Using the binomial distribution, it is found that there is a:
a) 0.3526 = 35.26% probability of rejecting a lot that is 3% defective.
b) 0.4295 = 42.95% probability of accepting a lot that is 4% defective.
For each device, there are only two possible outcomes, either it is defective, or it is not. The probability of a device being defective is independent of any other device, hence the binomial distribution is used to solve this question.
Binomial probability distribution
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.In this problem, the sample has 100 units, hence [tex]n = 100[/tex].
Item a:
3% of the pieces are defective, hence [tex]p = 0.03[/tex].
The probability is:
[tex]P(X \geq 4) = 1 - P(X < 4)[/tex]
In which:
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
Hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{100,0}.(0.03)^{0}.(0.97)^{100} = 0.0476[/tex]
[tex]P(X = 1) = C_{100,1}.(0.03)^{1}.(0.97)^{99} = 0.1471[/tex]
[tex]P(X = 2) = C_{100,2}.(0.03)^{2}.(0.97)^{98} = 0.2252[/tex]
[tex]P(X = 3) = C_{100,3}.(0.03)^{3}.(0.97)^{97} = 0.2275[/tex]
Then:
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0476 + 0.1471 + 0.2252 + 0.2275 = 0.6474[/tex]
[tex]P(X \geq 4) = 1 - P(X < 4) = 1 - 0.6474 = 0.3526[/tex]
0.3526 = 35.26% probability of rejecting a lot that is 3% defective.
Item b:
4% of the pieces are defective, hence [tex]p = 0.04[/tex].
Lot is accepted if less than 4 units are defective, hence:
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
[tex]P(X = 0) = C_{100,0}.(0.04)^{0}.(0.96)^{100} = 0.0169[/tex]
[tex]P(X = 1) = C_{100,1}.(0.04)^{1}.(0.96)^{99} = 0.0703[/tex]
[tex]P(X = 2) = C_{100,2}.(0.04)^{2}.(0.96)^{98} = 0.1450[/tex]
[tex]P(X = 3) = C_{100,3}.(0.04)^{3}.(0.96)^{97} = 0.1973[/tex]
Then:
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0169 + 0.0703 + 0.1450 + 0.1973 = 0.4295[/tex]
0.4295 = 42.95% probability of accepting a lot that is 4% defective.
A similar problem is given at https://brainly.com/question/24863377
Two polygons are similar. The corresponding angles of the polygons are- A congruent B proportional C regular D similar
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Answer:
A congruent
Step-by-step explanation:
In similar polygons, corresponding sides are proportional, and corresponding angles are congruent.
Andrew invests $9000
What are you asking?
The list of ordered pairs below represents a function.
{(-12, –8), (-2,7), (0,4), (-4,3)}
Find the range of the function. Write your answer' as a comma separated list.
Answer:
{-8, 3, 4, 7}
Step-by-step explanation:
range is y values in the ordered pairs
{-8, 3, 4, 7}
Evaluate. (2a−1/3)÷b/15 when a=−4/5 and b=−2.25 Enter your answer as a simplified mixed number in the box.
POSSIBLE POINTS: 33.33
homeowner collects data about the amount of oil A, in gallons, used to heat the house per month for 5 months and the
verage monthly temperature t, in degrees Fahrenheit, for those months. The scatter plot shows the data. The function
(t) = -1.4t + 96 best fits these data.
=============================================================
Explanation:
Check out the diagram below. I've plotted the regression line A(t) = -1.4t+96 on the same xy grid as the given scatterplot. This line tries to get as close as possible to all of the points.
From here, we plug in each of the temperatures mentioned in the five answer choices (10, 15, 68.5, 55, 0). The outputs form the second column of the table in that same diagram.
For example, if we plugged in t = 10, then,
A(t) = -1.4t+96
A(10) = -1.4(10)+96
A(10) = -14 + 96
A(10) = 82
Telling us that a temperature of 10 degrees F would have a predicted or estimated usage of roughly 82 gallons of oil. This points to choice A being one of the answers.
The other temperature values are handled the same way. Choice B is false because t = 15 does not lead to A(t) = 85. Instead, it's A(15) = 75 meaning it's 10 degrees off the mark.
