Answer:
(A) The probability that a bulb burns between 778 and 834 hours is 0.51118.
(B) The probability that the average light bulb life is at least 820 hours in a random sample of 40 bulbs is 0.00079
Step-by-step explanation:
Let X denote the life time of light bulbs.
It is provided that X follows a normal distribution with mean of 800 hours and standard deviation of 40 hours.
(A)
Compute the probability that a bulb burns between 778 and 834 hours as follows:
[tex]P(778<X<834)=P(\frac{778-800}{40}<\frac{X-\mu}{\sigma}<\frac{834-800}{40})\\\\=P(-0.55<Z<0.85)\\\\=P(Z<0.85)-P(Z<-0.55)\\\\=0.80234-0.29116\\\\=0.51118[/tex]
Thus, the probability that a bulb burns between 778 and 834 hours is 0.51118.
(B)
Compute the probability that the average light bulb life is at least 820 hours in a random sample of 40 bulbs as follows:
[tex]P(\bar X\geq 820)=P(\frac{\bar X-\mu}{\sigma/\sqrt{n}}\geq \frac{820-800}{40/\sqrt{40}})\\\\=P(Z>3.16)\\\\=1-P(Z<3.16)\\\\=1-0.99921\\\\=0.00079[/tex]
Thus, the probability that the average light bulb life is at least 820 hours in a random sample of 40 bulbs is 0.00079
Using the normal distribution and the central limit theorem, it is found that there is a:
a) 0.5111 = 51.11% probability that a bulb burns between 778 and 834 hours.b) 0.0008 = 0.08% probability that the average light bulb life is at least 820 hours.Normal Probability DistributionIn a normal distribution 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]
It 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, which is the percentile of X. By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem:
Mean of 800 hours, hence [tex]\mu = 800[/tex].Standard deviation of 40 hours, hence [tex]\sigma = 40[/tex].Item a:
The probability is the p-value of Z when X = 834 subtracted by the p-value of Z when X = 778, hence:
X = 834:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{834 - 800}{40}[/tex]
[tex]Z = 0.85[/tex]
[tex]Z = 0.85[/tex] has a p-value of 0.8023.
X = 778:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{778 - 800}{40}[/tex]
[tex]Z = -0.55[/tex]
[tex]Z = -0.55[/tex] has a p-value of 0.2912.
0.8023 - 0.2912 = 0.5111
0.5111 = 51.11% probability that a bulb burns between 778 and 834 hours.
Item b:
Sample of 40, hence [tex]n = 40, s = \frac{40}{\sqrt{40}}[/tex].
The probability is 1 subtracted by the p-value of Z when X = 820, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{820 - 800}{\frac{40}{\sqrt{40}}}[/tex]
[tex]Z = 3.16[/tex]
[tex]Z = 3.16[/tex] has a p-value of 0.9992.
1 - 0.9992 = 0.0008
0.0008 = 0.08% probability that the average light bulb life is at least 820 hours.
To learn more about the normal distribution and the central limit theorem, you can take a look at https://brainly.com/question/24663213
A popular podcast poses questions to subscribers at the end of each segment, asking listeners to enter their
responses on a website to join the sample. One of the questions was: "Do you regularly read nonfiction novels?" More
than 45,000 people responded, with 59 percent saying "Yes." Which of the following is true?
A) The sample is too small to draw any conclusion.
B) About 59% of people in the US regularly read nonfiction novels.
C) The poll uses voluntary response, so the results tell us little about the population of all adults.
D) The poll uses a convenience sample, so the results tell us little about the population of all adults.
E) The poll suffers from nonresponse bias, so the results tell us little about the population of all adults.
Answer:
The poll uses voluntary response, so the results tell us little about the population of all adults.
Step-by-step explanation:
I took the test
The one which is true would be; C poll uses voluntary response, so the results tell us little about the population of all adults.
How to calculate confidence interval for population mean for small sample?If the sample size is given to be n < 30, then for finding the confidence interval for mean of population from this small sample, we use t-statistic.
