Answer:
[tex] (240-210) -1.984 \sqrt{\frac{8.6^2}{100}+\frac{5.7^2}{100}}=27.953[/tex]
[tex] (240-210) +1.984 \sqrt{\frac{8.6^2}{100}+\frac{5.7^2}{100}}=32.047[/tex]
And the confidence interval for the difference is between:
[tex] 27.953 \leq \mu_1 -\mu_2 \leq 32.047[/tex]
Step-by-step explanation:
We have the following info given:
[tex] \bar X_1 = 240[/tex] sample mean for medium Pizzas from Prim's
[tex] \bar X_2 = 210[/tex] sample mean for medium Pizzas from Pizza Place
[tex] s_1 =8.6[/tex] sample deviation for Prim's
[tex] s_2 =5.7[/tex] sample deviation for Pizza Palca
[tex] n_1 =n_2 = 100[/tex] sample size selected for each case
The confidence interval for the difference of means is given by:
[tex] (\bar X_1 -\bar X_2) \pm t_{\alpha/2}\sqrt{\frac{s^2_1}{n_1} +\frac{s^2_2}{n_2}}[/tex]
And for the 95% confidence we need a significance level of [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], the degrees of freedom are given by:
[tex] df= n_1 +n_2 -2= 100+100-2 =98[/tex]
And the critical value would be
[tex] t_{\alpha/2}= 1.984[/tex]
And replacing we got:
[tex] (240-210) -1.984 \sqrt{\frac{8.6^2}{100}+\frac{5.7^2}{100}}=27.953[/tex]
[tex] (240-210) +1.984 \sqrt{\frac{8.6^2}{100}+\frac{5.7^2}{100}}=32.047[/tex]
And the confidence interval for the difference is between:
[tex] 27.953 \leq \mu_1 -\mu_2 \leq 32.047[/tex]
Answer:
E
Step-by-step explanation:
30 plus or minus 1.98 sqrt 8.6^2/100 + 5.7^2/100
Please help me i dont know how to do this
Answer:
26
Step-by-step explanation:
What is the length of a football
Answer: 10.5 to 11.5 inches
Answer:
10.5 to 11.5 inches
Step-by-step explanation:
An Epson inkjet printer ad advertises that the black ink cartridge will provide enough ink for an average of 245 pages. Assume that this claim is accurate and that the standard deviation for this population is 15 pages. A random sample of 33 customers was surveyed about the number of pages they were able to print with their black ink cartridges. What the probability that the sample mean will be 246 pages or more?
Answer:
35.2% probability that the sample mean will be 246 pages or more
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
[tex]\mu = 245 \sigma = 15, n = 33, s = \frac{15}{\sqrt{33}} = 2.61[/tex]
What the probability that the sample mean will be 246 pages or more?
This is 1 subtracted by the pvalue of Z when X = 246. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{246 - 245}{2.61}[/tex]
[tex]Z = 0.38[/tex]
[tex]Z = 0.38[/tex] has a pvalue of 0.6480.
1 - 0.6480 = 0.3520
35.2% probability that the sample mean will be 246 pages or more
From the 12 players who will travel, the coach must select her starting line-up. She will select a player for each of the five positions: center, power forward, small forward, shooting guard and point guard. How many ways are there for her to select the starting line-up
Answer:
95040 ways
Step-by-step explanation:
If we have 12 players, but of those 12 only 5 can be on the playing field, since there are only 5 positions, to know the different ways to assemble the team, we must calculate them by means of permutations, when n = 12 and r = 5.
nPr = n! / (n-r)!
replacing:
12P5 = 12! / (12-5)!
12P5 = 95040
In other words, there are a total of 95040 ways of assembling the equipment.
What is the factorization of the trinomial below?
x^3- 12x^2 + 35x
Answer:
Step-by-step explanation:
x • (x - 5) • (x - 7)
Answer:
x(x-5)(x-7)
Step-by-step explanation:
x³ - 12x² + 35x
x(x² - 12x + 35)
x(x-5)(x-7)
A college admissions officer takes a simple random sample of 100 entering freshmen and computes their mean mathematics SAT score to be 459. Assume the population standard deviation is o = 116. Construct a 90% confidence interval for the mean mathematics SAT score for the entering freshman class. Round the answer to the nearest whole number. < A 90% confidence interval for the mean mathematics SAT score is__________.
