Answer:
0.5675 = 56.75% probability that at least 22 of the 44 students selected are non-history majors.
Step-by-step explanation:
The students are chosen without replacement from the sample, which means that the hypergeometric distribution is used to solve this question. We are working also with a sample with more than 10 history majors and 10 non-history majors, which mean that the normal approximation can be used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Normal Probability Distribution
Problems of normal 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.
Approximation:
We have to use the mean and the standard deviation of the hypergeometric distribution, that is:
[tex]\mu = \frac{nk}{N}[/tex]
[tex]\sigma = \sqrt{\frac{nk(N-k)(N-n)}{N^2(N-1)}}[/tex]
In this question:
88 + 88 = 176 students, which means that [tex]N = 176[/tex]
88 non-history majors, which means that [tex]k = 88[/tex]
44 students are selected, which means that [tex]n = 44[/tex]
Mean and standard deviation:
[tex]\mu = \frac{44*88}{176} = 22[/tex]
[tex]\sigma = \sqrt{\frac{44*88*(176-88)*(176-44)}{176^2(175-1)}} = 2.88[/tex]
What is the probability that at least 22 of the 44 students selected are non-history majors?
Using continuity correction, as the hypergeometric distribution is discrete and the normal is continuous, 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 - 22}{2.88}[/tex]
[tex]Z = -0.17[/tex]
[tex]Z = -0.17[/tex] has a p-value of 0.4325
1 - 0.4325 = 0.5675
0.5675 = 56.75% probability that at least 22 of the 44 students selected are non-history majors.
The distribution of sample means uses
to measure how much distance
is expected on average between a sample mean and the population mean.
re
o the standard error of M
none of these
the standard deviation of the sample
the standard deviation of the population
< Previous
Next
Answer:
A: the standard error of the mean
Step-by-step explanation:
The most frequently used measure to determine how much difference there is between population mean and sample mean is by calculating the standard deviation of the sampling distribution of the mean. This standard deviation is also referred to as the sew Station.
Make x the subject
y = 4(3x-5)/9
Answer:
3/4y +5/3 = x
Step-by-step explanation:
y = 4(3x-5)/9
Multiply each side by 9
9y = 4(3x-5)/9*9
9y = 4(3x-5)
Divide each side by 4
9/4 y = 4/4 (3x-5)
9/4y = 3x-5
Add 5 to each side
9/4y +5 = 3x-5+5
9/4y +5 = 3x
Divide by 3
9/4 y *1/3 +5/3 = 3x/3
3/4y +5/3 = x
Find the interquartile range for a data set having the five-number summary: 4.6, 14.3, 19.7, 26.1, 31.2
======================================================
Explanation:
The five number summary is the set of these items, in this exact order
Min = smallest valueQ1 = first quartileMedian = middle most numberQ3 = third quartileMax = largest valueSo with the five number summary 4.6, 14.3, 19.7, 26.1, 31.2, we see that
Q1 = 14.3 and Q3 = 26.1
Subtracting these two values gets us the IQR (interquartile range)
IQR = Q3 - Q1
IQR = 26.1 - 14.3
IQR = 11.8
Thank you guys fir the help
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Answer:
A
Step-by-step explanation:
The function f(x) is required in the numerator, eliminating choices C and D.
The restriction is that function g cannot be zero, so we cannot have ...
3x +2 = 0
3x = -2
x = -2/3 . . . . . eliminates choice B; confirms choice A
What is the formula for margin of error?
Answer:
ME = z*s /√n
Step-by-step explanation:
The margin of error is obtained as the product of the critical value of the distribution at a certain α-level and the standard error :
The critical value = Z*
The standard error = standard deviation / √sample size
Standard deviation = s
Sample size = n
Margin of Error = z * s/√n
Fill in the blank with a number to make the expression a perfect squared… W squared + 6w +
Answer:
[tex](a+b)^{2} =a^{2}+2ab+b^{2}[/tex]
[tex](1)w^{2}+2(3)(1)w+3^{2}\\\\=(w+3)^{2}\\\\=(w+3)(w+3)[/tex]
Therefore, [tex]w^{2} +6w+9[/tex] makes a perfect squared.
Given the following matrices, what 3 elements make up the first column of the product matrix DA?
