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Related Questions
A university found that 20% of its students withdraw without completing the introductory statistics course. Assume that 20 students registered for the course. (Round your answers to four decimal places.) (a) Compute the probability that 2 or fewer will withdraw. (b) Compute the probability that exactly 4 will withdraw. (c) Compute the probability that more than 3 will withdraw. (d) Compute the expected number of withdrawals.
Answers
Answer:
(a) Probability that 2 or fewer will withdraw is 0.2061.
(b) Probability that exactly 4 will withdraw is 0.2182.
(c) Probability that more than 3 will withdraw is 0.5886.
(d) The expected number of withdrawals is 4.
Step-by-step explanation:
We are given that a university found that 20% of its students withdraw without completing the introductory statistics course.
Assume that 20 students registered for the course.
The above situation can be represented through binomial distribution;
[tex]P(X =r) = \binom{n}{r} \times p^{r} \times (1-p)^{n-r};x=0,1,2,3,......[/tex]
where, n = number of trials (samples) taken = 20 students
r = number of success
p = probability of success which in our question is probability
that students withdraw without completing the introductory
statistics course, i.e; p = 20%
Let X = Number of students withdraw without completing the introductory statistics course
So, X ~ Binom(n = 20 , p = 0.20)
(a) Probability that 2 or fewer will withdraw is given by = P(X [tex]\leq[/tex] 2)
P(X [tex]\leq[/tex] 2) = P(X = 0) + P(X = 1) + P(X = 2)
= [tex]\binom{20}{0} \times 0.20^{0} \times (1-0.20)^{20-0}+ \binom{20}{1} \times 0.20^{1} \times (1-0.20)^{20-1}+ \binom{20}{2} \times 0.20^{2} \times (1-0.20)^{20-2}[/tex]
= [tex]1 \times1 \times 0.80^{20}+ 20 \times 0.20^{1} \times 0.80^{19}+ 190\times 0.20^{2} \times 0.80^{18}[/tex]
= 0.2061
(b) Probability that exactly 4 will withdraw is given by = P(X = 4)
P(X = 4) = [tex]\binom{20}{4} \times 0.20^{4} \times (1-0.20)^{20-4}[/tex]
= [tex]4845\times 0.20^{4} \times 0.80^{16}[/tex]
= 0.2182
(c) Probability that more than 3 will withdraw is given by = P(X > 3)
P(X > 3) = 1 - P(X [tex]\leq[/tex] 3) = 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3)
= [tex]1-(\binom{20}{0} \times 0.20^{0} \times (1-0.20)^{20-0}+ \binom{20}{1} \times 0.20^{1} \times (1-0.20)^{20-1}+ \binom{20}{2} \times 0.20^{2} \times (1-0.20)^{20-2}+\binom{20}{3} \times 0.20^{3} \times (1-0.20)^{20-3})[/tex]
= [tex]1-(1 \times1 \times 0.80^{20}+ 20 \times 0.20^{1} \times 0.80^{19}+ 190\times 0.20^{2} \times 0.80^{18}+1140\times 0.20^{3} \times 0.80^{17})[/tex]
= 1 - 0.4114 = 0.5886
(d) The expected number of withdrawals is given by;
E(X) = [tex]n\times p[/tex]
= [tex]20 \times 0.20[/tex] = 4 withdrawals
Determine which consecutive integers do not have a real zero of f(x) = x^3 + 9x^2 + 8x – 5 between them.
A.) (–8, –7)
B.) (4, 5)
C.) (0, 1)
D.) (–2, –1)
Answers
Answer:
Option B (4,5)
Step-by-step explanation:
The integers (4, 5) do not have real zero.
What is zero of a function?Knowing what zeros represent can assist us in determining when and how to locate the zeros of functions given their expressions and a function's graph. The value of x when the function itself reaches zero is typically referred to as a function's zero.
A function's zero can take many different forms, but as long as they have a y-value of zero, we will consider them to be the function's zero.
Given Expression
f(x) = x³ + 9x² + 8x - 5
to find which is not a real zero,
condition of real zero is for any function f(a , b) if f(a).f(b) < 0 the function have at least a zero.
1: (-8, -7)
f(-8).f(-7) = [(-8)³ + 9(-8)² + 8(-8) - 5][(-7³) + 9(-7)² + 8(-7) - 5]
f(-8).f(-7) = (-5)(37)
f(-8).f(-7) = -185 < 0 points have at least a zero
2: (4, 5)
f(4).f(5) = [(4)³ + 9(4)² + 8(4) - 5][(5³) + 9(5)² + 8(5) - 5]
f(4).f(5) = 235 x 385
f(4).f(5) = 94,475 > 0
points do not have any zeros
3: (0, 1)
f(0).f(1) = [(0)³ + 9(0)² + 8(0) - 5][(1³) + 9(1)² + 8(1) - 5]
f(0).f(1) = -5 x 13
f(0).f(1) = -65 < 0
points have a zero
4: (–2, –1)
f(-2).f(-1) = [(-2)³ + 9(-2)² + 8(-2) - 5][(-1³) + 9(-1)² + 8(-1) - 5]
f(-2).f(-1) = 7 x (-5)
f(-2).f(-1) = -35 < 0
points have a zero
Hence only point (4, 5) do not have a zero.
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don't know if my answer is right
Answers
Answer:
168
Step-by-step explanation:
SA= 2B + hp
h=9
p=16
B= 1/2 bh
B= 1/2 6(4)
B=12 x 2 = 24
9 x 16= 144
144+24= 168
BRAINLIEST really needed!!
A teacher of statistics wants to know if a new teaching methodology that includes IT is efficient in terms of increased average score. He took a class with old methodology and a class with new methodology for samples and gave a same test. Open the file by clicking the file name above. Once you open the file and run Excel, you need not open it again. What is Ha? Find it from Excel output that you generate.
a) 0.62.
b) 0.5.
c) 0.31.
d) -0.5.
Answers
Answer:
The answer is 0.31
Step-by-step explanation:
Old Method New Method .
Mean 73.5625 Mean 75.70588
Standard Error 3.143736 Standard Error 2.923994
Median 72 Median 75
Mode 90 Mode 64
Standard deviation 12.57494 Standard deviation 12.05594
Sample Variance 158.1292 Sample Variance 145.3456
Kurtosis -1.14544 Kurtosis -0.76646
Skewness 0.171025 Skewness 0.091008
Range 39 Range 41
Minimum 55 Minimum 56
Maximum 94 Maximum 97
Sum 1177 Sum 1287
Count 16 Count 17
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: μNew< μOld
Alternative hypothesis: μNew > μOld
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the mean difference between sample means is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a two-sample t-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
[tex]SE=\sqrt{\frac{S_1^2}{n_1} +\frac{S_2^2}{n_2} } \\\\SE=4.29[/tex]
DF = 31
[tex]t = \frac{(x_1-x_2)-d}{SE} \\\\t = - 0.4997[/tex]
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between population means, and SE is the standard error.
The observed difference in sample means produced a t statistic of - 0.499. We use the t Distribution Calculator to find P(t < - 0.499) = 0.311
Therefore, the P-value in this analysis is 0.311.
Interpret results. Since the P-value (0.311) is greater than the significance level (0.05), we cannot reject the null hypothesis.
From the above test we do have sufficient evidence in the favor of the claim that new method is efficient than the old method.
if u dont know dont worry about it
Answers
Answer:
4/15
Step-by-step explanation:
The total number of spins completed is 6+8+7+9 = 30
The letter B came up 8 times
P(B) = number of B's over total
P(B) = 8/30 = 4/15
The moon has a diameter of approximately 2,200 miles. If the circumference of a circle can be found using the formula C = πd, what is the circumference of the moon? (Use 3.14 for π)
Answers
Answer:6908 (miles) ^2
Step-by-step explanation:
diameter=2200 miles
π=3.14
Circumference=π x diameter
Circumference=3.14 x 2200
Circumference=6908 (miles)^2
Answer:
The circumference is 6908 miles.
Step-by-step explanation:
so your answer is B.
Find the mean, median, mode and range for each set of data. Calculator usage is encouraged!
1. 23, 87, 19, 34, 37, 87, 81, 5, 14, 100, 26 Please help thank you!
Answers
Answer:
mean: 46.63636
median: 34
mode: 87
range:95
How To:
Step 1 : To find Mean
Average = ( 1 + 5 + 5 + 7 + 8 + 10 ) / 6
=36 / 6
Mean = 6
Step 2 : To find Median
Middle value = ( 5 + 7 ) / 2
= 12 / 2
Median = 6
Step 3 : To find Mode
Mode = 5 (The number with more repetition, here 5 is repeated two times)
Step 4 : To find Range
Range = Largest number - Smallest number
= 10-1
= 9
Range = 9
Answer:
Mean: 46.6
Mode: 87
Median: 34
Range: 95
Step-by-step explanation:
Mean: (finding the average)
Median: (the middle number of the data set)
Mode: (the most number repeated from the data set)
Range: (is the difference between the highest value and the lowest value)
first arrange the following data set.
