The probability that p(hat) < 0.04 if the fraction nonconforming really is 0.02 can be calculated using the normal approximation to the binomial distribution.
Explanation:To find the probability that p(hat) < 0.04 if the fraction nonconforming really is 0.02, we can use the normal approximation to the binomial distribution.
1. Calculate the mean of the sampling distribution using the formula:
μ = np = 50 * 0.02 = 1
2. Calculate the standard deviation using the formula:
σ = sqrt(npq)
where q = 1 - p = 1 - 0.02 = 0.98
σ = sqrt(50 * 0.02 * 0.98) ≈ 0.99
3. Convert p(hat) to a z-score using the formula:
z = (p(hat) - μ) / σ
z = (0.04 - 1) / 0.99 ≈ -0.96
4. Look up the z-score in the standard normal distribution table to find the corresponding probability.
P(z < -0.96) ≈ 0.166
Therefore, the probability that p(hat) < 0.04 if the fraction nonconforming really is 0.02 is approximately 0.166.
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Complete question:
A random sample of 50 units is drawn from a production process every half hour. The fraction of non-conforming product manufactured is 0.02. What is the probability that p(hat) < 0.04 if the fraction nonconforming really is 0.02?
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py+7=6y+q solve for y
We know that we are solving for y.
This is a step by step procedure to get the value of y.
First: Move all terms to the left side and set equal to zero.
Second: Then set each factor equal to zero.
The application is:
Given: py+7=6y+q
-6y -7 -6y -7 = 0
(p-6)y = q-7
divide both sides by p-6
y=(q-7)/(p-6)
Answer is y = (q – 7) / (p – 6)
The solution of expression for y as,
⇒ y = (q - 7) / (p - 6)
We have to given that,
An expression is,
⇒ py + 7 = 6y + q
Now, We can simplify the expression for y as,
⇒ py + 7 = 6y + q
Subtract 6y both side,
⇒ py - 6y + 7 = 6y + q - 6y
Subtract 7 both side,
⇒ py - 6y = q - 7
⇒ y (p - 6) = (q - 7)
Divide both side by (p - 6);
⇒ y = (q - 7) / (p - 6)
Therefore, The solution of expression for y as,
⇒ y = (q - 7) / (p - 6)
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what is 28.5 divided by 5
Find the quadratic function that is the best fit for f(x) defined by the table below
The quadratic equation defined by the table is f(x) = 2.35x^2 + 4.72x -1.55
How to determine the function?A quadratic function is represented as:
f(x) = ax^2 + bx + c
Using the table of values, we have:
a(0)^2 + b(0) + c = -1.55
This gives
c = -1.55
Also, we have:
a(2)^2 + b(2) + c = 17.29
4a + 2b -1.55 = 17.29
This gives
4a + 2b = 18.84
Divide through by 2
2a + b = 9.42 --- (2)
Also, we have:
a(4)^2 + b(4) + c = 54.93
16a + 4b -1.55 = 54.93
This gives
16a + 4b = 56.48
Divide through by 4
4a + b = 14.12 ---- (3)
Subtract (2) from (3)
2a = 4.7
Divide by 2
a = 2.35
Substitute a = 2.35 in 4a + b = 14.12
4*2.35 + b = 14.12
Evaluate
b = 4.72
Substitute values for a, b and c in f(x) = ax^2 + bx + c
f(x) = 2.35x^2 + 4.72x -1.55
Hence, the quadratic equation defined by the table is f(x) = 2.35x^2 + 4.72x -1.55
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2x+5=10
Solve for x
8x__=2
10x__= 5
—
2
6x__= 3
—
2
?? Can you fill in the blanks?
What is 36 divided by 3/4?
Which Rate Does Not Belong With The Other Three. Explain
60 mi/h
88 ft/s
500 ft/min
1,440 mi/day
88ft/s
hop this helps
Supposed to angles are supplementary and one of them measures 31° what is the measure of the other angle
There is 3/4 of a box of cereal remaining. You eat 2/5 of the remaining cereal. What fraction of the box do you eat?
how many integers from 1 to 700 are divisible by 2, 5 and 7
There are 10 integers from 1 to 700 that are divisible by 2, 5, and 7. This is calculated by finding the least common multiple (LCM) of the numbers, which is 70, and then determining how many multiples of 70 are within the given range.
Explanation:The question asks to find out how many integers from 1 to 700 are divisible by 2, 5, and 7. An integer divisible by 2, 5, and 7 is also divisible by their least common multiple (LCM). The LCM of 2, 5, and 7 is 70 since 2 x 5 x 7 = 70. So, the task is to find the number of multiples of 70 between 1 and 700.
To find the number of multiples of 70 in that range, you can use the following steps:
Divide the largest number in the range (700) by 70 to find the highest multiple within the range. ∑(700 ÷ 70 = 10).Since we started from 1 and 70 is the first multiple, the total count is the result of the division.Therefore, there are 10 integers from 1 to 700 that are divisible by 2, 5, and 7.
Give A={a,b,c},how many subsets does A have including 0?
Simplify the equation and write the answer without negative exponents
A factory makes an oil mixture by mixing oils of grades A and B as follows. For every 2.3 liters of grade A oil, 1.2 liters of grade B oil are mixed in. How many liters of grade A oil and grade B oil will the factory need to make 1000 liters of their oil mixture? Explain your solution.
use properties to find 4 times 23 times 25
Answer:
2300
Step-by-step explanation:
The second side of a triangular deck is 6 feet longer than the shortest side and a third side that is 6 feet shorter than twice the length of the shortest side. If the perimeter of the deck is 68 feet, what are the lengths of the three sides?
Answer: The required lengths of the three sides of the deck are 17 feet, 23 feet and 28 feet.
Step-by-step explanation: Given that the second side of a triangular deck is 6 feet longer than the shortest side and a third side that is 6 feet shorter than twice the length of the shortest side.
The perimeter of the deck is 68 feet.
We are to find the lengths of the three sides of the deck.
Let x feet be the length of the shortest side.
Then, according to the given information,
the length of the second side = (x+6) feet
and
the length of the third side = (2x-6) feet.
Since the perimeter of the deck is 68 feet, so we must have
[tex]x+x+6+2x-6=68\\\\\Rightarrow 4x=68x=\dfrac{68}{4}\\\\\Rightarrow x=17.[/tex]
Therefore the lengths of the three sides are
17 feet, (17+6) feet and (2×17-6) feet
= 17 feet, 23 feet and 28 feet.
Thus, the required lengths of the three sides of the deck are 17 feet, 23 feet and 28 feet.
What is the vertex of the graph of y+2x+3 = -(x+2)^2 + 1?
A. (-3,-33)
B. (-3,3)
C. (3,-24)
D. (3,21)
How do I solve this equation? I need a refresher on Algebra.
Final answer:
To solve an algebraic equation, identify knowns, find suitable equations, simplify algebraically, substitute known values, solve for the unknown, and check if the answer is reasonable.
Explanation:
To solve an algebraic equation, follow these systematic steps:
Firstly, identify the knowns and make a list of what is given or can be inferred from the problem.
Then, find the appropriate equation or set of equations that contain the unknown you need to solve for.
Simplify the algebra by eliminating terms wherever possible. This might require algebraic rearrangement such as dividing terms or multiplying both sides of the equation to isolate the unknown.
Substitute the known values into the equation.
Solve for the unknown and make sure to include units where necessary.
Finally, always check your answer to see if it is reasonable and makes sense.
These steps should yield a solution that is both accurate and verifiable.
PLEASE ASAP
Trapezoid W ′ X ′ Y ′ Z ′ is the image of trapezoid WXYZ under a dilation through point C. What scale factor was used in the dilation?
− 7/3
− 3/7
3/7
7/3
How are the values of the eights in 880 relared
The difference between two positive integers is 4. If the smaller is added to the square of the larger, the sum is 68. Find the integers.
Two positive integers x and y
x - y = 4
x² + y = 68
Findx and y
SolutionAdd the two equations together.
... (x - y) + (x² + y) = (4) + (68)
... x² + x = 72
Rearrange to standard form and factor.
... x² + x - 72 = 0
... (x + 9)(x - 8) = 0
Use the zero product rule to find the solutions. That rule says the product is zero when one or more factors is zero.
... x + 9 = 0 ⇒ x = -9
... x - 8 = 0 ⇒ x = 8 . . . . . . the positive solution
Then we can find y from
... 8 - y = 4
... y = 4 . . . . . . . add y-4 to the equation
The two positive integers are 8 and 4.
To solve for the two positive integers where their difference is 4 and the sum of the smaller and the square of the larger is 68, we set up a quadratic equation and solve for n to find that the integers are 4 and 8.
Explanation:The problem given is a classic algebra question where we are asked to determine two positive integers based on their relationship to each other and an additional numeric condition. We know that the difference between these two numbers is 4, and when the smaller integer is added to the square of the larger, the result is 68.
Let's denote the smaller number as n and the larger number as n+4, since there is a difference of 4 between them. Now, according to the second condition given, we can set up the following equation: n + (n+4)2 = 68.
Expanding the squared term and combining like terms, we get a quadratic equation: n2 + 8n + 16 + n = 68. Simplifying, n2 + 9n + 16 = 68. Further simplification leads to n2 + 9n - 52 = 0. Factoring this quadratic equation, we find the integers that satisfy the equation: n = 4 and n = -13. Since we are looking for positive integers, the solution is n = 4 and n+4 = 8.
Therefore, the two positive integers are 4 and 8.
i need help 7th grade 13 + p + - 4 3
How do you write 7/20 as a percentage??
I need help I am trying to find ft
1 foot = 12 inches
divide 69 by 12
69/12 = 5.75 feet
pre cal/cal master needed
g(x)={ ax-3, x<-2
{ x^2 -2x, x>-2
What value would the function g(x) have point discon. at x=-2 how to find?
Irrigation improves the yield of strawberries per acre according to the function S=-(w-2)^2 +50 where S is the number of pints of strawberries grown per acre and w is the acre-feet of water used. Strawberries sell for $3 per pint and water costs $5 per acre-foot. Graph the yield function.
You are building a new house on a cartesian plane whose units are measured in miles.
Your house is to be located at the point (6,0). Unfortunately, the
existing gas line follows the curve y=√16x^(2)+6x+19.
It costs 300 dollars per mile to install new pipe connecting your house to the existing line.
What is the least amount of money you could pay to get hooked up to the system?
what is 25.6 divided by 0.5 =
What is n in a(n-5)+6=bn.(You can use variables in the answer). Please explain, if you can.
What is the value of x in the equation 2x – 3 = 9 – 4x?
The length of a table is 6 feet. On a scale drawing, the length is 2 inches. Write three possible scales for the drawing
Answer:
The three possible scales for the drawing are 1 inch : 3 feet, 1 inch : 36 inch and 1 inch : 91.44 cm.
Step-by-step explanation:
It is given that the length of a table is 6 feet. On a scale drawing, the length is 2 inches.
The scale for drawing is
[tex]Scale=\frac{\text{Length in drawing}}{\text{Actual length}}=\text{Length in drawing}:\text{Actual length}[/tex]
First possible scale for the drawing is
2 inch : 6 feet
It can be written as
1 inch : 3 feet
We know that 1 feet = 12 in
1 inch : 36 inch
We know that 1 feet = 30.48 cm
1 inch : 91.44 cm
Therefore the three possible scales for the drawing are 1 inch : 3 feet, 1 inch : 36 inch and 1 inch : 91.44 cm.
The three possible scales for the drawing are 1 inch : 3 feet, 1 inch : 36 inch and 1 inch : 91.44 cm.
Here, we have,
It is given that the length of a table is 6 feet. On a scale drawing, the length is 2 inches.
The scale for drawing is
scale = length in drawn/actual length
scale = length in drawn : actual length
First possible scale for the drawing is
2 inch : 6 feet
It can be written as
1 inch : 3 feet
We know that 1 feet = 12 in
1 inch : 36 inch
We know that 1 feet = 30.48 cm
1 inch : 91.44 cm
Therefore the three possible scales for the drawing are 1 inch : 3 feet, 1 inch : 36 inch and 1 inch : 91.44 cm.
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