Answer:
a) 0.5768 = 57.68% probability that the shop sells at least 3 in a week.
b) 0.988 = 98.8% probability that the shop sells at most 7 in a week.
c) 0.0104 = 1.04% probability that the shop sells more than 20 in a month.
Step-by-step explanation:
For questions a and b, the Poisson distribution is used, while for question c, the normal approximation is used.
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}[/tex]
In which
x is the number of successes
e = 2.71828 is the Euler number
[tex]\lambda[/tex] is the mean in the given interval.
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.
The Poisson distribution can be approximated to the normal with [tex]\mu = \lambda, \sigma = \sqrt{\lambda}[/tex], if [tex]\lambda>10[/tex].
Poisson variable with the mean 3
This means that [tex]\lambda= 3[/tex].
(a) At least 3 in a week.
This is [tex]P(X \geq 3)[/tex]. So
[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]
In which:
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
Then
[tex]P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-3}*3^{0}}{(0)!} = 0.0498[/tex]
[tex]P(X = 1) = \frac{e^{-3}*3^{1}}{(1)!} = 0.1494[/tex]
[tex]P(X = 2) = \frac{e^{-3}*3^{2}}{(2)!} = 0.2240[/tex]
So
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0498 + 0.1494 + 0.2240 = 0.4232[/tex]
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 1 - 0.4232 = 0.5768[/tex]
0.5768 = 57.68% probability that the shop sells at least 3 in a week.
(b) At most 7 in a week.
This is:
[tex]P(X \leq 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)[/tex]
In which
[tex]P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-3}*3^{0}}{(0)!} = 0.0498[/tex]
[tex]P(X = 1) = \frac{e^{-3}*3^{1}}{(1)!} = 0.1494[/tex]
[tex]P(X = 2) = \frac{e^{-3}*3^{2}}{(2)!} = 0.2240[/tex]
[tex]P(X = 3) = \frac{e^{-3}*3^{3}}{(3)!} = 0.2240[/tex]
[tex]P(X = 4) = \frac{e^{-3}*3^{4}}{(4)!} = 0.1680[/tex]
[tex]P(X = 5) = \frac{e^{-3}*3^{5}}{(5)!} = 0.1008[/tex]
[tex]P(X = 6) = \frac{e^{-3}*3^{6}}{(6)!} = 0.0504[/tex]
[tex]P(X = 7) = \frac{e^{-3}*3^{7}}{(7)!} = 0.0216[/tex]
Then
[tex]P(X \leq 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) = 0.0498 + 0.1494 + 0.2240 + 0.2240 + 0.1680 + 0.1008 + 0.0504 + 0.0216 = 0.988[/tex]
0.988 = 98.8% probability that the shop sells at most 7 in a week.
(c) More than 20 in a month (4 weeks).
4 weeks, so:
[tex]\mu = \lambda = 4(3) = 12[/tex]
[tex]\sigma = \sqrt{\lambda} = \sqrt{12}[/tex]
The probability, using continuity correction, is P(X > 20 + 0.5) = P(X > 20.5), which is 1 subtracted by the p-value of Z when X = 20.5.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{20 - 12}{\sqrt{12}}[/tex]
[tex]Z = 2.31[/tex]
[tex]Z = 2.31[/tex] has a p-value of 0.9896.
1 - 0.9896 = 0.0104
0.0104 = 1.04% probability that the shop sells more than 20 in a month.
The probability of the selling the video recorders for considered cases are:
P(At least 3 in a week) = 0.5768 approximately.P(At most 7 in a week) = 0.9881 approximately.P( more than 20 in a month) = 0.0839 approximately.What are some of the properties of Poisson distribution?Let X ~ Pois(λ)
Then we have:
E(X) = λ = Var(X)
Since standard deviation is square root (positive) of variance,
Thus,
Standard deviation of X = [tex]\sqrt{\lambda}[/tex]
Its probability function is given by
f(k; λ) = Pr(X = k) = [tex]\dfrac{\lambda^{k}e^{-\lambda}}{k!}[/tex]
For this case, let we have:
X = the number of weekly demand of video recorder for the considered shop.
Then, by the given data, we have:
X ~ Pois(λ=3)
Evaluating each event's probability:
Case 1: At least 3 in a week.
[tex]P(X > 3) = 1- P(X \leq 2) = \sum_{i=0}^{2}P(X=i) = \sum_{i=0}^{2} \dfrac{3^ie^{-3}}{i!}\\\\P(X > 3) = 1 - e^{-3} \times \left( 1 + 3 + 9/2\right) \approx 1 - 0.4232 = 0.5768[/tex]
Case 2: At most 7 in a week.
[tex]P(X \leq 7) = \sum_{i=0}^{7}P(X=i) = \sum_{i=0}^{7} \dfrac{3^ie^{-3}}{i!}\\\\P(X \leq 7) = e^{-3} \times \left( 1 + 3 + 9/2 + 27/6 + 81/24 + 243/120 + 729/720 + 2187/5040\right)\\\\P(X \leq 7) \approx 0.9881[/tex]
Case 3: More than 20 in a month(4 weeks)
That means more than 5 in a week on average.
[tex]P(X > 5) = 1- P(X \leq 5) =\sum_{i=0}^{5}P(X=i) = \sum_{i=0}^{5} \dfrac{3^ie^{-3}}{i!}\\\\P(X > 5) = 1- e^{-3}( 1 + 3 + 9/2 + 27/6 + 81/24 + 243/120)\\\\P(X > 5) \approx 1 - 0.9161 \\ P(X > 5) \approx 0.0839[/tex]
Thus, the probability of the selling the video recorders for considered cases are:
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Vectors u and v are perpendicular. ||u|| = 5√2 units, and ||v|| = 6√2 units. ||u + v|| ≈ ? units
A. 11.04
B. 11.05
C. 15.55
D. 15.56
Answer:
15.56
Step-by-step explanation:
Given the vectors ||u|| = 5√2 units, and ||v|| = 6√2 units.
||u + v|| ≈ 5√2 + 6√2
||u + v|| ≈ (5+6)√2
Since √2≈ 1.4142
||u + v|| ≈ 11(1.4142)
||u + v|| ≈ 15.56
Hence the correct option is D
Answer: 11.05
Step-by-step explanation: got it right
Which of the following numbers has the greatest value?
89 3/4
66 1/2
55 2/3
74 1/4
106 5/6
Answer:
106 5/6
Step-by-step explanation:
55 < 66 < 74 < 89 < 106
the fractions are irrelevant because the whole numbers are all different
The greatest of the numbers will be 106 5/6 since 106 is greater than the rest of the integers present in the mixed fractions.
Finding greatest value in a sequenceThe greatest value is the highest value in a given set of number.
Given the following numbers
89 3/4
66 1/2
55 2/3
74 1/4
106 5/6
The greatest of the numbers will be 106 5/6 since 106 is greater than the rest of the integers present in the mixed fractions.
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The mean gross annual incomes of certified welders are normally distributed with the mean of $20,000 and a standard deviation of $2,000. The ship building association wishes to find out whether their welders earn more or less than $20,000 annually. The alternate hypothesis is that the mean is not $20,000.
Required:
What is the alternate hypothesis?
Answer:
H1 : μ ≠ 20000
Step-by-step explanation:
Given that :
Population mean salary, μ = 20,000
To test if mean salary is more or less Than population mean salary, μ, this means we are testing if the mean salary is different from 20,000
Hence, the hypothesis :
Null, H0 : The mean salary is 20000
Alternative, H1 : The mean salary is not 20000
Using notation :
H0 : μ = 20000
H1 : μ ≠ 20000
Hence, alternative hypothesis is : H1 : μ ≠ 20000
Which subset(s) of numbers does 5 3/8 belong to ?
Answer:
Rational number
Step-by-step explanation:
Given
[tex]5\frac{3}{8}[/tex]
Required
The subset it belongs to
Express as improper fraction
[tex]5\frac{3}{8} = \frac{43}{8}[/tex]
The above number is rational because it is represented by the division of 2 integers, i.e. 43 and 8 are integers
Express as decimals
[tex]5\frac{3}{8} = 5.375[/tex]
The above number cannot be classified as integers or whole because it has decimal parts
A random variable X is generated as follows. We flip a coin. With probability p , the result is Heads, and then X is generated according to a PDF f X|H which is uniform on [0,1] . With probability 1−p the result is Tails, and then X is generated according to a PDF f X|T of the form
f X|T (x)=2x,if x∈[0,1]. (The PDF is zero everywhere else.)
1. What is the (unconditional) PDF f X (x) of X ? For 0≤x≤1 : f X (x)=
2. Calculate E[X] .
Answer:
Following are the solution to the given points:
Step-by-step explanation:
For point a:
[tex]fx|H(x) = 1;0< x<1\\\\fX|T(x) = 2x; 0\leq x \leq 1\\\\fx(x) = P(H \bigcap X = x) +P(T \bigcap X=x)\\\\[/tex]
[tex]=P(H)fX|H(x)+P(T)fX|T(x)\\\\= p(1) + (1-p)2x\\\\= p(1 -2x)+2x\\\\[/tex]
Using the PDF of the X value
[tex]fX(x) =2x +p(1 - 2x); \ 0\leq x\leq 1[/tex]
0 ; otherwise
For point b:
[tex]E(X)=\int^{1}_{0} \ x fX (x)\ dx=\int^{1}_{0} \ x(2x+p(1-2x))\ dx\\\\=\int^{1}_{0} \ (2x^2+(x-2x^2)p) dx\\\\[/tex]
[tex]= 2(\frac{x^3}{3}) + (\frac{x^2}{2}-2(\frac{x^3}{3}) \begin{vmatrix} x=1\\ x=0\end{vmatrix} \\\\[/tex]
[tex]= \frac{2}{3} + (\frac{1}{2} - \frac{2}{3})p\\\\= \frac{2}{3} -\frac{p}{6}\\\\= \frac{(4 - p)}{6}[/tex]
2.WHICH OF THE FOLLOWING IS A NON- NUMERIC DATA ? Required to answer. Single choice.
(1) 1,2,3,4,5,6
(2) 2,8,4,5,8
(3) A,B,AB,O
(4) NONE OF THE ABOVE
Answer:
3.) A,B,AB,O
Step-by-step explanation:
Non-numeric data refers to categorical data, or data that is not expressed quantitatively. Answers (1) and (2) contain quantitative data, so they would be eliminated as potential answer choices and therefore (4) would also be eliminated. This leaves answer (3), which does not have quantitative data and is therefore non-numeric.
Find the measure of the missing angles.
Answer:
e- 77
d- 52
f- 51
Step-by-step explanation:
Step-by-step explanation:
d=52° (,vertically opposite angle)
77+52+f=180 (linear pair)
f=180- 129
f=51°
52+51+e=180
e=180- 103
e=77°
help i,m suck and i cant find the answer
HELP PLS !!! Pls pls pls pls pls pls pls pls pls
Answer:
x=7
Step-by-step explanation:
6x+11=7x+4
HELPinjjgk go hhjkkggb jjj
Answer:
what i dont understand
Step-by-step explanation:
On Monday, Main Street station sells 40 tickets.
There are four types of ticket; infant, child, adult and senior.
The bar chart shows the number of infant, child and adult tickets sold.
How many Senior tickets sold ?
Find how many adult tickets were sold than child tickets ?
BOTH QUESTIONS ANSWER NEEDED PLES HELP
Answer:
0 senior tickets were sold
5 more adult tickets were sold than chil tickets
Step-by-step explanation:
You need to see the frequency of each bar
Answer by Gauthmath
If f(x) = x - 5, what is the value of f(8)? -13 -3 3 13
Answer:
putting the value of X=8 in f(X)
f(8)= 8-5
f(8)= 3
Answer:
3
Step-by-step explanation:
We must plug in 8 into the equation of the function since f(x) = x - 5 for all values of x. Since 8 could be a value of x, we can plug it in:
[tex]f(8) = 8-5[/tex]
The value of 8 minus 5 is 3, so the value of f(8) is 3.
Three numbers are in the ratio of 1:2:4. If 3 is added to the first and 8 is subtracted from the third, the new numbers will be the first and third terms of an A.P., whose second term is the second number. Find the original numbers.
9514 1404 393
Answer:
5, 10, 20
Step-by-step explanation:
Suppose the three numbers are x, 2x, and 4x. Then they have the required ratios. After the transformation, we have ...
((x+3) +(4x -8))/2 = 2x . . . . . 2nd term is average of 1st and 3rd
5x -5 = 4x ⇒ x = 5
The original numbers are 5, 10, 20.
_____
After the adjustment, the arithmetic sequence is 8, 10, 12.
f (x) = 3r + 6. Find the inverse of f(x).
Answer:
The inverse is 1/3x -2
Step-by-step explanation:
f (x) = 3x + 6
y = 3x+6
Exchange x and y
x = 3y+6
Subtract 6 from each side
x-6 = 3y+6-6
x-6 = 3y
Divide by 3
1/3x - 6/3 = y
1/3x -2 = y
The inverse is 1/3x -2
What are the zeros of the polynomial function f(x)=x3-7x2+8x+16
Answer: x=4, -1
Step-by-step explanation:
Assuming you meant [tex]x^3-7x^2+8x+16[/tex], the zeros of the question are x = 4 and -1.
Step 1. Replace f(x) with y.
[tex]y = x^3-7x^2+8x+16[/tex]
Step 2. To find the roots of the equation, replace y with 0 and solve.
[tex]0 = x^3-7x^2+8x+16[/tex]
Step 3. Factor the left side of the equation.
[tex](x-4)^2 (x+1)=0[/tex]
Step 4. Set x-4 equal to 0 and solve for x.
[tex]x-4=0[/tex]
Step 5. Set [tex]x+1[/tex] equal to 0 and solve for x.
[tex]x=-1[/tex]
The solution is the result of [tex]x-4=0[/tex] and [tex]x+1=0[/tex].
[tex]x=4,-1[/tex]
5 times a certain number plus 6 has the same value as two times the same number minus 3 what is the number
Let the number be x
ATQ
[tex]\\ \sf\longmapsto 5x+6=2x-3[/tex]
[tex]\\ \sf\longmapsto 5x-2x=-3-6[/tex]
[tex]\\ \sf\longmapsto 3x=-9[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{-9}{3}[/tex]
[tex]\\ \sf\longmapsto x=-3[/tex]
can jack built 1/5 of a shed in the same time that kyle can build 5/8 of shed,
how much of a shed will jack have built when kyle finished building 1 shed?
=============================================================
Explanation:
Let's say the shed comes in 40 equal pieces. Each piece takes the same amount of time to assemble. Why am I picking 40? Because 8*5 = 40.
This will allow us to rewrite the fractions with a common denominator.
1/5 = 8/40 .... multiply top and bottom by 85/8 = 25/40 .... multiply top and bottom by 5So Jack can build 8/40 of the shed in the same amount of time Kyle can build 25/40 of the shed.
Instead of writing fractions (which honestly are a pain to deal with), I'm going to write "8 pieces" and "25 pieces" to represent "8/40" and "25/40" respectively. Just keep in mind that there are 40 pieces total.
So again, Jack can assemble 8 pieces in the time it takes Kyle to assemble 25 pieces.
---------------
The ultimate goal is to have Kyle assemble 40 pieces while Jack puts together some unknown number of pieces (some number between 8 and 40). Let's say it's x.
We can then form this proportion
[tex]\frac{\text{Jack's initial 8 pieces}}{\text{x pieces}}=\frac{\text{Kyle's initial 25 pieces}}{\text{goal of 40 pieces}}[/tex]
which simplifies or cleans up to
5/x = 25/40
-----------------
Let's solve for x using cross multiplication
8/x = 25/40
8*40 = x*25
320 = 25x
25x = 320
x = 320/25
x = 12.8
So in the time it takes Kyle to assemble all 40 pieces, Jack can put together 12.8 pieces of the shed. However, we can't have Jack put together some fractional piece, because each "piece" is as small as it gets. We can't get any smaller. It would be like saying a fractional part of an atom or a lego block.
So we'll round 12.8 down to 12.
Jack can assemble 12 pieces in the time it takes Kyle to assemble 40 pieces.
Let's then convert this back to fraction form
12 pieces = 12/40 of a shed = 3/10 of a shed.
What is the length of the line?
WILL GIVE BRAINLIEST!!
Answer:
18
Step-by-step explanation:
6^2 plus 3^2 = 324, square root 324 =18
Answer:
[tex]\sqrt{45}[/tex]
Step-by-step explanation:
The line represents the hypotenuse of a right triangle with legs 6 and 3. For any right triangle, the Pythagorean Theorem states that [tex]a^2+b^2=c^2[/tex], where [tex]a[/tex] and [tex]b[/tex] are two legs of the triangle and [tex]c[/tex] is the hypotenuse.
Therefore, we have:
[tex]6^2+3^2=c^2,\\c^2=36+9,\\c=\boxed{\sqrt{45}}[/tex]
consider a study conducted to determine the average protein intake among an adult population. Suppose that a confidence level of 85% is required with an interval about 10 units wide. if a preliminary data indicates a standard deviation of 20g, what sample of adults should be selected for the study?
Answer:
made up of about 20 common amino acids. The proportion of these amino acids varies as a characteristic of a given protein, but all food proteins—with the exception of gelatin—contain some of each. Amino nitrogen accounts for approximately 16% of the weight of proteins. Amino acids are required for the synthesis of body protein and other important nitrogen-containing compounds, such as creatine, peptide hormones, and some neurotransmitters. Although allowances are expressed as protein, a the biological requirement is for amino acids.
Proteins and other nitrogenous compounds are being degraded and resynthesized continuously. Several times more protein is turned over daily within the body than is ordinarily consumed, indicating that reutilization of amino acids is a major feature of the economy of protein metabolism. This process of recapture is not completely efficient, and some amino acids are lost by oxidative catabolism. Metabolic products of amino acids (urea, creatinine, uric acid, and other nitrogenous products) are excreted in the urine; nitrogen is also lost in feces, sweat, and other body secretions and in sloughed skin, hair, and nails. A continuous supply of dietary amino acids is required to replace these losses, even after growth has ceased.
Amino acids consumed in excess of the amounts needed for the synthesis of nitrogenous tissue constituents are not stored but are degraded; the nitrogen is excreted as urea, and the keto acids left after removal of the amino groups are either utilized directly as sources of energy or are converted to carbohydrate or fat.
Find the exact area of this triangle: 10V3 30° 20 [?] [ square units
Answer:
50√3 square units.
Step-by-step explanation:
Let the two sides of the triangle given be 'a' and 'b'.
Let the angle between them be θ
From the question given above, the following data were obtained:
Side a = 20 units
Side b = 10√3
Angle (θ) = 30°
Area (A) =?
A = ½ × ab × Sineθ
A = ½ × 20 × 10√3 × Sine 30
A = ½ × 20 × 10√3 × ½
A = 10 × 5√3
A = 50√3 square units
Therefore, the area of the triangle is 50√3 square units
Why school sucks: A makes you learn stuff you don’t care about and will never use B teachers suck and don’t teach property C they don’t teach you useful things like taxes bills ect D they overwork students E its not even about learning anymore all goals are is just good grades.
Why is our future determined on letters on a piece of paper? I’d rather die then be in this society
Answer:
I think answer is E
Step-by-step explanation:
The problem solving plan identifies steps to organize your information. Which of the following answer choices are included in the steps to organize your information?
A. Organize the problem and find the question.
B. Solve the problem and change your strategy if necessary.
C. Write the facts, organize your thoughts and define your strategy.
D. Organize the steps and underline the question.
c.write the fact,organize your thoughts and define your strategy.
Answer:
c
Step-by-step explanation:
find the area of the semi circle plss
Answer:
Step-by-step explanation:
Which confidence level would produce the widest interval when estimating the mean of a population from the mean and standard deviation of a sample of that population?
ASAP THANK YOU!!!!!
Answer:
54%
Step-by-step explanation:
that is the greatest percentile given
The confidence level of 54% would produce the widest interval when estimating the mean of a population from the mean and standard deviation of a sample of that population.
What is Confidence Interval?Confidence interval in statistics is defined as the certain range of values that you estimate for the unknown parameter lies within.
This means that, if you do your experiment more than once and do resampling, then this is the percentage that the parameters falls within a range.
From the definition of the confidence interval itself, it is clear that the level with the widest interval will be the highest confidence level.
So if you need a wider interval for estimating the mean of a population from the mean and standard deviation, you need to take higher confidence level.
Out of the given options, the highest level is 54%.
Hence the confidence level is 54%.
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You need to design a rectangle with a perimeter of 14.2 cm. The length must be 2.4 cm. What is the width of the
rectangle? (You might want to draw a picture.)
a) Let w = the width of the rectangle. Write the equation you would use to solve this problem.
b) Now solve your equation
* cm.
The width of the rectangle must be. Cm
Part (a)
Answer: 2(2.4+w) = 14.2--------------
Explanation:
L = 2.4 = length
W = unknown width
The perimeter of any rectangle is P = 2(L+W)
We replace L with 2.4, and replace P with 14.2 to get 14.2 = 2(2.4+w) which is equivalent to 2(2.4+w) = 14.2
========================================================
Part (b)
Answer: w = 4.7--------------
Explanation:
We'll solve the equation we set up in part (a)
2(2.4+w) = 14.2
2(2.4)+2(w) = 14.2
4.8+2w = 14.2
2w = 14.2-4.8
2w = 9.4
w = 9.4/2
w = 4.7
The width must be 4.7 cm.
Find two positive numbers whose difference is 28 and whose product is 1653
Answer:
Step-by-skfmckfmkfkfkfkfkkfkfkfkfkfkfoftep explanation:
Cl
WORTH 15 POINTSSSSSSSSS
Answer:
15
Step-by-step explanation:
Difference in distances = 75-60 = 15 miles
So Car A travels 15 miles more than Car A in an hour
Answered by Gauthmath
A market research company conducted a survey to find the level of affluence in a city. They defined the category "affluence" for people earning $100,000 or more annually. Out of 267 persons who replied to their survey, 32 are considered affluent. What is the 95% confidence interval for this population proportion? Answer choices are rounded to the hundredths place. 0.08 to 0.34 0.08 to 0.16 0.24 to 0.34 0.16 to 0.24
Answer:
0.08 ; 0.16
Step-by-step explanation:
Given :
x = 32 ; n = 267 ; phat = x / n = 32 / 267 = 0.11985
The Zcritical at 95% = 1.96
The confidence interval for proportion :
C. I = Phat ± Z*√(phat(1-phat))/n
C. I = 0.11985 ± 1.96√(0.11985(1-0.11985))/267
C. I = 0.11985 ± 1.96(0.0198765)
C. I = 0.11985 ± 0.0389581
C. I = 0.08 ; 0.158
C. I = 0.08 ; 0.16
Find the missing side round your answer to the nearest tenth
Answer: 15
Step-by-step explanation:
Jose saves $22.45 a week which is 37% of his weekly pay. How much is Jose's weekly pay?
