Complete Question
Polymer composite materials have gained popularity because they have high strength to weight ratios and are relatively easy and inexpensive to manufacture. However, their nondegradable nature has prompted development of environmentally friendly composites using natural materials. An article reported that for a sample of 10 specimens with 2% fiber content, the sample mean tensile strength (MPa) was 51.1 and the sample standard deviation was 1.2. Suppose the true average strength for 0% fibers (pure cellulose) is known to be 48 MPa. Does the data provide compelling evidence for concluding that true average strength for the WSF/cellulose composite exceeds this value? (Use α = 0.05.)
t=8.169
P-value= ?
Answer:
a) [tex]P-value=0[/tex]
b) Hence,We FAil to reject the alternative hypothesis and accept that the true average strength for the WSF/ cellulose composite exceeds 48 MPa.
Step-by-step explanation:
From the question we are told that:
Sample size [tex]n=10[/tex]
Mean [tex]\=x= 51.3[/tex]
Standard deviation [tex]\sigma=1.2[/tex]
Significance level is taken as [tex]\alpha=0.05[/tex]
t test statistics
[tex]t=8.169[/tex]
Therefore
[tex]P-Value=P(t>8.169)[/tex]
Critical point
[tex]t_{\alpha,df}[/tex]
[tex]\alpha=0.05[/tex]
[tex]df=10-1=>9[/tex]
Therefore
P-value from T distribution table
[tex]P-value=0[/tex]
Conclusion
[tex]P-value (0)< \alpha(0.05)[/tex]
We Reject the Null Hypothesis [tex]H_0[/tex]
Hence,We FAil to reject the alternative hypothesis and accept that the true average strength for the WSF/ cellulose composite exceeds 48 MPa.
Two cards are selected with replacement from a standard deck of 52 cards. Find the probability of selecting a heart and then selecting a diamond.
Answer: 50.2 is it
Step-by-step explanation: thats easy
Probability helps us to know the chances of an event occurring. The probability of selecting a heart and then selecting a diamond is 144/2652.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
Given that Two cards are selected with replacement from a standard deck of 52 cards. Therefore, the probability of selecting a heart and then selecting a diamond is,
Probability = (12/52) × (12/51)
Probability = 144/2652
Hence, The probability of selecting a heart and then selecting a diamond is 144/2652.
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Please see the attached picture
Answer:
C.I = (0.259,1.175) -> Fail to Reject H0
Step-by-step explanation:
300-20+100 divided by 4=
Answer:
95
Step-by-step explanation:
300-20=280
280+100=380
380÷4=95
There you go...
Fill in the blank with a number to make the expression a perfect square.
u^2- 18u +
Answer:
u^2- 18u +81 = (u-9)^2
Step-by-step explanation:
u^2- 18u +
Take the u coefficient
-18
Divide by 2
-18/2 = -9
Square it
(-9)^2 = 81
u^2- 18u +81 = (u-9)^2
Answer:
The blank should contain 81
Step-by-step explanation:
E = u^2 - 18u + (-18/2)^2
E = (u^2 - 18u + 9^2)
E = (u - 9)^2
To be perfectly correct what you have there is a perfect square, but you need to subtract out (9/2)^2 to make it a valid statement.
E = (u - 9)^2 - 81
Point A lies outside of plane P. How many planes can be drawn that pass through point A?
A. 0
B. an infinite number
C. 2
D. 1
Answer:
D.
Step-by-step explanation:
.
The number of planes that can be drawn that pass through point A is 1.
How to estimate the number of planes that can be drawn that pass through point A?
A perpendicular line creates an angle of 90° with a line or a plane. If a line exists to be drawn from a point to a line or a plane it can only be one. In this case, a line exists to be drawn through a point A to a plane P. If the line stands to be perpendicular, then it exists only one.
Therefore, the correct answer is option D. 1.
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A lawyer commutes daily from his suburban home to his midtown office. The average time for a one-way trip is 24 minutes, with a standard deviation of 3.8 minutes. Assume the distribution of trip times to be normally distributed.
(a) What is the probability that a trip will take at least ½ hour?
(b) If the office opens at 9:00 A.M. and he leaves his house at 8:45 A.M. daily, what percentage of the time is he late for work?
(c) If he leaves the house at 8:35 A.M. and coffee is served at the office from 8:50 A.M. until 9:00 A.M., what is the probability that he misses coffee?
(d) Find the length of time above which we find the slowest 10% of trips.
(e) Find the probability that 2 of the next 3 trips will take at least one half
1/2 hour.
Answer:
Step-by-step explanation:
a) Probability-Above 30 min = 5.72% = .0572
b) Probability-Above 15 min = 99.11% = .9911
c) *Probability-Between 1 - 59.49% = .4051
d) 19.136 minutes z = -1.28
a) The probability that trip will take at least 1/2 hour will be 0.0606.
b) The percentage of time the lawyer is late for work will be 99.18%.
c) The probability that lawyer misses coffee will be 0.3659.
d) The length of time above which we find the slowest 10% of trips will be 0.5438.
e) The probability that exactly 2 out of 3 trips will take at least one half
1/2 hour is 0.0103.
What do you mean by normal distribution ?
A probability distribution known as a "normal distribution" shows that data are more likely to occur when they are close to the mean than when they are far from the mean.
Let assume the time taken for a one way trip be x .
x ⇒ N( μ , σ ²)
x ⇒ N( 24 , 3.8 ²)
a)
The probability that trip will take at least 1/2 hour or 30 minutes will be :
P ( x ≥ 30)
= P [ (x - μ) / σ ≥ (30 - μ) / σ ]
We know that , (x - μ) / σ = z.
= P [ z ≥ (30 - 24) / 3.8)]
= P [ z ≥ 1.578 ]
= 1 - P [ z ≤ 1.578 ]
Now , using the standard normal table :
P ( x ≥ 30)
= 1 - 0.9394
= 0.0606
b)
The percentage of the time the lawyer is late for work will be :
P ( x ≥ 15)
= P [ z ≥ -2.368 ]
= P [ z ≤ 2.368]
= 0.9918
or
99.18%
c)
The probability that lawyer misses coffee :
P ( 15 < x < 25 ) = P ( x < 25 ) - P ( x < 15)
= P [ z < 0.263] - P ( z < -2.368)
or
= 0.3659
d)
The length of time above which we find the slowest 10% of trips :
P( x ≥ X ) ≤ 0.10
= 0.5438
e)
Let's assume that y represents the number of trips that takes at least half hour.
y ⇒ B ( n , p)
y ⇒ B ( 3 , 0.0606)
So , the probability that exactly 2 out of 3 trips will take at least one half
1/2 hour is :
P ( Y = 2 )
= 3C2 × (0.0606)² × ( 1 - 0.0606)
= 0.0103
Therefore , the answers are :
a) The probability that trip will take at least 1/2 hour will be 0.0606.
b) The percentage of time the lawyer is late for work will be 99.18%.
c) The probability that lawyer misses coffee will be 0.3659.
d) The length of time above which we find the slowest 10% of trips will be 0.5438.
e) The probability that exactly 2 out of 3 trips will take at least one half
1/2 hour is 0.0103.
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Next question
lets keep going
Answer:
U = 67.6 degrees
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos U = adj side / hypotenuse
cos U = sqrt(10)/ sqrt(69)
cos U = sqrt(10/69)
Taking the inverse cos of each side
cos ^-1( cos U) = cos ^-1(sqrt(10/69))
U = 67.62335
To the nearest tenth
U = 67.6 degrees
Step-by-step explanation:
here's the answer to your question
Below is the graph of a polynomial function with real coefficients
(a) The function f is increasing over which intervals? Choose all that apply.
D(-0, -8)
O (-5,-2) O (-8, -2) O (-2,
2) (2,5)
O (5, 0 )
?
(b) The functionfhas local maxima at which x-values? If there is more than one value,
separate them with commas.
(c) What is the sign of the leading coefficient of f?
Select One
(d) Which of the following is a possibility for the degree of f? Choose all that apply.
4
5
6
Please help if you can thank you
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Answer:
(a) (-∞, -8), (-5, -2), (2, 5)
(b) -8, -2, 5
(c) negative
(d) 6
Step-by-step explanation:
(a) The function is increasing on intervals where the graph slopes upward left-to-right. Those are (-∞, -8), (-5, -2), and (2, 5).
__
(b) The local maxima are at the right end of each interval on which the function is increasing: -8, -2, 5.
__
(c) The function opens downward (∩), so has a negative leading coefficient.
__
(d) There are three local maxima and two local minima (left end of an increasing interval), so a total o 5 turning points. The degree of the polynomial is at least one more than this: 6.
An electronic switching device occasionally malfunctions, but the device is considered satisfactory if it makes, on average, no more than 0.20 error per hour. A particular 5-hour period is chosen for testing the device. If no more than 1 error occurs during the time period, the device will be considered satisfactory.
(a) What is the probability that a satisfactory device will be considered unsatisfactory on the basis of the test? Assume a Poisson process.
(b) What is the probability that a device will be accepted as satisfactory when, in fact, the mean number of errors is 0.25? Again, assume a Poisson process.
Solution :
It is given that the device works satisfactorily if it makes an average of no more than [tex]0.2[/tex] errors per hour.
The number of errors thus follows the Poisson distribution.
It is given that in [tex]5[/tex] hours test period, the number of the errors follows is
= [tex]0.2 \times 5[/tex]
= 1 error
Let X = the number of the errors in the [tex]5[/tex] hours
[tex]$X \sim \text{Poisson } (\lambda = 0.2 \times 5 =1)$[/tex]
Now that we want to find the [tex]\text{probability}[/tex] that a [tex]\text{satisfactory device}[/tex] will be misdiagnosed as "[tex]\text{unsatisfactory}[/tex]" on the basis of this test. We know that device will be unsatisfactory if it makes more than [tex]1[/tex] error in the test. So we will determine probability that X is greater than [tex]1[/tex] to get required answer.
So the required probability is :
[tex]P(X>1)[/tex]
[tex]$=1-P(X \leq 1)$[/tex]
[tex]$=1-[P(X=0)+P(X=1)]$[/tex]
[tex]$=1- \left( \frac{e^{-1} 1^0}{0!} + \frac{e^{-1} 1^0}{1!} \right) $[/tex]
[tex]$=1-(2 \times e^{-1})$[/tex]
[tex]$=1-( 2 \times 0.367879)$[/tex]
[tex]$=1-0.735759$[/tex]
[tex]=0.264241[/tex]
So the [tex]\text{probability}[/tex] that the [tex]\text{satisfactory device}[/tex] will be misdiagnosed as "[tex]\text{unsatisfactory}[/tex]" on the basis of the test whose result is 0.264241
please help i need this by tonight
Answer:
The measure of ∠1 and ∠2 is 105° and 75° respectively
Step-by-step explanation:
In the given figure, line a is parallel to line b.
We need to find the measure of angles 1 and 2.
∠2 = 75° (because they form corresponding angles)
We know that, interior angles add up to 180. So,
∠1 +75 = 180
∠1 = 180-75
∠1 = 105°
So, the measure of ∠1 and ∠2 is 105° and 75° respectively.
please help me with geometry
Answer:
A. If the side lengths are the same, then a triangle is not scalene.
Step-by-step explanation:
A triangle can be defined as a two-dimensional shape that comprises three (3) sides, three (3) vertices and three (3) angles.
Simply stated, any polygon with three (3) lengths of sides is a triangle.
In Geometry, a triangle is considered to be the most important shape.
Generally, there are three (3) main types of triangle based on the length of their sides and these include;
I. Equilateral triangle: it has all of its three (3) sides and interior angles equal.
II. Isosceles triangle: it has two (2) of its sides equal in length and two (2) equal angles.
III. Scalene triangle: it has all of its three (3) sides and interior angles different in length and size respectively.
A physical trainer decides to collect data to see if people are actually weight changing weight during the shelter in place. He believes there will not be a meaningful change in weight due to the shelter in place order. He randomly chooses a sample of 30 of his clients. From each client, he records their weight before the shelter in place order, and again 10 days after the order. A summary of the data is below.
The trainer claims, "on average, there is no difference in my clients' weights before and after the shelter in place order." Select the pair of hypotheses that are appropriate for testing this claim.
H0: µd = 0
H1: µd < 0 (claim)
H0: µd = 0 (claim)
H1: µd ≠ 0
H0: µd ≠ 0 (claim)
H1: µd = 0
H0: µd = 0 (claim)
H1: µd > 0
H0: µd = 0
H1: µd > 0 (claim)
H0: µd = 0
H1: µd ≠ 0 (claim)
H0: µd = 0 (claim)
H1: µd < 0
H0: µd ≠ 0
H1: µd = 0 (claim)
b) Select the choice that best describes the nature and direction of a hypothesis test for this claim.
This is a right-tail t-test for µd.
This is a right-tail z-test for µd.
This is a two-tail t-test for µd.
This is a two-tail z-test for µd.
This is a left-tail t-test for µd.
This is a left-tail z-test for µd.
c) Find the standardized test statistic for this hypothesis test. Round your answer to 2 decimal places.
d) Find the P-value for this hypothesis test. Round your answer to 4 decimal places.
e) Using your previous calculations, select the correct decision for this hypothesis test.
Fail to reject the alternative hypothesis.
Reject the alternative hypothesis.
Fail to reject the claim.
Reject the claim.
Fail to reject the null hypothesis.
Reject the null hypothesis.
f) Consider the following statements related to the trainer's claim. Interpret your decision in the context of the problem (ignoring the claim) and interpret them in the context of the claim.
Answer:
H0: µd = 0 (claim)
H1: µd ≠ 0
This is a two-tail t-test for µd
Step-by-step explanation:
This is a paired (dependent) sample test, with its hypothesis is written as :
H0: µd = 0
H1: µd ≠ 0
From the equality sign used in the hypothesis declaration, a not equal to ≠ sign in the alternative hypothesis is used for a two tailed t test
The data isn't attached, however bce the test statistic cannot be obtained. However, the test statistic formular for a paired sample is given as :
T = dbar / (Sd/√n)
dbar = mean of the difference ; Sd = standard deviation of the difference.
A smartphone consumes 4 watts of power when charging. Your power company charges 12 cents per kilowatt hour (kWh). If you leave your smartphone plugged in to the wall outlet for 24 hours, how many cents does this cost
Answer:
[tex]C=1.15cents[/tex]
Step-by-step explanation:
Generally the equation for is mathematically given by
Charge Power P=4watts
Rate r=12cents/hour
Time consumed T=24
Generally
Power consumed by smartphone in 24 hours
[tex]P_t=P*T\\\\P_t=24*4[/tex]
[tex]P_t=0.096kwh[/tex]
Therefore the Cost will be
[tex]C=12*0.096kwh[/tex]
[tex]C=1.15cents[/tex]
A coffee pot holds 3 3/4 quarts of coffee. How much is this in cups
Answer:
15 cups
Step-by-step explanation:
1 quart = 4 cups
3.75 quarts = (3.75 * 4) cups
3.75 quarts = 15 cups
3.75 quarts mean 15 cups
What is unitary method?The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
Given
1 quart = 4 cups
3.75 quarts = (3.75 * 4) cups
3.75 quarts = 15 cups
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How do you Graph 3x+4y< -16 on the coordinate plane
9514 1404 393
Answer:
see attached
Step-by-step explanation:
Take note of the inequality symbol. It is < (not ≤), so the "equal to" case is not included. That means the line 3x+4y=-16 is not part of the solution set. That boundary line is graphed as a dashed line.
Take note of where the variables are in relation to the inequality symbol. Both are on the "less than" side, so the shading of the graph will be where the values of x and y are less than those on the boundary line. The boundary line has a negative slope, so the values less than those on the boundary are to the left and below the line.
Plot the dashed boundary line 3x +4y = -16, or y = -3/4x -4, and shade the area below and to its left.
Find m
a 24.7
b 79.2
c 68.3
d 57.4
e 46.5
f 80.1
g 35.6
Answer:
68.3 degrees
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan I = opp side / adj side
tan I = sqrt(82) / sqrt(13)
tan I = sqrt(82/13)
Taking the inverse tan of each side
tan ^-1 ( tan I) = tan ^-1( sqrt(82/13))
I = 68.2892
Rounding to the nearest tenth
I = 68.3 degrees
what’s the value of x? and what’s the measure of angel JHK?
Answer:
x = 14
JHK = 21
Step-by-step explanation:
The angles are vertical angles and vertical angles are equal
3x-21 = x+7
Subtract x from each side
3x-x -21 = x+7-x
2x-21 = 7
Add 21 to each side
2x-21+21 = 7+21
2x = 28
Divide by 2
2x/2 =28/2
x = 14
JHK = 3x-21 = 3(14) -21 = 42-21 = 21
Answer:
Because ∠GHI and ∠JHK are vertical angles, they're congruent. Therefore, set their angle measures equal to each other & solve for x.
[tex]x+7=3x-21\\x-3x=-7-21\\-2x=-28\\x=\frac{-28}{-2} =14\°[/tex]
Substitute in the value of x to find ∠JHK:
[tex]3x-21=3(14)-21=42-21=21\°[/tex]
The graph below shows two polynomial functions, f(x) and g(x): Graph of f of x equals x squared minus 2 x plus 1. Graph of g of x equals x cubed plus 1 Which of the following statements is true about the graph above? (4 points) g(x) is an even degree polynomial with a positive leading coefficient. g(x) is an odd degree polynomial with a negative leading coefficient. f(x) is an even degree polynomial with a positive leading coefficient. f(x) is an odd degree polynomial with a negative leading coefficient.
9514 1404 393
Answer:
(c) f(x) is an even degree polynomial with a positive leading coefficient.
Step-by-step explanation:
The leading terms of the two functions are ...
f(x): x² (even degree, positive coefficient: 1)
g(x): x³ (odd degree, positive coefficient: 1)
Then it is true that ...
f(x) is an even degree polynomial with a positive leading coefficient
If 25 burgers feed 15 kids how many burgers would feed 55 kids
Answer:
1375
Step-by-step explanation:
Please help!! Given the recursive formula shown, what are the first 4 terms of the sequence?
Answer:
C
Step-by-step explanation:
the fibrin definition tells us that the first term of the sequence a1 = 6
so, B is out.
and for every following term we always add 7 to every previous term to create the next one.
so, when I add 7 to 6, what is my second term in the sequence ? 7+6 = 13
not 42, not -7
therefore, only C is correct.
and 13+7 = 20
and 20+7 = 27
it all fits
For a sample variance of n = 36 that has a sample variance of 1,296, what is the estimated error for the sample?
Answer:
6
Step-by-step explanation:
Given :
Sample size, n = 36
Sample variance, s² = 1296
The estimated standard error can be obtained using the relation :
Standard Error, S. E = standard deviation / √n
Standard deviation, s = √1296 = 36
S.E = 36/√36
S.E = 36/6
S.E = 6
Hence, estimated standard error = 6
give me a answer, pls
Answer:
C
Step-by-step explanation:
evaluate (-1)^6-4^0+(3/7)^0
Answer:
The answer is 1
.............
please mark this answer as brainlist
PLS HELP
Which of the following is the correct notation for the complex number 76+√-49
A) 76 − 7i
B) 7i + 76
C) 76 + 7i
D) 76+i√49
Answer:
C. 76 + 7i
Step-by-step explanation:
49 squared is 7 and since it's negative, it is an imaginary number. Therefore, it is 7i. Which leaves C to be the correct option.
Can someone let me know if this is right? Show work.
Answer:
I'd be estimatining the answer between 29-31.
Draw a line of best fit. It will be easier to make the estimation.
PLEASEEEE HELP
In the diagram, AABC-ADEC What is the value of x?
Similar triangles are proportional, meaning one will be a factor larger or smaller than the other. This factor will be the same for all of the sides. So, we can say that one corresponding pair of sides is equal to another corresponding pair of sides.
BA / ED = AC / CD
42 / 6 = (64 - x) / (x)
6(64 - x) = 42(x)
384 - 6x = 42x
384 = 48x
x = 8
Hope this helps!
the length of a rectangle is 4 meters longer than the width. if the area is 22 square meters , find the rectangle dimension
Let breadth be x
Length=x+4We know
[tex]\boxed{\sf Area_{(Rectangle)}=Length\times Breadth}[/tex]
[tex]\\ \sf\longmapsto x(x+4)=22[/tex]
[tex]\\ \sf\longmapsto x^2+4x=22[/tex]
[tex]\\ \sf\longmapsto x^2+4x-22=0[/tex]
By solving[tex]\\ \sf\longmapsto x=-2\pm\sqrt{26}[/tex]
It doesnot have any real roots
A woman is 42years old. Her daughter is 1/3 of her age. Three years ago the sum of her age was
Answer:
50
Step-by-step explanation:
So we know that 42/3=14.
3 years before was:
14-3=11
42-3=39
The sum of 11+39 is 50
It is estimated that 75% of all young adults between the ages of 18-35 do not have a landline in their homes and only use a cell phone at home.
(a) On average, how many young adults do not own a landline in a random sample of 100?
(b) What is the standard deviation of probability of young adults who do not own a landline in a simple random sample of 100?
(c) What is the proportion of young adults who do not own a landline?
(d) What is the probability that no one in a simple random sample of 100 young adults owns a landline?
(e) What is the probability that everyone in a simple random sample of 100 young adults owns a landline?
(f) What is the distribution of the number of young adults in a sample of 100 who do not own a landline?
(g) What is the probability that exactly half the young adults in a simple random sample of 100 do not own a landline?
Answer:
a) 75
b) 4.33
c) 0.75
d) [tex]3.2 \times 10^{-13}[/tex] probability that no one in a simple random sample of 100 young adults owns a landline
e) [tex]6.2 \times 10^{-61}[/tex] probability that everyone in a simple random sample of 100 young adults owns a landline.
f) Binomial, with [tex]n = 100, p = 0.75[/tex]
g) [tex]4.5 \times 10^{-8}[/tex] probability that exactly half the young adults in a simple random sample of 100 do not own a landline.
Step-by-step explanation:
For each young adult, there are only two possible outcomes. Either they do not own a landline, or they do. The probability of an young adult not having a landline is independent of any other adult, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [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]
And p is the probability of X happening.
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]
75% of all young adults between the ages of 18-35 do not have a landline in their homes and only use a cell phone at home.
This means that [tex]p = 0.75[/tex]
(a) On average, how many young adults do not own a landline in a random sample of 100?
Sample of 100, so [tex]n = 100[/tex]
[tex]E(X) = np = 100(0.75) = 75[/tex]
(b) What is the standard deviation of probability of young adults who do not own a landline in a simple random sample of 100?
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100(0.75)(0.25)} = 4.33[/tex]
(c) What is the proportion of young adults who do not own a landline?
The estimation, of 75% = 0.75.
(d) What is the probability that no one in a simple random sample of 100 young adults owns a landline?
This is P(X = 100), that is, all do not own. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 100) = C_{100,100}.(0.75)^{100}.(0.25)^{0} = 3.2 \times 10^{-13}[/tex]
[tex]3.2 \times 10^{-13}[/tex] probability that no one in a simple random sample of 100 young adults owns a landline.
(e) What is the probability that everyone in a simple random sample of 100 young adults owns a landline?
This is P(X = 0), that is, all own. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{100,0}.(0.75)^{0}.(0.25)^{100} = 6.2 \times 10^{-61}[/tex]
[tex]6.2 \times 10^{-61}[/tex] probability that everyone in a simple random sample of 100 young adults owns a landline.
(f) What is the distribution of the number of young adults in a sample of 100 who do not own a landline?
Binomial, with [tex]n = 100, p = 0.75[/tex]
(g) What is the probability that exactly half the young adults in a simple random sample of 100 do not own a landline?
This is P(X = 50). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 50) = C_{100,50}.(0.75)^{50}.(0.25)^{50} = 4.5 \times 10^{-8}[/tex]
[tex]4.5 \times 10^{-8}[/tex] probability that exactly half the young adults in a simple random sample of 100 do not own a landline.
What is the probability of throwing a total score of 10 or less with two dice?
hope it helps
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