Answer:
a) 0.0645 = 6.45% probability that the 90 orders can be filled without reordering components.
b) 0.4062 = 40.62% probability that the 100 orders can be filled without reordering components.
c) 0.9034 = 90.34% probability that the 100 orders can be filled without reordering components
Step-by-step explanation:
For each component, there are only two possible outcomes. Either it is defective, or it is not. The components can be assumed to be independent. This means that we use the binomial probability distribution 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.
3% of the components are identified as defective
This means that [tex]p = 0.03[/tex]
a. If the manufacturer stocks 90 components, what is the probability that the 90 orders can be filled without reordering components?
0 defective in a set of 90, which is [tex]P(X = 0)[/tex] when [tex]n = 90[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{90,0}.(0.03)^{0}.(0.97)^{90} = 0.0645[/tex]
0.0645 = 6.45% probability that the 90 orders can be filled without reordering components.
b. If the manufacturer stocks 102 components, what is the probability that the 100 orders can be filled without reordering components?
At most 102 - 100 = 2 defective in a set of 102, so [tex]P(X \leq 2)[/tex] when [tex]n = 102[/tex]
Then
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{102,0}.(0.03)^{0}.(0.97)^{102} = 0.0447[/tex]
[tex]P(X = 1) = C_{102,0}.(0.03)^{1}.(0.97)^{101} = 0.1411[/tex]
[tex]P(X = 2) = C_{102,2}.(0.03)^{2}.(0.97)^{100} = 0.2204[/tex]
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0447 + 0.1411 + 0.2204 = 0.4062[/tex]
0.4062 = 40.62% probability that the 100 orders can be filled without reordering components.
c. If the manufacturer stocks 105 components, what is the probability that the 100 orders can be filled without reordering components?
At most 105 - 100 = 5 defective in a set of 105, so [tex]P(X \leq 5)[/tex] when [tex]n = 105[/tex]
Then
[tex]P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{105,0}.(0.03)^{0}.(0.97)^{105} = 0.0408[/tex]
[tex]P(X = 1) = C_{105,0}.(0.03)^{1}.(0.97)^{104} = 0.1326[/tex]
[tex]P(X = 2) = C_{105,2}.(0.03)^{2}.(0.97)^{103} = 0.2133[/tex]
[tex]P(X = 3) = C_{105,3}.(0.03)^{3}.(0.97)^{102} = 0.2265[/tex]
[tex]P(X = 4) = C_{105,4}.(0.03)^{4}.(0.97)^{101} = 0.1786[/tex]
[tex]P(X = 5) = C_{105,5}.(0.03)^{5}.(0.97)^{100} = 0.1116[/tex]
[tex]P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.0408 + 0.1326 + 0.2133 + 0.2265 + 0.1786 + 0.1116 = 0.9034[/tex]
0.9034 = 90.34% probability that the 100 orders can be filled without reordering components
Vertical Angles
Find the unknown angles.
i don't know how to do these help me understand please. its probably super easy just give a me a formula or something
Answer:
1. m<2 = 115 °
2. m<5 = 83 °
3. m<8 = 45 °
4. m<4 = 137 °
Step-by-step explanation:
1. Determination of m<2
m<1 = 115 °
m<2 =?
m<2 = m<1 (vertically opposite angles are equal)
m<2 = m<1
m<2 = 115 °
2. Determination of m<5
m<6 = 83 °
m<5 =?
m<5 = m<6 (vertically opposite angles are equal)
m<5 = m<6
m<5 = 83 °
3. Determination of m<8
m<9 = 45 °
m<8 =?
m<8 = m<9 (vertically opposite angles are equal)
m<8 = m<9
m<8 = 45 °
4. Determination of m<4
m<3 = 137 °
m<4 =?
m<4 = m<3 (vertically opposite angles are equal)
m<4 = m<3
m<4 = 137 °
The prime factorization of a number is 3 x 4 x 4 x 4 x 7 x
7. What is the correct way to write this using exponential
notation?
Answer:
3 x [tex]4^{3}[/tex] x [tex]7^{2}[/tex]
Step-by-step explanation:
Fill in the missing statements and reasons in the proof:
Answer:
2. definition of congruence
Step-by-step explanation:
sorry I just know that one
How do you covert 40% into a fraction ?
Answer:
2/5
Step-by-step explanation:
Build me a 100ft roller coaster ride using math?
Show me how to work this out please
Answer:
it's A
Step-by-step explanation:
the reason why it's A is that X can not have to repeating numbers
ABC is a three digit number where each number represents a different digit. If A < C what is the greatest possible number?