Answer:
A 90% confidence interval for the mean mathematics SAT score is (440, 478).
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.9}{2} = 0.05[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.05 = 0.95[/tex], so [tex]z = 1.645[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.645*\frac{116}{100} = 19[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 459 - 19 = 440
The upper end of the interval is the sample mean added to M. So it is 459 + 19 = 478
A 90% confidence interval for the mean mathematics SAT score is (440, 478).
The 90% confidence interval for the SAT score is between 440 and 478.
mean (μ) = 459, standard deviation (σ) = 116, sample (n) = 100, confidence = 90% = 0.90
α = 1 - C = 1 - 0.90 = 0.1
α/2 = 0.1/2 = 0.05
The z score of α/2 is equal to the z score of 0.45 (0.5 - 0.05) which is equal to 1.645.
The margin of error (E) is given by:
[tex]E=z_\frac{\alpha}{2} *\frac{\sigma}{\sqrt{n} } \\\\E=1.645*\frac{116}{\sqrt{100} } =19[/tex]
The confidence interval = μ ± E = 459 ± 19 = (440, 478)
The 90% confidence interval for the SAT score is between 440 and 478.
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Dok = (6, 12) (3,6)
The scale factor is
A. 1/2
B. 2
C. 4
Answer:
A. 1/2
Step-by-step explanation:
For 6 to become 3 and 12 to become 6, the (6,12) is being multiplied by 1/2.
Answer:
Step-by-step explanation:
The scale factor is from (6, 12) to (3, 6) is a.
1/2(6) = 3
1/2(12)= 6
After collecting the data, Christopher finds that the total snowfall per year in Reamstown is normally distributed with mean 94 inches and standard deviation 14 inches. What is the probability that, in a randomly selected year, the snowfall was greater than 52 inches? Use the empirical rule. Provide the final answer as a percent rounded to two decimal places.
Answer:
99.85
Step-by-step explanation:
$99.85\text{ %}$
Notice that 52 inches is three standard deviations less than the mean. Based on the Empirical Rule, 99.7% of the yearly snowfalls are within three standard deviations of the mean. Since the normal distribution is symmetric, this implies that 0.15% of the yearly snowfalls are less than three standard deviations below the mean. Alternatively, 99.85% of the yearly snowfalls are greater than three standard deviations below the mean.
At a certain gas station, 40% of the customers use regular gas (A1), 35% use plus gas (A2), and 25% use premium (A3). Of those customers using regular gas, only 40% fill their tanks (event B). Of those customers using plus, 80% fill their tanks, whereas of those using premium, 70% fill their tanks.
Required:
a. What is the probability that the next customer will request extra unleaded gas and fill the tank?
b. What is the probability that the next customer fills the tank?
c. If the next customer fills the tank, what is the probability that regular gas is requested?
Answer:
A) 0.28
B) 0.615
C) 0.26
Step-by-step explanation:
We are given;
Probabilities of customers using regular gas:P(A1) = 40% = 0.4
Probabilities of customers using plus gas: P(A2) = 35% = 0.35
Probabilities of customers using premium gas: P(A3) = 25% = 0.25
We are also given with conditional probabilities of full gas tank:
P(B|A1) = 40% = 0.4
P(B|A2) = 80% = 0.8
P(B|A3) = 70% = 0.7
A) The probability that next customer will requires extra unlead gas(plus gas) and fill the tank is:
P(A2 ∩ B) = P(A2) × P(B|A2)
P(A2 ∩ B) = 0.35 × 0.8
P(A2 ∩ B) = 0.28
B)The probability of next customer filling the tank is:
P(B) = [P(A1) • P(B|A1)] + [P(A2) • P(B|A2)] + [P(A3) • P(B|A3)]
P(B) = (0.4 × 0.4) + (0.35 × 0.8) + (0.25 × 0.7)
P(B) = 0.615
C)If the next customer fills the tank, probability of requesting regular gas is;
P(A1|B) = [P(A1) • P(B|A1)]/P(B)
P(A1|B) = (0.4 × 0.4)/0.615
P(A1|B) = 0.26
Find the area of the shape shown below.
