y}{x\sqrt{x^2+y^2}+x^2+y^2}\ln\left(\sin\left(\dfrac yx\right)\right)+\dfrac1x\cot\left(\dfrac yx\right)\ln\left(x+\sqrt{x^2+y^2}\right)\right)\,\mathrm dy[/tex]
Complete the table. Round your entries to the
nearest thousandth.
a
b
C
dz
ex
ASAP
a=2,5937
b=2,7048
c=2,7181
d=2,7183
e=2,7183
Given that the supply and demand function for the product type is Qd = [tex]\sqrt{260-p}[/tex],
Qs = [tex]\sqrt{p-14}[/tex]. consumer surplus ??.
The following data represent the chemistry grades for a random sample of 12 freshmen at a certain college along with their scores on an intelligence test administered while they were still seniors in high school.
Test Chemistry Student Score,
x Grade, y
1 2 3 4 5 6 7 8 9 10 11 12 65 50 55 65 55 70 65 70 55 70 50 55 85 74 76 90 85 87 94 98 81 91 76 74
Compute and interpret the sample correlation coefficient.
Answer:
R = 0.862
Strong positive relationship
Step-by-step explanation:
Given the data:
Test Chemistry Student Score,
x Grade, y
1 2 3 4 5 6 7 8 9 10 11 12
Score,x = 65 50 55 65 55 70 65 70 55 70 50 55
Grade, y = 85 74 76 90 85 87 94 98 81 91 76 74
Using technology :
The CORREL function in excel, calculators will give accurate value of the correlation Coefficient between two variables, x and y. The correlation Coefficient obtained using technology is : 0.862
The correlation Coefficient value ranges between (-1 and 1) with values closer to either - 1 or 1 reflecting stronger relationship. A value of 0 means there is no relationship between the variables. Negative values indicate negative relationships while positive indicates positive association between the variables.
Therefore. With a correlation Coefficient of 0.862, the correlation Coefficient can be interpreted as meaning that ; there is a strong positive relationship between score and grade.
What is the surface area of this figure in square centimeters?
A.96
B.75
C.84
D.60
9514 1404 393
Answer:
A. 96
Step-by-step explanation:
The surface area is the sum of the areas of the two triangular bases and the areas of the three rectangular lateral faces.
A = 2(1/2)bh + PH
where b is the base of the triangle, h is its height, P is the perimeter of the triangle, and H is the height of the prism.
A = (3 cm)(4 cm) +(3 +4 +5 cm)(7 cm) = 12 cm² +84 cm²
A = 96 cm²
The surface area of the triangular prism is 96 square cm.
The sum of 3 times a number and 7 is equal to 2. Turn into an equation
What is the order of rotational symmetry for the figure?
A. 4 or more
B. 2
C. 1
D. 3
Find the missing segment in the image below
Answer:
x = 42
Step-by-step explanation:
24+8 = 32
[tex]\frac{x}{24}[/tex] = [tex]\frac{x+14}{32}[/tex]
32x = 24(x+14)
32x = 24x+336
8x = 336
x = 42
Identify the sampling designs that use voluntary response sampling. Check all that apply.
A pharmaceutical company advertises for subjects to participate in an online survey about insulin pumps for diabetics.
An online poll is created for sports fans to vote on the winner for the Super Bowl.
Each employee is given a mandatory survey to complete about health benefits.
After each customer service call, callers are asked to stay on the line to complete a brief satisfaction survey.
A census taker randomly calls homes to gather data about household income and family demographics.
A used car dealer surveys potential customers about the type of car they are interested in so he can plan his future inventory.
2,3,6
Answer:
An online poll is created for sports fans to vote on the winner for the Super Bowl.
Each employee is given a mandatory survey to complete about health benefits.
A used car dealer surveys potential customers about the type of car they are interested in so he can plan his future inventory.
2,3,6 : B,C,F
ED2021
I want a correct answer you can take your time. If I was born on December 24, two thousand and four and my classmate was born on April 9, two thousand and six, how many months, years and days are we apart?
Answer:
5years, 3months, 16 days
Suppose that 25% of people own dogs If you pick three people at random, what
is the probability that they all three own a dog? (Let me add that we don’t know the
populations size so calculate the probability as if the population is infinite.)