Answer:
879
Step-by-step explanation:
Because C is greater than A, C has to be the largest possible number so that A can be as large as possible. because C is the largest possible number, which is 9, the next largest number is 8, which in this case is A. The next biggest number is 7 which is B.
To sum it all up, the number is 879.
Let C be the first quadrant portion of the circle of radius 3 centered on the origin. Find the line itegral for x^2+y^2 over C.
simplify
6x²+x-2/2x²+x-1
Answer:
[tex]5x^{2} +2x-1[/tex][tex]5x^{2}+2x-1[/tex]
The area of the cirle is: | I
10 in
Answer:
Step-by-step explanation:
diameter = 10 in
radius = 5 in
area = π5² = 25π ≅ 78.5 in²
plz help me. I'm confused on hw
Increase 60kg by 25%
can anyone pls help me with this question I'm stuck
Answer:
I think 24
let b=3
l=4
and h=2
Answer:
864
Good luck!
In Dylan's grade, there are 80 students. Currently, 40% of them are enrolled in health. How many students are enrolled in health?
Answer:
32
Step-by-step explanation:
Convert 40 percent to a decimal, which is 0.4, then multiply 0.4 with 80 and you get 32.
hayden and jamie completed 20 math problems together, jamie completed 2 more than twice the number that hayden completed. Let p represent the number of math problems hayden completed. Write an equation that can be used to find the number of math problems that jamie completed.
Answer:
2p+2+p = 20
Step-by-step explanation:
Let p represent the number of Math problems Hayden completed.
Let 2p+2 represent the number of Math problems Jamie completed.
Next, we have to add them together so that the total Math problems they completed will be equal to 20.
Let's solve.
2p+2+p = 203p+2 = 203p = 20-23p = 18p = [tex]\frac{18}{3}[/tex]p = 6Therefore, Hayden completed 6 Math problems.
Next, we have to get how many problems Jamie completed.
Let's solve.
2p+2 = ?2(6)+2 = ?12+2 = ?14Therefore, Jamie completed 14 Math problems.
Let's check.
2p+2+p = 2014+6 = 2020 = 20It's correct!
If y = 24 when x = 6, find y when x = -4 answer
Answer:
-16
Step-by-step explanation:
24/6 = y/-4
6y = -96 cross multiply
y=-16
PLS, I NEED HELP! Translate this sentence into a compound inequality with math symbols.
Springfield’s monthly temperatures range from a high of 101o F to a low of – 8o F.
Answer:
8o F at least I'm pretty sure 101o F ≥ 8o
Step-by-step explanation:
Correct me If im wrong
How many solutions does the system have?
You can use the interactive graph below to find the answer.
y = 3x + 3
y = -2x + 3
Choose 1 answer:
Exactly one solution
B
No solutions
Infinitely many solutions
please help i’ll mark u
Answer:
4:12
4/12
4 to 12
Graph the line that passes through the points (-4, 6) and (-8,5) and determine the equation of the line.
8. A drug and placebo were tested on 23 people each to study their effect on cholesterol. The mean cholesterol levels with the people on the new drug are 195 and SD of 35. The values for placebo sample are 245 and SD of 31. Using 5% level of significance, does the drug have effect on lowering the cholesterol.
Answer:
The drug have effect on lowering the cholesterol.
Step-by-step explanation:
H₀ : μ₁ - μ₂ = 0
⇒ H₀ : μ₁ = μ₂
H₁ : μ₁ - μ₂ < 0
⇒H₁ : μ₁ < μ₂
Now,
given , n₁ = 23 , n₂ = 23
∴ Degree of freedom = v = n₁ + n₂ - 2
= 23 + 23 - 2 = 44
⇒v = 44
Now,
Given, level of significance = 5% = 0.05
For the given significance level, critical time t = 1.68
As
Decision rule states that'if t < 1.68 , reject H₀
Now,
For Drug:
mean = m₁ = 195
SD = d₁ = 35
People = n₁ = 23
For placebo :
mean = m₂ = 245
SD = d₂ = 31
People = n₂ = 23
Now,
Variance = [tex]\frac{(23-1)35^{2} + (23-1)31^{2} }{23 + 23 - 2}[/tex] = 1093
Standard Deviation, S = 33.06
Point estimate = m₁ - m₂ = 195 - 245 = -50
Standard deviation error = S×([tex]\frac{1}{n_{1} } + \frac{1}{n_{2} }[/tex] ) = 9.75
Now,
Test statistics = [tex]-\frac{50}{\sqrt{9.75} } = -5.13[/tex]
⇒ t < 6.13
⇒Reject H₀
⇒The drug have effect on lowering the cholesterol.
help pls i really need help
===========================================================
Explanation:
1/3 converts to the decimal form 0.333333... where the 3's go on forever
5/3 is a similar story but 5/3 = 1.666666.... where the '6's go on forever
The notation [tex]0.\overline{6}[/tex] indicates that the 6's go on forever.
So, [tex]0.\overline{6} = 0.666666\ldots[/tex]
The horizontal bar tells us which digits repeat. As another example, [tex]0.\overline{123} = 0.123123123123\ldots[/tex]
The three dots just mean "keep this pattern going forever".
----------
Everything mentioned so far has the decimal portions go on forever repeating some pattern over and over.
The only one that doesn't do this is 33% which converts to the decimal form 0.33
The value 0.33 is considered a terminating decimal since "terminate" means "stop". So this is the value that doesn't fit in with the other three items mentioned.
3(2x - 1) + 7 = -44 solve for x
Answer:
I love algebra anyways
The ans is in the picture with the steps how i got it
(hope this helps can i plz have brainlist :D hehe)
Step-by-step explanation:
answer is x =-8
hope that helps^^
Consider a student loan of $22,500 at a fixed APR of 9% for 30 years.
a. Calculate the monthly payment.
b. Determine the total amount paid over the term of the loan
c. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest.
a. The monthly payment is 5
(Do not round until the final answer. Then round to the nearest cent as needed.)
b. The total payment over the term of the loan is s
(Round to the nearest cent as needed.)
c. Of the total payment over the term of the loan, % is paid toward the placipal and % is paid toward interest.
(Round to the nearest tenth as needed)
Answer:
Lo averiguaste, lo siento, amigos míos, por haberlos ayudado. pero la respuesta es 456 $.
Step-by-step explanation:
Four friends go to dinner. Each chooses a different meal. When the check comes, they decide they will each pay the same amount. If the costs of the meals (including tax and tip) were $12.20, $11.00, $8.50, and $7.50, what should each friend pay so they cover the whole bill?
Answer: Each friend should pay $9.80
Step-by-step explanation: First add up all their checks, then divide them by 4 (4 because there 4 friends) to get the amount each friend needs to pay.
$12.20 + $11.00 + $8.50 + $7.50= $39.20
39.30 / 4 = $9.80
Find the degree measure of the indicated angle.
?
40°
80°
Answer:
60
because you need to add the number to get 180 so I would be 80+20 = 120+60=180 I hope it helps!
The tide is the regular rising or falling of the ocean’s surface. This is due in large part to the gravitational forces of the moon. The following table represents water level of the tide off the coast of Kings Point, N.Y., for a 24 hour period, February 9th through February 10th of 2009.
Hour
Measurement in feet above the average low tide
0
-0.98
2
5.83
4
7.78
6
7.34
8
2.33
10
-0.47
12
-0.21
14
5.32
16
8.83
18
8.31
20
3.80
22
-0.28
24
0.53
Plot the data points given in the table using hour as the independent variable. Does this data indicate that a sine regression may be appropriate in this case? Explain.
a.
Yes, in the scatterplot the wavelike behavior is apparent although not precise.
b.
Yes, the scatterplot shows an increase over time.
c.
No, there is no correlation between the points.
d.
No, the scatterplot depicts a hyperbole.
Answer:
Option AStep-by-step explanation:
Points plotted.
See the graph attached.
Correct choice is:
A. Yes, in the scatterplot the wavelike behavior is apparent although not preciseOPTION A
#CcarryOnLearning
Decide whether a discrete or continuous random variable is the best model for each of the following variables:
a. The time for a computer algorithm to assign an image to a category.
b. The number of bytes used to store a file in a computer.
c. The ozone concentration in micrograms per cubic meter.
d. The ejection fraction (volumetric fraction of blood pumped from a heart ventricle with each beat).
e. The fluid flow rate in liters per minute.
Answer:
a) Continuous
b) Discrete
c) Continuous
d) Continuous
e) Continuous
Step-by-step explanation:
Discrete variable:
Countable amounts(0, 1, 2, 3,...)
Continuous variables:
Can be decimal values.
a. The time for a computer algorithm to assign an image to a category.
Time can have decimal values, so continuous
b. The number of bytes used to store a file in a computer.
The number of bytes is never decimal, so discrete
c. The ozone concentration in micrograms per cubic meter.
Can be decimal value, so continuous
d. The ejection fraction (volumetric fraction of blood pumped from a heart ventricle with each beat).
Can be decimal value, so continuous
e. The fluid flow rate in liters per minute.
Can be decimal value, so continuous
where is the most optimal position to send your bean bag in relation to opponent's bean bag?
Answer:
right side
Step-by-step explanation:
use the sumilar triangles to find the value of the missing side b