23, 87, 19, 34, 37, 87, 81, 5, 14, 100, 26
so:
5, 14, 19, 23, 26, 34, 37, 81, 87, 87, 100
Lets us first find the mean by adding up all the numbers and dividing it by the amount of numbers in the data set.
Mean: 5 + 14 + 19 + 23 + 26 + 34 + 37 + 81 + 87 + 87 + 100 = 513/11 = 46.6
Mode: 87
Median: 34
Range: 100 - 5 = 95
the length of a rectangle is 4 unit less than the width. which expression represents the perimeter of the rectangle
Answers
Answer:
Length: 11
Width: 5
Step-by-step explanation:
Let W = width
Let L = length
Length is 4 less than 3 times the width ==> L = 3*W - 4
Let P = Perimeter = 2*W + 2*L
Perimeter is 22 more than twice the width ==> P = 2*W + 22
Setting the 2 expressions for the perimeter equal to each other gives
2*W + 2*L = 2*W + 22
2*L = 22
L = 11
So 11 = 3*W - 4
3*W = 15
W = 5
The length is 11 and the width is 5
Check: 3*W - 4 = 11 = Length
Perimeter = 32 = 22 more than 2*5 = 10
True or false
Writing a check on an account with insufficient funds is allowed under certain conditions?
Answers
Alex and Annie each have 3 boxes of crayons. each box has 10 crayons. how many crayons do Alex and Annie have in all?
Answers
Answer:
60
Step-by-step explanation:
they each have 3 boxes, so you can multiply 3 by 2 to get 6. if each box has 10 crayons, then multiply 6 by 10 to get 60.
The total number of crayons that Alex and Annie have in all will be 30 crayons.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Alex and Annie each have 3 boxes of crayons. Each box has 10 crayons. Then the total number of crayons is given as,
Total = 3 x 10
Total = 30
The total number of crayons that Alex and Annie have in all will be 30 crayons.
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what kind of novel is nutshell?
Answers
Answer:
i dont know what is it
den
if a line is perpendicular to y=-2/3x+2, will it be perpendicular to 2x+3y=12?
Answers
Answer:
3x + 2y = -2
Step-by-step explanation:
Given Equation is − 2 x + 3 y = 12
3 y = 2 x + 12
y = ( 2 /3 ) y + 12
Slope of this line is m = 2/ 3
Slope of Line A m a = 2
Slope of Line B m b = 2/ 3
Slope of Line C m c = − ( 2 /3 )
Slope of Line D m d = − ( 3 /2 )
since m d = − 1 /m , D is perpendicular to the given line
BRAINLIEST ASAP! LENGTH OF AC?
Answers
Answer:
2.33 units
Step-by-step explanation:
[tex]\tan 25\degree =\frac{AC}{5}\\\\0.46630 = \frac{AC}{5}\\\\AC = 0.46630 \times 5\\AC =2.3315\\AC = 2.33 \: units[/tex]
Pls answer this question I give brainliest thank you! Number 2
Answers
Answer:
Step-by-step explanation:
Answer:
D. 625
Step-by-step explanation:
If the side length for each block is 2 1/2 then two blocks together make 5 so 4 blocks going up makes the height 10 and two blocks for the width make 5 and the 5 blocks on the bottom going across for length make 12 1/2 and 5*10*12 1/2= 625
A store sells gift cards in preset amounts. You can purchase gift cards for $20 or $30. You have spent $680 on gift cards. Write an equation in standard form to represent this situation. What are three combinations of gift cards you could have purchased?
Let x be the number of gift cards for $20, and let y be the number of gift cards for $30. Write an equation in standard form to represent this situation
Answers
Answer:
20x + 30y = 680
Step-by-step explanation:
Give me a good rating please!
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The equation represents the number of $20 and $30 gift cards bought.
20x + 30y = 680
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
Number of gift cards for $20 = x
Number of gift cards for $30 = y
Total amount spend on gift card = $680
The equation represents the number of $20 and $30 gift cards bought.
20x + 30y = 680
Thus,
The equation represents the number of $20 and $30 gift cards bought.
20x + 30y = 680
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At Silver Gym, membership is $35 per month, and personal training sessions are $30 each. At Fit Factor,
membership is $85 per month, and personal training sessions are $20 each. In one month, how many
personal training sessions would Sarah have to buy to make the total cost at the two gyms equal?
Sarah would have to buy
equal.
personal training sessions to make the total cost at the two gyms
Answers
Answer:
5 sessions each
Step-by-step explanation:
Let the personal training sessions be x.
Then at Silver Gym Sarah would spend:
35 + 30xAnd at Fit Factor she would spend:
85 + 20xSince total costs are same, the amounts will be equal:
35+30x = 85 + 20x30x - 20x = 85 - 3510 x = 50x= 50/10x= 5So Sarah would buy 5 training sessions for each of the gyms.
And she would spend $185 at each.
The number of cars sold at a dealership over several weeks is given below.
14, 23, 31, 29, 33
What is the standard deviation for this set of population data?
Standard deviation: Sigma = StartRoot StartFraction (x 1 minus mu) squared + (x 2 minus mu) squared + ellipsis + (x N minus mu) squared Over N EndFraction EndRoot
6.9
12.4
15.4
47.2
Answers
Answer:
A. 6.9
Step-by-step explanation:
Edge 2020
The standard deviation for the set of population data given in the question is 6.9
How to determine the meanData = 14, 23, 31, 29, 33Number of data (n) = 5Summation of data = 14 + 23 + 31 + 29 + 33 = 130Mean (μ) =?Mean = summation of data / number
μ = 130 / 5
μ = 26
How to determine the standard deviationData = 14, 23, 31, 29, 33Mean (μ) = 26Number of data (n) = 5Standard deviation (σ) =?σ = √[[(x₁ - μ)² + (x₂ - μ)² + (x₃ - μ)² + (x₄ - μ)² + (x₅ - μ)²] / n]
σ = √[[(14 - 26)² + (23 - 26)² + (31 - 26)² + (29 - 26)² + (33 - 26)²] / 5]
σ = √[236 / 5}
σ = 6.9
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PLEASE HELP MEE :)
40 POINTS
WILL MARKE BRAINLIEST
Which would be the best name for a
function that takes the time spent
heating a kettle and returns the
temperature of the kettle?
Both of possible:-))
Answers
answer: Time (distance)
*assuming the dependent variable is in brackets
Which best describes a fraction?
» A fraction is the denominator divided by the numerator.
» A fraction is the numerator divided by the denominator.
1.) A fraction is the numerator multiplied by the denominator.
()) A fraction is the denominator multiplied by the numerator.
Answers
A fraction is the numerator divided by the denominator best describes a fraction.
Given,
- A fraction is the denominator divided by the numerator.
- A fraction is the numerator divided by the denominator.
- A fraction is the numerator multiplied by the denominator.
- A fraction is the denominator multiplied by the numerator.
We need to find which option best describes a fraction.
What is a fraction?A fraction has two parts: Numerator and Denominator.
It is in the form of Numerator / Denominator.
We have,
- A fraction is the denominator divided by the numerator.
It is written as denominator / Numerator.
- A fraction is the numerator divided by the denominator.
It is written as Numerator / Denominator
- A fraction is the numerator multiplied by the denominator.
It is written as Numerator x Denominator.
- A fraction is the denominator multiplied by the numerator.
It can be written as Denominator x Numerator.
We see that the option "a fraction is a numerator divided by the denominator" is the correct answer.
Thus A fraction is the numerator divided by the denominator best describes a fraction.
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A bag contains 3 red marbles and 6 blue marbles. A second bag contains 6 green marbles and 4 yellow marbles. You choose a marble from bag A and then a marble from bag B, what would be the probability of selecting one blue marble and one yellow marble?
Answers
Answer:
4/15
Step-by-step explanation:
Bag A
3 red marbles and 6 blue marbles. = 9 marbles
P(blue) = blue/total =6/9 = 2/3
Bag B
6 green marbles and 4 yellow marbles. = 10 marbles
P(yellow) = yellow/total=4/10 = 2/5
P(blue,yellow) = 2/3 * 2/5 = 4/15
A random sample of n = 45 observations from a quantitative population produced a mean x = 2.5 and a standard deviation s = 0.26. Your research objective is to show that the population mean μ exceeds 2.4. Calculate the p-value for the test statistic z = 2.58. (Round your answer to four decimal places.)
Answers
Answer:
P-value (t=2.58) = 0.0066.
Note: as we are using the sample standard deviation, a t-statistic is appropiate instead os a z-statistic.
As the P-value (0.0066) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the population mean μ exceeds 2.4.
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the population mean μ exceeds 2.4.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=2.4\\\\H_a:\mu> 2.4[/tex]
The significance level is 0.05.
The sample has a size n=45.
The sample mean is M=2.5.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=0.26.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.26}{\sqrt{45}}=0.0388[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{2.5-2.4}{0.0388}=\dfrac{0.1}{0.0388}=2.58[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=45-1=44[/tex]
This test is a right-tailed test, with 44 degrees of freedom and t=2.58, so the P-value for this test is calculated as (using a t-table):
[tex]P-value=P(t>2.5801)=0.0066[/tex]
As the P-value (0.0066) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the population mean μ exceeds 2.4.
Solve by the method of your choice 6x-2y= 16, 5x+y=24
Answers
(5x+y=24)*2
__________
6x-2y=16
10+2y=48 Add the equations”+”
—-
16x=64
X=4
So y=1
A 5000-seat theater has tickets for sale at $28 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $153 comma 200?
Answers
Answer:
Let's denote:
x: number of ticket 28$
y: number of ticket 40$
Then, we have:
x + y =5000
28x + 40y = 153200
=> 28(5000 - y) + 40y = 153200
=> 12y = 153200 - 140000
=> 12y =13200
=> y = 1100 (ticket 40$)
=> x = 5000 - 1100 = 3900 (ticket 28$)
Which one of the following is not a fixed cost in owning a vehicle?
1 point
Gas
Insurance
Registration
Tags
Answers
Step-by-step explanation:
tags is not a fixed cost
Solve this system of equations.
2x + 6y = −6,
4x − 3y = −12
What is the solution to the system of equations?
Answers
Answer:
x = -3 and y = 0
Step-by-step explanation:
It would be more direct to apply elimination in this problem, rather than substitution:
2x + 6y = -6 ⇒ 2x + 6y = -6 ⇒ 10x = - 30
+ 2(4x - 3y = -12) + 8x - 6y = -24
Now let us solve for x through simply algebra:
10x = -30,
x = -3
Substitute this value of x into the first equation to get the value of y:
2( -3 ) + 6y = -6,
-6 + 6y = -6,
6y = 0,
y = 0
Answer:
-3 and 0
Step-by-step explanation:
i hope this helps :)
What’s the correct answer for this?
Answers
Answer:
c
Step-by-step explanation:
What can be determined by looking at the factored form of the polynomial f(x) = (x + 7)(x - 2) ?
A
The graph of the polynomial has zeros at (0,-7) and (0,2)
В
The graph of the polynomial has zeros at (7,0) and (-2,0)
C
The graph of the polynomial has zeros at (-7,0) and (2,0)
D
The graph of the polynomial has zeros at (0,7) and (0,-2)
Answers
Answer:
C . The graph of the polynomial has zeros at (-7,0) and (2,0)
Step-by-step explanation:
f(x) = (x + 7)(x - 2)
Zero's obtained:
(x+7)(x-2) = 0x+7 = 0 ⇒ x = -7x-2 = 0 ⇒ x = 2Coordinates:
(-7, 0) and (2, 0)Correct answer choice is:
C . The graph of the polynomial has zeros at (-7,0) and (2,0)
BRAINLIST+11 Pts!!!
Jim just found a job with a take-home pay of $950 per month. He must pay $400 for rent and $100 for groceries each month. He also spends $100 per month on transportation. If he budgets $50 each month for clothing, $100 for restaurants and $50 for everything else, how long will it take him to save $1,800?
Answers
Answer:12 months
Step-by-step explanation:
400+400=800 so 950-800=150 1800/150=12
please help me. how do you do this?
Answers
Explanation:
Each "square" in the table has two lines. The top line matches the label of the degree of the polynomial. The bottom line matches the name for the number of terms.
Where one or the other is missing, fill it in according to the description above.
For example, the "square" in the lower right corner will say ...
quartic
trinomial
The number of new contributors to a public radio station's annual fund drive over the last ten years is 63, 58, 61, 72, 98, 103, 121, 147, 163, 198 Using Microsoft Excel, develop a linear regression model that predicts the number of new contributors. Explain the slope of this model. Based on this model, how many new contributors would you predict for the following year?
Answers
Answer:
The number of potential members predicted in next year's estimate becomes 193. The further explanation is given below.
Step-by-step explanation:
The slope of the model,
m = 15.345
c = 24
After comparing with the equation,
⇒ [tex]y=mx+c[/tex]
we get,
⇒ [tex]=15.345x + 24[/tex]
The slope seems to be a positive value which also means that another always improves this as component decreases. Which ensures that perhaps the number of contributors rising as time went by.
So that the above is the right answer.