We have to figure out what the product of DA is,
[tex]\begin{bmatrix}-1&2&3\\8&-4&0\\6&7&1\\ \end{bmatrix}\begin{bmatrix}1\\3\\5\\ \end{bmatrix}=\begin{bmatrix}a\\b\\c\\ \end{bmatrix}[/tex]
We know that,
[tex]\begin{bmatrix}a&b&c\\d&e&f\\g&h&i\\\end{bmatrix}\begin{bmatrix}x\\y\\z\\\end{bmatrix}=\begin{bmatrix}ax+by+cz\\dx+ey+fz\\gx+hy+iz\\\end{bmatrix}[/tex]
So,
[tex]a=-1\cdot1+2\cdot3+3\cdot5=-1+6+15=20[/tex]
[tex]b=8\cdot1+(-4)\cdot3+0\cdot5=8-12=-4[/tex]
[tex]c=6\cdot1+7\cdot3+1\cdot5=6+21+5=32[/tex]
So the solution is,
[tex]a,b,c=\boxed{20,-4,32}[/tex]
Hope this helps :)
what is the hcf of 40,50???
Answer:
10
Step-by-step explanation:
10
700,000 rounded to the nearest hundred thousand
Answer:
700,000
Step-by-step explanation:
700,000 is already a 100,000, therefore there is no rounding to do.
Answer:
700,000 is the answer
Step-by-step explanation:
Which is the answer choice to this question?
Answer:
D
Step-by-step explanation:
Graph it
Given two dependent random samples with the following results: Population 1 30 35 23 22 28 39 21 Population 2 45 49 15 34 20 49 36 Use this data to find the 90% confidence interval for the true difference between the population means. Assume that both populations are normally distributed. Step 1 of 4: Find the point estimate for the population mean of the paired differences. Let x1 be the value from Population 1 and x2 be the value from Population 2 and use the formula d=x2−x1 to calculate the paired differences. Round your answer to one decimal place.
Answer:
(-14.8504 ; 0.5644)
Step-by-step explanation:
Given the data:
Population 1 : 30 35 23 22 28 39 21
Population 2: 45 49 15 34 20 49 36
The difference, d = population 1 - population 2
d = -15, -14, 8, -12, 8, -10, -15
The confidence interval, C. I ;
C.I = dbar ± tα/2 * Sd/√n
n = 7
dbar = Σd/ n = - 7.143
Sd = standard deviation of d = 10.495 (using calculator)
tα/2 ; df = 7 - 1 = 6
t(0.10/2,6) = 1.943
Hence,
C.I = - 7.143 ± 1.943 * (10.495/√7)
C.I = - 7.143 ± 7.7074
(-14.8504 ; 0.5644)
a jet flew 2660 miles in 4.75 hours. what is the rate of speed in miles per hour? (the proportion would be 2660:4.75::x:1 set the proportion in fractional form and proceed to fin
Answer: It travels 560 miles per hour.
Step-by-step explanation:
using the proportion,
2660:4.75:x:1
or, 2660:4.75= x:1
or, 2660/4.75 = x/1
or, 2660 = 4.75x
or, x = 2660/4.75
so, x = 560
Answer:
Step-by-step explanation:
Bonjour,
4,75 h = 4+0,75*60 =
4h 45mn = 4*60 + 45 =240+45 => 265mn
265mn -> 2660 miles
1 mn -> 2660/265
60 mn -> (2660*60)/265=> 602,26miles/h
A ball is thrown upward with an initial velocity (v) of 13 meters per second. Suppose that the initial height (h) above the ground is 7 meters. At what time t will the ball hit the ground? The ball is on the ground when S=0. Use the equation S=−5t2+vt+h.
Answer:
the correct answer is, 4
in order for the parallelogram to be rhombus x=?
Answer:
14
Step-by-step explanation:
The angles created by the diagonals of a rhombus add up to 360 meaning each one is 90 degrees
5x+20 = 90
subtract 20 from both sides
5x = 70
divide by 5 on both sides
x=14
dùng tiền gửi ngân hàng trả tiền cho người bán 100.000.000
Answer:
Sorry, i dont know
Step-by-step explanation:
I dont know the answer to this question.....
find the value of the trigonometric ratio
Answer:
ur box cannot be opend repain the window
Step-by-step explanation:
please mark this answer as brainlist
What is the order of rotational symmetry for the figure?