Answer:
1/64
Step-by-step explanation:
25% own a dog, so picking one person has a probability of 1/4 (0.25) for that person to own a dog.
picking 3 people means combining (multiplying) the probabilities of the non-overlapping and non-depending events.
picking the third person has 1/4 chance of owning a dog (as the population is "infinite") combined with the chance that also the second pick owned a dog, which has to be combined with the chance of the first pick owning a dog.
so,
1/4 × 1/4 × 1/4 = 1/4³ = 1/64 = 0.015625
Plz someone help me
Step-by-step explanation:
yo
so sorry I can't
really answer it
suppose that 16% of crimes of this type end up in a criminal charge. this district has a false conviction rate of 5% (meaning the subject was charged but did not commit the crime) and fail to charge at a rate of 10% (meaning the person committed the crime but was not charged). if a randomly chosen suspect is charged, what is the chance that the suspect actually committed the crime
Answer:
0.9 = 90% probability that the suspect actually committed the crime.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Charged
Event B: Committed the crime.
16% of crimes of this type end up in a criminal charge.
This means that [tex]P(A) = 0.16[/tex]
Probability of being charged and committing the crime:
90% of 16%, so:
[tex]P(A \cap B) = 0.9*0.16[/tex]
What is the chance that the suspect actually committed the crime?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.9*0.16}{0.16} = 0.9[/tex]
0.9 = 90% probability that the suspect actually committed the crime.
Please help.........
Answer:
a
Step-by-step explanation:
find the hcf of 100,24
Answer:
4
Step-by-step explanation:
24 = 2^3 x 3
100 = 2^2 x 5^2
HCF = 2^2 = 4
Based on a random sample of 50, a 95% confidence interval for the population proportion was computed. Holding everything else constant, which of the following will reduce the length of the confidence interval by half? (CHECK ALL THAT APPLY): A. Quadruple the sample size. B. Change the confidence level to 68%. C. Double the sample size. D. Change the confidence level to 99.7%. E. Decrease the sample proportion by half.
The length of the confidence interval is the margin of error, which is the ratio of the standard deviation and the square root of sample size. Hence, to reduce the length of confidence interval by half, Quadruple the sample size.
Recall :
Margin of Error = σ/√nEvaluating an hypothetical scenario :
Let standard deviation, σ = 2
Sample size = 50
Margin of Error = 2/√50 = 0.554
Using Quadruple of the sample size : (50 × 4) = 200 samples
Margin of Error = 2/√200 = 0.277(0.227 ÷ 0.554) = 0.5
Therefore, increasing the sample size, reduces the margin of error. Hence, using quadruple the sample size, will reduce the margin of error by half.
Learn more : https://brainly.com/question/13403969
SCALCET8 4.7.011. Consider the following problem: A farmer with 950 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the four pens
Answer:
For any rectangle, the one with the largest area will be the one whose dimensions are as close to a square as possible.
However, the dividers change the process to find this maximum somewhat.
Letting x represent two sides of the rectangle and the 3 parallel dividers, we have 2x+3x = 5x.
Letting y represent the other two sides of the rectangle, we have 2y.
We know that 2y + 5x = 750.
Solving for y, we first subtract 5x from each side:
2y + 5x - 5x = 750 - 5x
2y = - 5x + 750
Next we divide both sides by 2:
2y/2 = - 5x/2 + 750/2
y = - 2.5x + 375
We know that the area of a rectangle is given by
A = lw, where l is the length and w is the width. In this rectangle, one dimension is x and the other is y, making the area
A = xy
Substituting the expression for y we just found above, we have
A = x (-2.5x+375)
A = - 2.5x² + 375x
This is a quadratic equation, with values a = - 2.5, b = 375 and c = 0.
To find the maximum, we will find the vertex. First we find the axis of symmetry, using the equation
x = - b/2a
x = - 375/2 (-2.5) = - 375/-5 = 75
Substituting this back in place of every x in our area equation, we have
A = - 2.5x² + 375x
A = - 2.5 (75) ² + 375 (75) = - 2.5 (5625) + 28125 = - 14062.5 + 28125 = 14062.5
Step-by-step explanation:
When x = 12, the value of the expression is ???
Find the area of the shaded part !
Answer:
Step-by-step explanation:
Semicircle:
Shaded area of semicircle = area of outer semicircle - area of inner semicircle
Outer semicircle:
d = 40 m r = 40/2 = 20m
Area of outer semicircle = πr²
= 3.14*20*20
= 1256 m²
Inner semicircle:
d = 30 m r = 30/2 = 15 m
Area of outer semicircle = πr²
= 3.14*15*15
= 706.5 m²
Shaded area of semicircle = 1256 - 706.5 = 549.5 m²
Shaded area of semicircle in both sides = 2 * 549.5 = 1099 m²
Rectangle on both sides:
Length = 50 m
width = 30 m
Area of shaded rectangles on both sides = 2* (length *width)
= 2* 50 * 30
= 3000 m²
Shaded area = 1099 + 3000 = 4099 m²
Angle Sum Theorem Acellus
20 120 y = ?
We know
Sum of two interior angles=exterior angle
[tex]\\ \sf\longmapsto 20°+120°=<y[/tex]
[tex]\\ \sf\longmapsto <y=20°+120°[/tex]
[tex]\\ \sf\longmapsto <y=140°[/tex]
Hope it helps
A clothing manufacturer purchased 50 yd of cotton and 80 yd of wool for a total cost of $1,330. Another purchase, at the same prices, included 75 yd of cotton and 20 yd of wool for a total cost of $895. Find the cost per yard of the cotton and of the wool.
Answer:
The cotton is $9 per yard and the wool is $11 per yard
Step-by-step explanation:
Create a system of equations where c is the cost per yard for the cotton and w is the cost per yard for the wool.
50c + 80w = 1330
75c + 20w = 895
Solve by elimination by multiplying the bottom equation by -4:
50c + 80w = 1330
-300c - 80w = -3580
Add these together and solve for c:
-250c = -2250
c = 9
Plug in 9 as c into one of the equations, and solve for w:
50c + 80w = 1330
50(9) + 80w = 1330
450 + 80w = 1330
80w = 880
w = 11
The cotton is $9 per yard and the wool is $11 per yard.
it would take 15 men 8 days to dig a trench 240 m long find how many days less it would take 18 men to dig a trench 360m long working at the same rate
Answer:
24 men will take 3 days to dig a 72 meter trench.
Step-by-step explanation:
If 16 workers dig an 80-meter long trench in five days, how long will it take 24 workers to dig a 72-meter long trench?
If 16 workers take 5 days to dig an 80 meter long trench,
24 workers will definitely take lesser time to dig a 72 meter long trench as both the length of the trench and the number of workers is more
Lets write these values down in order: Number of Workers, Length of Trench, Number of Days:
16 80 5
24 72 ?
Lets represent the ? as x:
We know that Ratio of Trench length to men = 80/16 : 72/24 or 5 : 3
Which means that the first set (16 men) will take 5 days to dig a trench of 80 meters.
And therefore from the above ratio (5: 3), 24 men will take 3 days to dig a 72 meter trench.
HOPE IT WILL DEFINITELY HELP YOU
in isosceles triangle XYZ, angle X=117°. calculate angleZ
Answer:
31.5
Step-by-step explanation:
Angle Z+ Angle X+ Angle Y=180
As the triangle is isosceles, Z=X, hence Z=63/2=31.5
A few more problems and then I’m done
Answer:
((c)).g(x) = 3 × 2^x +2..
A car rental firm has 410 cars. Sixty-five of these cars have defective turn signals and 35 have defective tires. (Enter your probabilities as fractions.)
(a) What is the probability that one of these cars selected at random does not have defective turn signals?
(b) What is the probability that one of these cars selected at random has no defects if no car has 2 defects?
Answer:
(a)
Number of cars with defective turn signals = 65
Number of cars with no defective turn signals = 410 - 65 = 345
Required probability:
P = 345/410*100% ≈ 84.15%(b)
Number of cars with defects = 65 + 35 = 100
Number of cars with no defects = 410 - 100 = 310
Required probability:
P = 310/410*100% ≈ 75.61%About 12.5% of restaurant bills are incorrect. If 200 bills are selected at ran- dom, find the probability that at least 22 will contain an error. Is this likely or unlikely to occur
Answer:
0.7734 = 77.34% probability that at least 22 will contain an error. Probability above 50%, which means that this is likely to occur.
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
About 12.5% of restaurant bills are incorrect.
This means that [tex]p = 0.125[/tex]
200 bills are selected at random
This means that [tex]n = 200[/tex]
Mean and standard deviation:
[tex]\mu = E(X) = np = 200*0.125 = 25[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{200*0.125*0.875} = 4.677[/tex]
Find the probability that at least 22 will contain an error.
Using continuity correction, this is [tex]P(X \geq 22 - 0.5) = P(X \geq 21.5)[/tex], which is 1 subtracted by the p-value of Z when X = 21.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{21.5 - 25}{4.677}[/tex]
[tex]Z = -0.75[/tex]
[tex]Z = -0.75[/tex] has a p-value of 0.2266.
1 - 0.2266 = 0.7734
0.7734 = 77.34% probability that at least 22 will contain an error. Probability above 50%, which means that this is likely to occur.