Let the sample mean given as [tex]\overline{x}[/tex] and
The sample standard deviation s, and
The sample size = n, and
The level of significance = [tex]\alpha[/tex]
About 59% of the 45,000 people responded as "Yes" to the question
The sample size is n = 45,000.
The sample proportion is p = 0.59.
The sample selected is a voluntary sample, such that the individuals provided their responses voluntarily. So, the sample is not a true representative of the population.
Thus the results tell us little about the population of all adults because of the large sample size.
The correct option is C poll uses voluntary response, so the results tell us little about the population of all adults.
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Please help it's already late. Will mark brainliest for the first answer.
Answer:
check the first two and the last one
Step-by-step explanation:
you use multiplying/dividing and adding/subtraction to get the answer
10x+45x-13 = 11(5x+6)
55x-13 = 11(5x+6) combine like terms
55x-13 = 55x+66 distribute the 11 to the 5x and 6
-13 = 66 cancel out equal terms on both sides
the statement is false meaning there is equation has no solution
Answer:
check the first two and the last one
Step-by-step explanation:
Select the correct answer.
Which point is a point where the graph of y= (x + 2)(x2 + 4x+3) crosses the x-axis?
Answer:
A. (-3,0)
Step-by-step explanation: you have to set the equation y to zero and than calculate the x
--> (x + 2)(x2 + 4x+3) = 0
--> (x+2) = 0 and (x2 +4x + 3) =0
--> X = -2 and D= (4² - 4*2*3) = 4
X = (-4 + [tex]\sqrt{4}[/tex]) / 2 of X = (-4 + [tex]\sqrt{4}[/tex]) / 2
x= -1 x=-3
Answer:
The answer is (-3,0)
Write in normal form 2.8 x 10⁶ ?
Answer
The answer is2600000
Help plzzz will give brainliest
Answer:
1/3 and false at least i think wait for other answer to make sure it is correct
Step-by-step explanation:
What is An equivalent fraction to 1/6
Answer:
2/12
Step-by-step explanation:
Suppose that you draw one card from a well-shuffled deck of 52 playing cards. What is the probability that the card that you draw is a black 7 or a black 8
The probability that the card that you draw is a black 7 or a black 8 is 1/13
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
P(E) = Number of favorable outcomes / total number of outcomes
So, the probability that the card that you draw is a black 7 = 4/52
So, the probability that the card that you draw is a black 8 = 2/26
Therefore,
the probability that the card that you draw is a black 7 or a black 8 = 4/52 - 2/26 = 1/13
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Which of the tables represents a function? 50 points i will give braileist
Table P
Input Output
6 3
1 2
6 7
Table Q
Input Output
5 1
7 8
5 6
Table R
Input Output
2 5
6 7
9 8
Table S
Input Output
3 6
4 7
4 5
Question 2 options:
1)
Table P
2)
Table Q
3)
Table R
4)
Table S
Answer:
Table RStep-by-step explanation:
Table P
Not a function as repeat input of 6 with different outputsTable Q
Not a function as repeat input of 5 with different outputsTable R
FunctionTable S
Not a function as repeat input of 4 with different outputsDetyra 3: Takim me furnitorin
Rovena shkon me makinë nga restoranti
te furnitori i perimeve, 9 km larg. Secili nga
shokët mban shënim të gjitha udhetimet qe
bëhen në lidhje me restorantin dhe kohen
e shpenzuar në takime ne menyre qe
shpenzimet t'u rimbursohen dhe te dine sa
kohe po investojne
a Vizatoni një grafik të largesës në varësi te
kohës për udhëtimin e Rovenes
b Ne cilen orë kthehet ajo ne restorant
c Për sa kohë nuk ishte ajo ne restorant
Artesohun
50
The base of a triangle is nine centimeters longer than the perpendicular height. If the area of the triangle is 180 square centimeters, what is the length of the base, in centimeters?
Answer:
The base is 24 cm long.