A. 4 or more
B. 2
C. 1
D. 3
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Answer:
C. 1
Step-by-step explanation:
The only rotation that maps the figure to itself is rotation by 360°. The rotational order is 1.
f(x) = 4-x2 and g=(x)=2x+5 what is the value of (f(g(-2))
Answer:
f(g(-2)) = 3
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Functions
Function NotationComposite FunctionsStep-by-step explanation:
Step 1: Define
Identify
f(x) = 4 - x²
g(x) = 2x + 5
Step 2: Find g(-2)
Substitute in x [Function g(x)]: g(-2) = 2(-2) + 5Multiply: g(-2) = -4 + 5Add: g(-2) = 1Step 3: Find f(g(-2))
Substitute in x [Function f(x)]: f(g(-2)) = 4 - (1)²Evaluate exponents: f(g(-2)) = 4 - 1Subtract: f(g(-2)) = 3Find the equation of a line that is perpendicular to x+y=8 and passes through the point (8, 10).
Answer:
Y = -x + 2
Step-by-step explanation:
y = -x + 8
y = 1x + b
10 = 8 + b
b = 2
Answer:
y-y1=m(x-x1)
y-10=8(x-8)
y-10=8x-64
y-10+64-8x
y+54-8x
y-8x+54
AB is tangent to the circle at B. M∠A = 27 and mBC=114 (The figure is not drawn to scale.)
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Answer:
a. x = 60
b. y = 93
Step-by-step explanation:
The relevant relations are ...
external angle A is half the difference of intercepted arcs BC and BDinscribed angle y° is half the measure of intercepted arc CDthe sum of arcs of a circle is 360°__
Using these relations, we have ...
A = (BC -x°)/2
x° = BC -2A = 114° -2(27°)
x° = 60°
__
y° = CD/2 = (360° -BC -BD)/2 = (360° -114° -60°)/2
y° = 93°
Pls if anyone knows the answer that will be greatly appreciated :)
Answers:
The areas from left to right are: 13 m^2, 49 m^2, 24 m^2, 14 m^2
The largest area occurs when the rectangle is a square
===========================================================
Explanation:
The area rectangle formula is base*height, or length*width, whichever you prefer.
From left to right, we have these areas:
1*13 = 13 m^27*7 = 49 m^212*2 = 24 m^25*9 = 14 m^2We get the largest area (49 m^2) when the figure is a square. This happens with any problem in which we have a fixed amount of fencing and we want to max out the area. So it's not particular to this specific problem only.
Why a square? Well an informal way to think of it would be to consider that as one dimension goes up, the other goes down, and vice versa. Think of it like a see-saw. As the examples show, if one dimension is particularly large, then its area wont be as big compared to when the dimensions are closer together. It's only when all dimensions are equal is when we max the area out entirely.
I am sry but he has don wrong calculation the answer is last one 9*5=45m and its the answer.
and the noticiable thing is the larger the shape is the area increases.
A California distributor of sporting equipment expects to sell 10,000 cases of tennis balls during the coming year at a steady rate. Yearly carrying costs (to be computed on the average number of cases in stock during the year) are $10 per case, and the cost of placing an order with the manufacturer is $45. Determine the economic order quantity, that is, the order quantity that minimizes the inventory cost.
The economic order quantity is 300 cases of tennis balls.
The economic order quantity (EOQ) is the minimum quantity that the distributor can order per order to minimize inventory costs.
Data and Calculations:
Sales of tennis balls for the coming year = 10,000 units
Carrying (holding) costs per case = $10
Cost of placing orders with the manufacturer = $45 per order
Economic Order Quantity (EOQ) = square root of (2 * Annual Demand/Sales * Ordering cost)/Carrying cost per case
= square root of (2 * 10,000 * $45)/$10
= square root of 90,000
= 300 cases of tennis balls
This implies that the distributor will place about 33 orders (10,000/300) in the coming year. With each order, the quantity placed is 300 units.
Thus, the economic order quantity that will minimize the California distributor's inventory costs for the year is 300 cases of tennis balls.
Learn more about economic order quantity here: https://brainly.com/question/9068415
There are 36 tables and 7 booths in the family restaurant. Each table seats 4 people. If the restaurant can seat up to 179 people, what is the capacity of each booth?
4 people
5 people
6 people
7 people
Answer:
5 people.
Step-by-step explanation:
First we need to find how many people 36 tables seats. In order to do this, we need to multiply 36 (tables) by 4 (people sitting) to get 144. Now just subtract 144 from 179 to see how many people are left, here we get 35. Since there are 7 booths, we divide 35 by 7 to get 5. Each booth holds 5 people.
(179-36x4)/7=5
If the two lines below are perpendicular and the slope of the red line is
what is the slope of the green line?