Choice C is true though. Plugging t = 68.5 into A(t) leads to A(t) = 0.1 which rounds to 0 assuming we're only worried about whole numbers. If your teacher is considering decimal values, then choice C is unfortunately false. For now I'll assume your teacher wants you to round.
If we tried t = 55, then we'd get A(15) = -1.4*55+96 = 19 which is not 5 as we'd want. This rules out choice D.
Lastly, plug in t = 0 to find that A(t) = 96. This leads to choice E being one of the answers.
For the graph attached statements A, C and E are true.
Function that fits the given data in the graph,
A(t) = -1.4t + 96Here, t = temperature in Fahrenheit
A(t) = Oil used in gallons
By substituting the value of 't' in the equation we can get the amount of oil used A(t) to heat the house.
Option A
By substituting t = 10°F,
A(10) = -1.4(10) + 96
= 82 gallons
Therefore, statement is true.
Option B
For t = 15°F,
A(15) = -2.4(15) + 96
= 60 gallons
Statement is False.
Option C
For t = 68.5°F
A(5) = -1.4(68.5) + 96
= 0.1 gallons
≈ 0 gallons
Statement is True.
Option D
For t = 55°F,
A(55) = -1.4(55) + 96
= 19 gallons
Statement is False.
Option E
For t = 0°F
A(0) = -1.4(0) + 96
= 96 gallons
Statement is true.
Therefore, statements given in options A, C and E are True.
Learn more,
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Please help and only answer if correct!
Answer: So last time it was 1/4 and 4 so it's no different it just going down by one so it's 1/3 and 3 if it's not I give up.
Step-by-step explanation:
Where , the distance between the points ( a, c) and ( b, c) is ( ) units
Answer:
I would love to help but there is no upload. Would you mind creating a new question with a picture or data of the graph
Step-by-step explanation:
The graph of y=⅔ x - 12 intersects the y-axis at Q (0, -12) and is perpendicular to a line joining Q to the point P ( x , 0). Find x
if a- b= 2 and ab= 15 then a3-b3?
a) 30 b) 98 c) 20 d) 60
full explanation please
Answer:
The answer is 98
Step-by-step explanation:
A = 5
B = 3
a_b = 2
a × b = 5 × 3 = 15
A3 _ b3 =(5) bower 3 _ (3) power 3 = 98
HELP ME I WILL GIVE POINTS
Answer:
1. 32
3. -11
Step-by-step explanation:
(To meet character limit)
Answer:
1.) 35
2.) -20
Step-by-step explanation:
which letter onthe diagram below represents a diameter of the circle.
H e l p this is confusing
Answer:
The answer would be 780 miles
Step-by-step explanation:
The reason that that's the answer because since it says that they will average about 65 miles per hour on a 12 hour trip, you have to multiply 65 time 12, which is 780 miles, so
65 miles x 12 hours = 780 miles :)
Hope this helped!
I NEED ANSWER NOW PLSSSSS
HELP ASAP
I WILL GIVE BRAINLIEST
How is the product of 2 and 5 shown on a number line?
2-1 0 1 2 3 4 5.7.1
-10
101235
7.
-13-
3-L 1 2 3
5
-1012
4 5
Answer:
4th option
Step-by-step explanation:
2x-5 means yo have to take minus 5 twice. So you start from 0 and jump back 5 steps twice. So 4
Harper was out at a restaurant for dinner when the bill came. She wanted to leave a tip of 16%. What number should she multiply the cost of the meal by to find the total plus tip in one step?
Answer:
Harper would take the Total Bill after tax and mutiply it by 0.16.
The formula for this would be
Total Bill = x
Tip = 16% -> 16/100 = 0.16
So
0.16x
Triangle A is a scaled version of triangle B. The dimensions of triangle A are twice the dimensions of triangle B. The area of triangle B is 40.5 sq cm. What is the area of triangle A?
Step-by-step explanation:
the lengths of any line (side, height,...) in A is twice as long as in B.
now, the area of a triangle is
baseline × height / 2
so, two lines are multiplied. that means the factor 2 gets multiplied in 2 times. and that means the area increases by the factor 2×2 = 4
therefore, the area of A is
40.5 × 4 = 162 cm²
Bạn dự định đi học thêm vào mùa hè này. Nếu đi học bạn sẽ không thể đi làm với thu nhập là 5 triệu đồng và không thể ở nhà nghỉ ngơi. Học phí là 2 triệu, tiền mua giáo trình 300 ngàn, sinh hoạt phí là 1.5 triệu. Hãy xác định chi phí cơ hội của việc đi học thêm vào mùa hè này.