2
4
2
N.
2
units
Answer: 10units^2
Step-by-step explanation:
You can find the area of the trapezoid by multiplying the sum of the bases (the parallel sides) by the height (the perpendicular distance between the bases), and then dividing by 2.
The larger base is 2+2+4=8
so
A=(2+8)*2/2
=10
In a recent survey of 200 elementary students, many revealed they preferred math than English. Suppose that 80 of the students surveyed were girls and that 120 of them were boys. In the survey, 60 of the girls, and 80 of the boys said that they preferred math more.
Required:
a. Calculate an 80% confidence interval for the difference in proportions.
b. What is the standard error of the difference in the probability between that girls prefer math more and boys prefer math more?
1. 0.4097
2. 0.0042
3. 0.0833
4. 0.0647734
c. What is the difference in the probability between that girls prefer math more and boys prefer math more?
1. 0.0833
2. 0.5
3. 0.0042
4. 0.4097
Answer:
Step-by-step explanation:
a) Confidence interval for the difference in the two proportions is written as
Difference in sample proportions ± margin of error
Sample proportion, p= x/n
Where x = number of success
n = number of samples
For the girls,
x = 60
n1 = 80
p1 = 60/80 = 0.75
For the boys
x = 80
n2 = 120
p2 = 80/120 = 0.67
Margin of error = z√[p1(1 - p1)/n1 + p2(1 - p2)/n2]
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.8 = 0.2
α/2 = 0.2/2 = 0.1
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.1 = 0.9
The z score corresponding to the area on the z table is 1.282. Thus, z score for confidence level of 80% is 1.282
Margin of error = 1.282 × √[0.75(1 - 0.75)/80 + 0.67(1 - 0.67)/120]
= 1.282 × √0.00418625
= 0.081
Confidence interval = 0.75 - 0.67 ± 0.081
= 0.08 ± 0.081
b) The formula for determining the standard error of the distribution of differences in sample proportions is expressed as
Standard error = √{(p1 - p2)/[(p1(1 - p1)/n1) + p2(1 - p2)/n2}
Therefore,
Standard error = √{(0.
75 - 0.67)/[0.75(1 - 0.75)/80 + 0.67(1 - 0.67)/120]
Standard error = √0.08/0.00418625
Standard error = 4.37
c) the difference in the probability between that girls prefer math more and boys prefer math more is
0.75 - 0.67 = 0.08
Suppose there are 310 first-year lawyers in a particular metropolitan area with an average starting salary of $156,000 and a standard deviation of $13,000. What is the standard error of the mean for a random sample of 33 first-year lawyers?
Answer:
$ 2263
Step-by-step explanation:
In this case to calculate the standard error of the mean, we only need the standard deviation (sd) and the number of the random sample (n).
sd = 13000
n = 33
SE = sd / (n ^ (1/2))
replacing:
SE = 13000 / (33 ^ (1/2))
SE = 2263.01
What the standard error of the mean for a random sample of 33 first-year lawyers means is $ 2263
The standard error of the mean is $2263
Calculation of the standard error of the mean:Since here are 310 first-year lawyers in a particular metropolitan area with an average starting salary of $156,000 and a standard deviation of $13,000.
So, the standard error is
[tex]= 13000 \div (33 ^ {(1\div 2))}[/tex]
= 2263.01
Therefore, we can conclude that The standard error of the mean is $2263
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Want Brainliest? Get this correct , Which of the two functions below has the smallest minimum y-value?
Answer:
B. g(x)
Step-by-step explanation:
g(x) is a function of odd degree, so will tend toward negative infinity as an extreme value.
f(x) is an even-degree function with a positive leading coefficient. Its minimum value is -2.
g(x) has the smallest minimum value
This area model represents the product of 27 and another number. What is the
other number?
20
600
160
210
56
60
38
Answer:
The other number is 25
See explanation below
Step-by-step explanation:
The question is incomplete. Since we were not given the area or the answer to the multiplication of the two numbers, I would show you how to multiply two 2-digit numbers using the area model.
Let's assume we want to find the area model of 27 and 25.
We would write the multiplicands(the two digit numbers) in expanded form as tens and ones.
So, 27 becomes 20 and 7
25 becomes 20 and 5.
Then draw a box that is 2 by 2 grid ( 2 rows and 2 columns)
Then multiply the 1st column by the 1st row, 2nd column by 2nd row. Afterwards sum the values obtained together.
For the question: 25×27
20×20, 20×5, 20×7, 5÷7
400, 100, 140, 35
Their sum = 400 + 100+ 140 +35
= 675
See attachment for diagram.
In this question only one of the numbers is given. The area of the two numbers wasn't given.
Assuming the area of the two numbers was given and one if the numbers was also given, we would apply area model of division.
Example: Area of the both numbers = 675, the other number given = 27. Find the other number.
The area model of solving division is gotten from finding the area of a rectangle.
Since Area of a rectangle = Length × Width
Then the the value of length would be greater than value of breadth.
675÷27 = 25
So break it down to 20 and 5. Hence You divide first by 20 in first column. Then divide the remainder (135) by 5 in second column.
See diagram for explanation
Help me do it please, I'm stuck.
Answer:
2/1
Step-by-step explanation:
So you want to find a point where the line crosses a intersection near perfectly, point A (1,3) and then a second point, B (2,5)
and then you count up from point a, on the Y axis until you are even with the second point, that number is your RISE
it is 2
then you just count over to point B from that spot where you counted up. RUN TO IT
1
so it is 2/1 or just 2
((point (0,1) would have worked too))
(-36)1/2= -6 1/6
a.-6
b.1/2
c.no real numbers
Answer:
c
Step-by-step explanation:
(WITH IMAGE) What is the value of m?
Answer:
10
Step-by-step explanation:
The two marked angles are a linear pair, so have a sum of 180°.
(2m +10) +(5m +100) = 180
7m +110 = 180 . . . . . . . collect terms
7m = 70 . . . . . . . . . . . . subtract 110
m = 10 . . . . . . . . . . . . . divide by 7
Please answer this correctly
Answer:
left, if looking from person's point of view
Step-by-step explanation:
Answer:
It would be A
Step-by-step explanation:
If you cut off the overlapping cubes, you get the image on A.
Which of the given expressions results in 0 when evaluated at x = 5? A. 5x(x − 7) B. (x − 8)(x − 5) C. (x + 7)(x − 2) D. (x + 5)(x − 8)
Answer:
B. (x - 8)(x - 5)
Step-by-step explanation:
If you plugged in x = 5 into the 2nd equation, you would see that you would be multiplying by 0, which would turn everything zero.
the length of a rectangular park excerdees its width of 17m if the perimeter of the park find the dimension of the park
Answer:
math papa look on that website
Step-by-step explanation:
No-Toxic-Toys currently has $400,000 of equity and is planning an $160,000 expansion to meet increasing demand for its product. The company currently earns $140,000 in net income, and the expansion will yield $70,000 in additional income before any interest expense.
The company has three options: (1) do not expand, (2) expand and issue $160,000 in debt that requires payments of 9% annual interest, or (3) expand and raise $160,000 from equity financing. For each option, compute (a) net income and (b) return on equity (Net Income ÷ Equity). Ignore any income tax effects. (Round "Return on equity" to 1 decimal place.)