A. -2/5
B. 2/5
C. 5/2
D. -5/2
Answer:
B. 2/5
Step-by-step explanation:
Which of the following is the graph of f(x)−1?
Answer:
was assigned with this problem (the reference text is attached):
Which of the following, if included in a student's paper, would NOT be an example of plagiarism?
1. In the game of baseball, which is rather boring, the batter stands on home base (Hughes 1).
2. Baseball is rather surprisingly known as "America's Favorite Pastime."
3. Baseball is "a rather boring sport played between two teams of nine players" (Hughes 1).
4. All of these are plagiarism.
The answer tells that only the third choice is NOT a plagiarism. My question is, why is the first choice a plagiarismwas assigned with this problem (the reference text is attached):
Which of the following, if included in a student's paper, would NOT be an example of plagiarism?
1. In the game of baseball, which is rather boring, the batter stands on home base (Hughes 1).
2. Baseball is rather surprisingly known as "America's Favorite Pastime."
3. Baseball is "a rather boring sport played between two teams of nine players" (Hughes 1).
4. All of these are plagiarism.
The answer tells that only the third choice is NOT a plagiarism. My question is, why is the first choice a plagiarism
Zoe earns 22.50 per hour plus 3% commission on sales. last week she worked 34 hours and made sales totalling 15280. Calculate her pay for the week.
Answer: $1,223.40.
Step-by-step explanation:
Since she earns $22.5 per hour, for 34 hours, she would earn:
$22.5 × 34 = $765
She earn 3% of her sales, therefore find 3% of $15,280:
$15280(3%) = $15280(0.03) = $458.4
Add them together:
$765 + $458.4 = $1223.4
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Answer:
$1,223.40
Step-by-step explanation:
Zoe's total pay is the sum of the products of hours and hourly rate, and sales and commission rate.
Pay = (34 h)($22.50/h) +($15,280)(.03) = $765.00 +458.40
Pay = $1,223.40
Zoe's pay for the week is $1,223.40.
Please help me with this question
Find the difference between each number:
-11 to -3 is +8
-3 to 5 is +8
The difference is 8
Use the following formula:
Bn = b1 + d(b -1)
Answer: bn = -11 + 8( b-1)
London bought snacks for her team's practice. She bought a bag of apples for $2.25
and a 18-pack of juice bottles. The total cost before tax was $9.63. Write and solve an
equation which can be used to determine j, how much each bottle of juice costs?
Answer:
j = $7.38 / 18
Step-by-step explanation:
1. We have to find the total cost of a 18 juice bottles pack
= $ 9.63 - $ 2.25
= $ 7.38
2. To find how much each bottle of juice costs :
j = $ 7.38 / 18 #
A sample of 1700 computer chips revealed that 35% of the chips do not fail in the first 1000 hours of their use. The company's promotional literature claimed that over 32% do not fail in the first 1000 hours of their use. Is there sufficient evidence at the 0.02 level to support the company's claim
Answer:
The p-value of the test is 0.004 < 0.02, which means that there is sufficient evidence at the 0.02 level to support the company's claim.
Step-by-step explanation:
The company's promotional literature claimed that over 32% do not fail in the first 1000 hours of their use.
At the null hypothesis, we test if the proportion is of at most 32%, that is:
[tex]H_0: p \leq 0.32[/tex]
At the alternative hypothesis, we test if the proportion is more than 32%, that is:
[tex]H_1: p > 0.32[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.32 is tested at the null hypothesis:
This means that [tex]\mu = 0.32 \sigma = \sqrt{0.32*0.68}[/tex]
A sample of 1700 computer chips revealed that 35% of the chips do not fail in the first 1000 hours of their use.
This means that [tex]n = 1700, X = 0.35[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.35 - 0.32}{\frac{\sqrt{0.32*0.68}}{\sqrt{1700}}}[/tex]
[tex]z = 2.65[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a sample proportion above 0.35, which is 1 subtracted by the p-value of z = 2.65.
Looking at the z-table, z = 2.65 has a p-value of 0.9960.
1 - 0.9960 = 0.004.
The p-value of the test is 0.004 < 0.02, which means that there is sufficient evidence at the 0.02 level to support the company's claim.
Round to the nearest whole number.
6.4
Answer:
6
Step-by-step explanation:
Therefore, the number 6.4 rounded to the nearest whole number is 6. * If the number you are rounding off is followed by 0,1,2,3,4, round the number down. To find 6.4 rounded to the nearest whole number.
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