Answer:
4 better inbox
Step-by-step explanation:
please help me on my math , I need help :(
Answer:
ask sombody else
Step-by-step explanation:
guess we dont
Nina and Jo both ran a 9 km race.
Nina took 1 hour 15 minutes to run the whole race.
Jo started the race 4 minutes later than Nina but caught up when they had both travelled 6 km.
If Nina and Jo both ran at constant speeds, what is Jo's speed to 2 dp?
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Answer:
7.83 km/h
Step-by-step explanation:
At her constant pace, Nina's time for 6 km will be found by the proportion ...
(time for 6 km)/(6 km) = (time for 9 km)/(9 km)
time for 6 km = (6 km)/(9 km) × (75 min) = 50 min
Jo's time for the same distance will be 4 minutes less: 50 -4 = 46 min. Jo's speed is ...
speed = distance/time
= (6 km)/(46/60 h) = 360/46 h ≈ 7.83 km/h . . . . Jo's speed
_____
Additional comment
From the 6 km point, the remaining race is half the distance already run, so will take half the time already taken. As we know, Nina will finish in 25 more minutes; Jo will finish in 46/2 = 23 more minutes, 2 minutes ahead of Nina.
The sum of two numbers is 65. The larger number is 5 more than the smaller number. What are the numbers?
Step-by-step explanation:
the numbers : x, y
x + y = 65
x = y + 5
we use the second equation in the first equation :
y + 5 + y = 65
2y + 5 = 65
2y = 60
y = 30
x = y + 5 = 30 + 5 = 35
Plz help!!!!! Need theses as soon as possible. No links plz!!!!
Answer:
1. 3
2. 0, 620
3. Positive
4. 2006
5. 2637
What is the slope of the function?
O-6
O 4
O 4
O 6
Answer:
12/2 = 6
Step-by-step explanation:
2 ways to do it, graph it, or do the slop finding formula y2-y1/x2-x1
answer:
Step-by-step explanation:
I hope she is correct answer
PLS HELP NOW! WILL GIVE BRAINLIEST TO WHO EVER ANSWERS FIRST
Answer:
y = 1.6x −5
Step-by-step explanation:
We start with two points, let’s say (0,-5) and (4,1.4).
The equation is:
y=mx+b
m is the slope and b the y-intercept.
We can find the slope by:
[tex]\frac{y_2-y_1}{x_2-x_1} = \frac{-5-1.4}{0-4} = 1.6[/tex]
Then solve the equation for b:
y = 1.6x + b ->
−5 = 1.6(0) + b ->
b = -5.
So the final equation is:
y = 1.6x −5.
Hope that helps! :)
PLEASE HURRY NEED HELP!!!!!
The Jayden family eats at a restaurant that is having a 15% discount promotion. Their meal costs $78.88 before the discount, and they leave a 20% tip. If the tip applies to the cost of the meal before the discount, what is the total cost of the meal? Round your intermediate calculations and answer to the nearest cent.
Answer:
80.22
Step-by-step explanation:
3^4x-1=15
Need help with this log question
Answer:
x=16/81
Step-by-step explanation:
3^4x-1=15
81x-1=15
81x=15+1
81x+16
divide both sides by 81
x=16/81
Cinco múltiplos del 12
Answer:
60 Sana po makatulong pa brainlest please
solve for x
2/x -2 = 3/2x +3
Step-by-step explanation:
On a recent vacation to the Philippines, Sama bought milk from two different stores. What is the difference in price between the two-unit rates for each carton of milk?
and
Derrick earns $14 per hour working at Pizza Palace. What will Derrick's new hourly rate be after a 4.5% raise.
Please solve this correctly. I will give Brainliest.
Answer:
yes because that are true
For a given two-digit number, the second digit is 2 more than 5 times the
first digit. Also, 5 times the first digit is 3 more than the second digit. Find
the two-digit number.
Answer:
no solution
Step-by-step explanation:
U=5t+2
5t=u+3
5t=5t+5
t=t+1
0=1
No solution
4x + y = 16
y = 0.5x -2
Answer:
x = 4, y = 0
Step-by-step explanation:
