Answer:
a) 0.0618 = 6.18% probability that the sample will contain at least three defectives.
b) 0.076 = 7.6% probability that the sample will contain at least three defectives
Step-by-step explanation:
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]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
Sample of 20 items is selected from the machine.
This means that [tex]n = 20[/tex]
5% defectives
This means that [tex]p = 0.05[/tex]
(a) the normal approximation to the binomial
The mean is:
[tex]\mu = E(X) = np = 20*0.05 = 1[/tex]
The standard deviation is:
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{20*0.05*0.95} = 0.9747[/tex]
The probability is, using continuity correction, [tex]P(X \geq 3 - 2.5) = P(X \geq 2.5)[/tex] , which is 1 subtracted by the pvalue of Z when X = 2.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2.5 - 1}{0.9747}[/tex]
[tex]Z = 1.54[/tex]
[tex]Z = 1.54[/tex] has a pvalue of 0.9382
1 - 0.9382 = 0.0618
0.0618 = 6.18% probability that the sample will contain at least three defectives.
(b) the exact binomial tables
This is:
[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]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{20,0}.(0.05)^{0}.(0.95)^{20} = 0.358[/tex]
[tex]P(X = 1) = C_{20,1}.(0.05)^{1}.(0.95)^{19} = 0.377[/tex]
[tex]P(X = 2) = C_{20,2}.(0.05)^{2}.(0.95)^{18} = 0.189[/tex]
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.358 + 0.377 + 0.189 = 0.924[/tex]
[tex]P(X \geq 3) = 1 - P(X < 3) = 1 - 0.924 = 0.076[/tex]
0.076 = 7.6% probability that the sample will contain at least three defectives
Two forces of 90 newtons and 58 newtons act simultaneously on an object. The angle between the two forces is 57°. Find the magnitude of the resultant, to the nearest 10th of a newton.
Answer:
131.0 N
Step-by-step explanation:
Let the 90 N force is acting a horizontal force on the object
Horizontal force = 90 + 58sin33
Vertical force = 58cos33
∴The resultant force = √(90 + 58sin33)² + (58cos33)²
= 131.0 N
Buffer stock is the level of stock
Answer:
akuy3uwujwu
Step-by-step explanation:
uwoedihwo
Answer:
Safety stock inventory, sometimes called buffer stock, is the level of extra stock that is maintained to mitigate risk of run-out for raw materials or finished goods due to uncertainties in supply or demand.
HOPE IT HELPS...
HAVE A GREAT DAY : P
Lebrun loaned $20,000 to his daughter to help her buy a house. When she sold the house four years later, she paid him the $20,000 along with an interest of $3000. What was the annual interest rate? Round answer to two decimal places.
Answer:
3.75%
Step-by-step explanation:
Total interest (4 years) - $3000
Annual interest (1 year) - $3000 ÷ 4 = $750
Annual interest rate (1 year) - [tex]\frac{750}{20 000}[/tex] × 100% = 3.75%
Checking:
Interest after 1 year - [tex]\frac{3.75}{100}[/tex] × $20,000 = $750
Interest after 4 years - $750 × 4 = $3000 (Correct)
Answer:
The interest rate was 3.75%.
Step-by-step explanation:
Attention: I am assuming simple interest here since I am not told otherwise.
Knowing Lebrun's interest was a total of $3000 on the $20000 loan, we can safely assume that it was a $750 interest flat fee paid on top of the loan amount dividing the $3000 by the four years it took for them to return the loan.
Dividing the amount of interest, in dollars, by the total amount of the loan and multiplying by 100, you will get the interest rate on the loan:
[tex]\frac{750}{20000}=\frac{75}{2000}=\frac{15}{400}=\frac{3}{80}\\\\\frac{3}{80}*100=\frac{3}{8}*10=\frac{30}{8}=3\frac{3}{4} =3.75\%[/tex]
What are the next terms in the sequence 19, 36, 53,70
what's wrong with the table
Answer:
On the one that says "3-24" its supposed to be "3-18". On the one that says "4-32" its supposed to be "4-24".
In your own words, explain what a rational expression is and give and example of one.
Answer:
A rational expression is when the numerator and the denominator are polynomials. An example is 5/x − 2
What is the approximate area inside the rectangle but
outside the semicircle?
Answer:
128 - 32pi
OR
27.469
Step-by-step explanation:
The area of the rectange is 8 x 16 = 128
The area of the semicircle is pi * 8^2 divided by 2
(pi * 8^2)/2
(pi * 64)/2
pi * 32
So the area of the rectangle outside the semicircle is: 128 - 32pi
In approximate form it is: 27.469
How much time will it take for an amount of Rs900 to yield Rs81 as interest at 4.5% per annum of simple interest
Answer:
T=2 years.hope it will help u.
what is the slope of the line passing through po bye A and B?
8x + 9y - 6x - 3y i forgot how to do these lol
En una habitación del Grand Hotel de Indianápolis se pueden hospedar un máximo de 2 personas. Si el hotel cuenta con 12 pisos y cada piso con 12 habitaciones. ¿Cuántas personas pueden hospedarse en el hotel al no haber vacantes?
Answer:
la solucion es 288
Step-by-step explanation:
porque 12 pisos •12 habitaciones es 144 habitaciones y multiplicar 144 con 2 personas tenemos 288.
espero que esto ayude!!
Three of 25 students in an art class are left-handed. in another words, 12% of the students in the class are left handed what does number 3 represent
Answer:
The number of students that are left handed
Step-by-step explanation:
Answer:
it represent 3 students
At the book sale, all books cost less than $5.
Answer:
then the books will cost 5.30
Step-by-step explanation:
don't forget to add 6 cents per dollar
Ryan earns $20 for every lawn that he mows.
How much will Ryan earn if he mows 15 lawns?
20*15=300
It's "too short", but there's not much else to say here.
Answer:
Ryan will earn $300 if he mows 15 lawns.
Step-by-step explanation:
$20 × 15 = $300
help please
find the surface area of the following prism
Answer: 163
Step-by-step explanation:
Can some body help me?
Answer:
24
Step-by-step explanation:
2(54-6x)=73-7x
108-12x=73-7x
108-73=-7x+12x
35=5x
x=7
UW=73-7x=73-7(7) = 73-49 = 24
What is the slope-intercept equation for the line below?
(4, 3)
(0, 1),
Answer:D is correct
Step-by-step explanation:
y=1/2x+1
Please help it’s pretty easy and I’ll reward brainiest
Puadratic Relations 1
00:00
Israh Doukhi: Attempt 1
Question 5 (1 point)
3
Which statement is true about first and second differences in quadratic relations?
First differences are different second differences are the same
First differences are different, second differences are different.
First differences are the same
Answer is in the photo. I can only upload it to a file hosting service. link below!
tinyurl.com/wpazsebu
Day Care Tuition A random sample of 50 four-year-olds attending day care centers provided a yearly tuition average of $3987 and the population standard deviation of $630. Find the 90% confidence interval of the true mean. If a day care center were starting up and wanted to keep tuition low, what would be a reasonable amount to charge
Answer:
We have to find the 90% confidence interval for the mean
Given sample size
Sample mean
Population standard deviation
Here the confidence level is 90% then
And
The 90% confidence interval is
Here is the critical value at 0.05
From the tables
Now the 90% confidence interval is =
=
=(3840.44, 4133.56)
Hence the 90% confidence interval for the mean is (3840.44, 4133.56)
What is the area of an equilateral triangle with sides of length 20?
Answer:
173.2
Step-by-step explanation:
area of equilateral triangle = √3 / 4 l^2
so area =173.2
F(x)=x^2+1 what is f(f(x))?
Answer:
Answer
Find out f(f(x)) .
To prove
As given in the question
f(x) = x² + 1
Now
f(f(x)) = f (x² + 1)
Now find out the value of f (x² + 1).
f(f(x)) = f (x² + 1)
= (x² + 1)² + 1
Using formula
(a + b)² = a² + b² + 2ab
Apply in the above function
f(f(x)) = (x² + 1)² + 1
f(f(x)) = [tex]x^{4}[/tex] + 1 + [tex]2x^{2}[/tex] + 1
Simplify
f(f(x)) = [tex]x^{4}[/tex] + [tex]2x^{2}[/tex] + 2
Thus the value of f(f(x)) is: f(f(x)) = [tex]x^{4}[/tex] + [tex]2x^{2}[/tex] + 2
Step-by-step explanation:
What is the approximate area of the figure below?
Answer:
96
Step-by-step explanation:
Factor this expression.
3х2 - 15х
O A. 3(x - 5)
O B. 3(x2 - 5)
O C. 3x(x2 - 5)
O D. 3x(x - 5)
Answer:
D
Step-by-step explanation:
i need helpon this
please
On a map of Northern Virginia, 1 inch = 4 miles.
The distance from Springfield to Dulles
International Airport is 5.8 inches on the map.
What is the actual distance to the airport?
Answer:
sorry I don't know this average because it's confusing
A train travels 240 miles in 6 hours, moving at a constant speed.
How long will it take the train to travel 360 miles at this speed?
1.5 hours
2.5 hours
9 hours
O 60 hours
CAN SOMEONE HELP ME PLS
Answer:
Step-by-step explanation:
speed = 240 miles/(6 hours) = 40 miles/hour
360 miles × 1 hour/(40 miles) = 9 hours
Solve using the linear combination method.
4x - 3y = 26
3x + 2y = 11
Answer: X= 5
Step-by-step explanation:
I think that's the answer your looking for??
Tell whether the ordered pair (-1,3) is a solution of the system of linear equations. y=-7x-4 and y=8x+5
Answer:
Since it does not plug in to the second linear equation, the ordered pair is not a solution of the linear system.
Step-by-step explanation:
(-1,3); y = -7x -4 y = 8x + 5 3 =7 - 4 3 =/ - 8 + 5
For a system of equations to have no real solution, the lines of the equations must be parallel to each other. The ordered pair (-1,3) is not the solution of the given system of equations.
What is the System of equations?Inconsistent SystemFor a system of equations to have no real solution, the lines of the equations must be parallel to each other.
Consistent System
1. Dependent Consistent System
For a system of the equation to be a Dependent Consistent System, the system must have multiple solutions for which the lines of the equation must be coinciding.
2. Independent Consistent System
For a system of the equation to be an Independent Consistent System the system must have one unique solution for which the lines of the equation must intersect at a particular.
The solution of the equation can be found by plotting the equation on the graph. Therefore, the point at which the equation will intersect will the solution of the system of equation.
Since the solution of the system of equation is (-0.6, 0.2), there exists only one single solution for the system of equation. therefore, the (-1,3) is not the solution of the system of equation.
Hence, the ordered pair (-1,3) is not the solution of the given system of equations.
Learn more about System of equation:
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Help me with 15 :)plz