Step-by-step explanation:
Equations
Let's call
b= base of the triangle
h=height of the triangle
The base is 9 cm longer than the height, thus:
b = h + 9
The area of the triangle is:
[tex]\displaystyle A=\frac{bh}{2}[/tex]
[tex]\displaystyle A=\frac{(h+9)h}{2}[/tex]
And its value is 180:
[tex]\displaystyle \frac{(h+9)h}{2}=180[/tex]
Multiplying by 2:
[tex](h+9)h=360[/tex]
Operating:
[tex]h^2+9h-360=0[/tex]
Factoring:
[tex](h-15)(h+24)=0[/tex]
The only valid positive solution is:
h = 15 cm
And b = h + 9 = 24
b = 24 cm
The base is 24 cm long.
Apply the distributive property to the expression to write an equivalent expression. 5x + 35 Complete the statements. Find the GCF of . Now, factor out the GCF by dividing each term in the expression by . 5x divided by the GCF is , and 35 divided by the GCF is . The equivalent expression is .
Answer:
Apply the distributive property to the expression to write an equivalent expression.
5x + 35
Complete the statements.
Find the GCF of
✔ 5x and 35
.
Now, factor out the GCF by dividing each term in the expression by
✔ 5
.
5x divided by the GCF is
✔ x
, and 35 divided by the GCF is
✔ 7
.
The equivalent expression is
✔ 5(x + 7)
.
The equivalent expression is 5(x + 7).
Calculation of the equivalent expression;Here we need to apply the distributive property
The equation is 5x + 35
Now we have to determine the GCF by dividing the 5
So, it comes 5(x + 7).
Hence, we can conclude that The equivalent expression is 5(x + 7).
Learn more about expression here: https://brainly.com/question/24441611
.
Find the slope of each graph. Express the answer in simplest form.Can you please show me a graph you answer
Answer:
[tex]m=\frac{3}{2}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Find points from graph.
Point (-4, -2)
Point (0, 4)
Step 2: Find slope m
Substitute: [tex]m=\frac{4+2}{0+4}[/tex]Add: [tex]m=\frac{6}{4}[/tex]Simplify: [tex]m=\frac{3}{2}[/tex]And we have our final answer!
Work out 4/7 + 2 1/3
It's 61/21. That's the answer.
What is the value of this expression if h = 8,7 = -1, and k = -12? 13 20
Answer:
Step-by-step explanation:
What is the value of this expression if h = 8,7 = -1, and k = -12? 13 20
What is the domain of the relation graphed below? There are 6 points on a coordinate plane. The points are (negative 5, 0), (negative 4, 1), (negative 3, 4), (1, negative 2), (2, 4), (5, negative 3).
Answer:
3
Step-by-step explanation:
the cost of 2 cups of strawberries is $6. write an expression for the relationship between the cost, c, and the cups of strawberries,s.
2cup=6$
Im sorry if it isnt good.
please help it’s due right now. ofc it’s a quiz:D
Answer:
D is the answer.
Step-by-step explanation:
Y is going up by 3, while x is going up by 2. 3 over 2, which is the last answer.
we now its 3/2 because of the formula rise/run (rise over run).
Tell me weather the transformation is a dilation Explain
Answer:
A dialation is an enlargment or reduction of a figure. The size changes. To find dilation, multiply each point by a scale factor(k). (x, y)➡(kx, ky)
Ex. scale factor is 3
(2, 5)➡(6, 15)
Step-by-step explanation:
I just learned this.
4) Transforme, observando os exemplos:
180’ = 180’ : 60=3°
180”= 180” : 60 = 3’
⦁ 120’ em graus
⦁ 300’ em graus
⦁ 420’ em graus
⦁ 120” em minutos
Answer:
63
Step-by-step explanation:
fhj v
A high school math class has 28 students: 18 seniors and 10 juniors. What is the probability that four randomly selected students will be seniors?
Answer:
18/28, or percentage wise, approximately 64.2%
Step-by-step explanation:
Take the seniors and divide it by the total # of students, and you got your probability!
A music store owner noted that CD sales had dropped 12% from one quarter to the next. If the owner sold 460 units in the first quarter, how many did she sell in the next quarter?
Answer:
404.8
Step-by-step explanation:
100%=460
12%=x
x=(12*460)/100
x=55.2
Answer=460-x
If an items costs $41.04, including an 8% sales tax, what was the cost of
the item before taxes?
Answer:
$38
Step-by-step explanation:
I solved this by doing a proportion, 41.04/108 = x/100 to find the original price before the 8% tax. To solve this proportion you have to isolate the variable, so you would do the cross product and multiply (41.04 x 100) and have that equal to 108x. So then because you have 108x = 4104, isolate x by dividing by 108 and you get 38, thus $38.
You can also check your work by multiplying 38 by 0.08 to find the amount of sales tax added, and if you do this you will get the value $41.04.
A percentage is a number or ratio that represents a fraction of 100.
If an item costs $41.04, including an 8% sales tax then the cost of the item before the tax is $37.76.
What is a percentage?A percentage is a number or ratio that represents a fraction of 100.
Example:
50% = 50/100 = 1/2
20% = 20/100 = 1/5
25% = 25/100 = 1/4
10% = 10/100 = 1/10
5% = 5/100 = 1/20
We have,
Cost of an item including tax = $41.04
Sales tax = 8%
8% = 8/100
The cost of the item without the sales tax:
= 41.04 - (8% of 41.04)
= 41.04 - (8/100 x 41.04)
= 41.04 - 3.2832
= 37.76
Thus,
The cost of the item before the tax is $37.76.
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I can identify and use inverses to solve equations with one variable.
Answer:
[tex] \boxed{x = 4.0497}[/tex]
Step-by-step explanation:
[tex] \boxed{question \: \underline{4}.} \\ 5 {x}^{2} - 7(9.5 + 3) = - 5.5 \\ 5 {x}^{2} - 66.5 - 21 = - 5.5 \\ 5 {x}^{2} = - 5.5 + 87.5 \\ 5 {x}^{2} = 82 \\ {x}^{2} = \frac{82}{5} \\ {x}^{2} = 16.4 \\ x = \sqrt{16.4} \\ \boxed{ x = 4.0496913463}[/tex]
♨Rage♨........if you still need my help with the rest....then post each question seperatly.♨
The original price of pair of jeans is $40. The sales prices is 20% off the original price. What is the discount? Answer must be listed in $ form.
Answer:
The discount is $20 off or 50% off.
Step-by-step explanation:
It is easy math.
6 More Than a Number is 14 what is the number?
Answer:
8
Step-by-step explanation:
a+6=14
a=14-6
a=8
Therefore
8+6=14
FEMALE REPRODUCTIVE SYSTEM (SE-7)
(have this done correctly for brainiest)
label the image with the words below.
Answer:
reproductive
Step-by-step explanation:
12=r-(34-2) equation
Will give brainlist to who finds this out!
Answer:
1
2
4
Step-by-step explanation:
Answer:
[tex]\sqrt{1}, \sqrt{4}, \sqrt{9}[/tex]
Step-by-step explanation:
First, remember that rational numbers either terminate or have repeating decimals. Those three are the only answers with perfect squares, [tex]\sqrt{1} = 1, \sqrt{4} = 2, \sqrt{9} = 3[/tex]. As you can see all of these answers terminate and therefore are rational, the rest go one forever while never repeating.
what is the value of f(g(-3)?
Answer:
f(x) + g(x) = (-2x + 8)+ 3x
f(x) + g(x) = -2x + 8 + 3x Combine like terms.
f(x) + g(x) = x + 8
f(x) + g(x) = (f+g)(x) = x + 8
(f + g)(-1) = -1 + 8
(f + g)(-1) = 7
Step-by-step explanation:
8x2+4x−3 is divided by 2x−1
I hope it is helpful for you
Answer:
the answer is 1
Step-by-step explanation: i took the test on k12 hope this helps