Answer:
Down below
Step-by-step explanation:
1. It does not expanda. Net income= $100,000 (as given in the question)
b. Return on equity= (net income)/(shareholder’s equity)
Shareholder’s equity= $400,000
Thus return on equity= 100000/400000 = 0.25 or 25%
2. It expands and issue $160,000 in debt
a. Net income= $100000 + 50000 – 12800 (debt interest 8% of $160000)
= $137,200
b. Return on equity= (net income)/(shareholder’s equity)
= 137200/400000
=0.343 or 34.3%
3. It expands and raises equity of $160000
a. Net Income= $100000 + 50000
= $150000
b. Return on equity= (net income)/(shareholder’s equity)
= 150000/(400000 + 160000)
Where ($560,000) 400000 + 160000 is shareholder’s equity
= 0.27 or 27%
A marketing firm wants to estimate how much root beer the average teenager drinks per year. A previous study found a standard deviation of 1.12 liters. How many teenagers must the firm interview in order to have a margin of error of at most 0.1 liter when constructing a 99% confidence interval
Answer:
At least 832 teenargers must be interviewed.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.99}{2} = 0.005[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
How many teenagers must the firm interview in order to have a margin of error of at most 0.1 liter when constructing a 99% confidence interval
At least n teenargers must be interviewed.
n is found when M = 0.1.
We have that [tex]\sigma = 1.12[/tex]
So
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.1 = 2.575*\frac{1.12}{\sqrt{n}}[/tex]
[tex]0.1\sqrt{n} = 2.575*1.12[/tex]
[tex]\sqrt{n} = \frac{2.575*1.12}{0.1}[/tex]
[tex](\sqrt{n})^{2} = (\frac{2.575*1.12}{0.1})^{2}[/tex]
[tex]n = 831.7[/tex]
Rounding up
At least 832 teenargers must be interviewed.
Please help! Correct answer only, please! Which of the following is a Hamiltonian Circuit, beginning at vertex A, for the given graph? A. ADBCA B. ABCDA C. ACBDA D. all of the above
Answer: d) all of the above
Step-by-step explanation:
A Hamiltonian circuit is where you follow the path of the circuit touching EVERY VERTEX only ONE time.
Notice that each path given allows every vertex to be touched and each vertex is touched only once.
Therefore, all the options given are valid paths for a Hamiltonian circuit.
What is the volume, to the nearest whole cubic inch, of a cylinder with a height of 10 inches and a radius of 8 inches? Use
* = 3.14 and round your answer to the whole number.
cubic inches
Answer:
2,009.6 inches³
Step-by-step explanation:
The formula for the volume of a cylinder:
V = πr²h
Let's substitute into the given equation:
V = πr²h
V = (3.14)(8²)(10)
Solve:
V = (3.14)(8²)(10)
V = (3.14)(64)(10)
V = (200.96)(10)
V = 2,009.6
Therefore, the volume of the cylinder is 2,009.6 cubic inches.
Consider the probability that at least 91 out of 155 students will pass their college placement exams. Assume the probability that a given student will pass their college placement exam is 59%.Approximate the probability using the normal distribution. Round your answer to four decimal places.
Answer:
0.5616 = 56.16% probability that at least 91 out of 155 students will pass their college placement exams.
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x sucesses 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 samples can be 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.
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].
In this problem, we have that:
[tex]n = 155, p = 0.59[/tex]
So
[tex]\mu = E(X) = np = 155*0.59 = 91.45[/tex]
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{155*0.59*0.41} = 6.12[/tex]
Probability that at least 91 out of 155 students will pass their college placement exams.
Using continuity correction, this is [tex]P(X \geq 91 - 0.5) = P(X \geq 90.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 90.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{90.5 - 91.45}{6.12}[/tex]
[tex]Z = -0.155[/tex]
[tex]Z = -0.155[/tex] has a pvalue of 0.4384
1 - 0.4384 = 0.5616
0.5616 = 56.16% probability that at least 91 out of 155 students will pass their college placement exams.
9 m
11 m
6 m
4 m
Find the area of this figure.
Answer: 30 for addition and 2376 for multipaction
Step-by-step explanation: Depending on how what algebraic expression.
In a recent survey, a random sample of 130 families were asked about whether they have a pet, and 67 reported that they have a pet. What value of z should be used to calculate a confidence interval with a 90% confidence level
Answer:
z = 1.645 should be used.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]z = 1.645[/tex].
z = 1.645 should be used.
In a data distribution, the first quartile, the median and the means are 30.8, 48.5 and 42.0 respectively. If the coefficient skewness is −0.38
a) What is the approximate value of the third quartile (Q3 ), correct to 2 decimal places.
b)What is the approximate value of the variance, correct to the nearest whole number
Answer:
a) The third quartile Q₃ = 56.45
b) Variance [tex]\mathbf{ \sigma^2 =2633.31}[/tex]
Step-by-step explanation:
Given that :
[tex]Q_1[/tex] = 30.8
Median [tex]Q_2[/tex] = 48.5
Mean = 42
a) The mean is less than median; thus the expression showing the coefficient of skewness is given by the formula :
[tex]SK = \dfrac{Q_3+Q_1-2Q_2}{Q_3-Q_1}[/tex]
[tex]-0.38 = \dfrac{Q_3+30.8-2(48.5)}{Q_3-30.8}[/tex]
[tex]-0.38Q_3 + 11.704 = Q_3 +30.8 - 97[/tex]
[tex]1.38Q_3 = 77.904[/tex]
Divide both sides by 1.38
[tex]Q_3 = 56.45[/tex]
b) The objective here is to determine the approximate value of the variance;
Using the relation
[tex]SK_p = \dfrac{Mean- (3*Median-2 *Mean) }{\sigma}[/tex]
[tex]-0.38= \dfrac{42- (3 *48.5-2*42) }{\sigma}[/tex]
[tex]-0.38= \dfrac{(-19.5) }{\sigma}[/tex]
[tex]-0.38* \sigma = {(-19.5) }{}[/tex]
[tex]\sigma =\dfrac {(-19.5) }{-0.38 }[/tex]
[tex]\sigma =51.32[/tex]
Variance = [tex]\sigma^2 =51.32^2[/tex]
[tex]\mathbf{ \sigma^2 =2633.31}[/tex]
About 19% of the population of a large country is hopelessly romantic. If two people are randomly selected, what is the probability both are hopelessly romantic? What is the probability at least one is hopelessly romantic?
(a) The probability that both will be hopelessly romantic is
0.0361.
(Round to four decimal places as needed.)
(b) The probability that at least one person is hopelessly romantic is
0.3439.
(Round to four decimal places as needed.)
Answer:
a)
The probability that both will be hopelessly romantic is
P(X = 2) = 0.0361
b)
The probability that at least one person is hopelessly romantic is
P( X>1) = 0.3439
Step-by-step explanation:
a)
Given data population proportion 'p' = 19% =0.19
q = 1-p = 1- 0.19 =0.81
Given two people are randomly selected
Given n = 2
Let 'X' be the random variable in binomial distribution
[tex]P(X=r) =n_{C_{r} } p^{r} q^{n-r}[/tex]
The probability that both will be hopelessly romantic is
[tex]P(X= 2) =2_{C_{2} } (0.19)^{2} (0.81)^{2-2}[/tex]
P(X = 2) = 1 × 0.0361
The probability that both will be hopelessly romantic is
P(X = 2) = 0.0361
b)
The probability that at least one person is hopelessly romantic is
P( X>1) = 1-P(x<1)
= 1 - ( p(x =0)
= [tex]1- 2_{C_{0} } (0.19)^{0} (0.81)^{2-0}[/tex]
= 1 - (0.81)²
= 1 -0.6561
= 0.3439
The probability that at least one person is hopelessly romantic is
P( X>1) = 0.3439
A high tech company operates a satellite which can measure the size of features on the surface of the earth. They use this technology to measure a particular rectangular field and find it's length to be 311 \pm± 1.89 (in meters) and it's width to be 354 \pm± 1.39 (in meters). They plan to report the area of the field as A\pm\Delta AA ± Δ A in units of acres. (1 acre = 4840 square yards & 1 meter = 1.094 yards) What is \Delta AΔ A?
Answer:
1 acre
Step-by-step explanation:
