Answer:
a) 0.1558 = 15.58% probability of finding 4 cars with the defect in a random sample of 7000 cars.
b) 0.1557 = 15.57% probability of finding 4 cars with the defect in a random sample of 7000 cars. These probabilities are very close, which means that the approximation works.
Step-by-step explanation:
Binomial 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.
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^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
To use the Poisson approximation for the binomial, we have that:
[tex]\mu = np[/tex]
1 in every 2500 automobiles produced has a particular manufacturing defect.
This means that [tex]p = \frac{1}{2500} = 0.0004[/tex]
a) Use a binomial distribution to find the probability of finding 4 cars with the defect in a random sample of 7000 cars.
This is [tex]P(X = 4)[/tex] when [tex]n = 7000[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 4) = C_{7000,4}.(0.0004)^{4}.(0.9996)^{6996} = 0.1558[/tex]
0.1558 = 15.58% probability of finding 4 cars with the defect in a random sample of 7000 cars.
(b) The Poisson distribution can be used to approximate the binomial distribution for large values of n and small values of p.
Using the approximation:
[tex]\mu = np = 7000*0.0004 = 2.8[/tex]. So
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 4) = \frac{e^{-2.8}*(2.8)^{4}}{(4)!} = 0.1557[/tex]
0.1557 = 15.57% probability of finding 4 cars with the defect in a random sample of 7000 cars. These probabilities are very close, which means that the approximation works.
Please answer this correctly without making mistakes my homework is due today
Answer:
3 T 2,973 lb
Step-by-step explanation:
[tex]1t + 2t = 3t \\ 1263 + 1710 = 2973[/tex]
A website lists homes for sale in a suburban town. The site provides information including neighborhood, selling
price, age of the home in years), number of bedrooms, and whether the home has a garage. Which of the variables
is a categorical variable?
neighborhood
selling price
age of the home
number of bedrooms
Answer:
neighborhood
Step-by-step explanation:
Variables can be classified as categorical(qualitative) and quantitative.
Categorical variables:
Its variables are labels(for example, good/bad, yes/no,...)
Quantitative variables:
It's variables are numbers.
In this question:
The only variable which the answer is a label is the neighborhood. So this is the answer.
Identify the true statement about the given patterns.
Pattern C: 4, 5, 6, 7, 8, ...
Pattern D: 2, 3, 4, 5, 6, ...
The terms in Pattern D are 2 more than the terms in Pattern C.
The terms in Pattern D are 1 more than the terms in Pattern C.
The terms in Pattern C are 2 times the terms in Pattern D.
The terms in Pattern C are 2 more than the terms in Pattern D.
Answer:
The 4th option i.e. 'The terms in Pattern C are 2 more than the terms in Pattern D' is correct.
Step-by-step explanation:
Given the patterns
Pattern C: 4, 5, 6, 7, 8, ...
Pattern D: 2, 3, 4, 5, 6, ...
If we carefully analyze, it is clear that terms in the pattern C are 2 more than the terms in Pattern D.
In other words, if we add 2 in each term of the Pattern D, we will get the pattern C.
For example,
Pattern D: 2, 3, 4, 5, 6, ...
Now, add 2 in each term of Pattern D
i.e.
2+2 = 4
3+2 = 5
4+2 = 6
5+2 = 7
6+2 = 8
It is clear that we get the results 4, 5, 6, 7, 8 when we add 2 in each term of Pattern D.
As 4, 5, 6, 7, 8 represent Pattern C. Therefore, we conclude that the terms in Pattern C are 2 more than the terms in Pattern D.
Hence, the 4th option i.e. 'The terms in Pattern C are 2 more than the terms in Pattern D' is correct.
Answer:
4, 5, 6, 7, 8 when we add 2 in each term of Pattern D
Step-by-step explanation:
How many 1/6 cups are in 2 1/2 cups
Answer:
15
Step-by-step explanation:
2 1/2 = 5/2 = 15/6
Y is inversely proportional to the square of x. If Y = 3 when x = 3, then Y =
ş, when x is
?
Answer:
It will be same the value of second Y
Answer:
y = [tex]\frac{27}{x^2}[/tex]
Step-by-step explanation:
Assuming you require the equation of proportion.
Given y is inversely proportional to x² , then the equation relating them is
y = [tex]\frac{k}{x^2}[/tex]
To find k use the condition if y = 3, then x = 3, that is
3 = [tex]\frac{k}{3^2}[/tex] = [tex]\frac{k}{9}[/tex] ( multiply both sides by 9 )
27 = k
y = [tex]\frac{27}{x^2}[/tex] ← equation of proportion
Peter is a college professor. His gross salary is
$112,000. If he has to pay 25% income tax what is
Peter's net income?
Answer:
peters net income is 28,000
What would be the final elevation if a moth is flying at at 9 meters above the ground and changes by -4?
a. 5 meters
b. -5 meters
c. 13 meters
d. -13 meters
Evaluate the function for x = 3.5 f(x)=[2.5x]
a 8.75
b 8
c 9
Answer:
The correct option is a. 8.75.
Step-by-step explanation:
Given:
f(x)=[2.5x] .............................. (1)
Where;
x = 3.5
The function can be evaluated by substituting x = 3.5 into equation (1), we have:
f(3.5) = 2.5 * 3.5
f(3.5) = 8.75
This implies the value of the function is 8.75. Therefore, the correct option is a. 8.75.
Earl attaches a wire from the top of a 16-foot flagpole and stakes it to the ground 12 feet from the base
of the pole. How many feet long is the wire?
16 Ft
Answer:
16 feet
Step-by-step explanation:
We are told that:
Earl attaches a wire from the top of a 16-foot flagpole and stakes it to the ground
Therefore, we can conclude that the Length of the wire = Length of the flagpole
The length of the wire = 16 ft
Therefore, the wire is 16 feet long.
1. During the month of March, it rained 1.8 inches. In April, it rained 1.75 inches.
How much did it rain over these 2 months?
It rained 3.55 over the 2 months. First you would have to add 1.8 and 1.75 because that how much they rained each month. Then you’ll have to add them together to find the answer which is 3.55. So the total inches of rain it rained both months together was 3.55 inches.
What could be used as a common denominator for 3/8 and 9/20?
If f(x)=-x+2 find f(4)
Answer:
-2
Step-by-step explanation:
-4+2=-2
Answer:
f(4) = -2
Step-by-step explanation:
[tex]f(x)=-x+2\\\\f(4)=-(4)+2\\\\f(4)=-4+2\\\\\boxed{f(4)=-2}[/tex]
Hope this helps!
The difference of 5c and 4c is 602 what is c?
Answer:
I believe c = 602
5c-4c=602
c=602
If x = 15 cm and y = 2/5 cm, what is the length of z?
Answer:
option b. 5 cm
Step-by-step explanation:
y² + x² = z²
(2/5)²+(/15)²=z²
2×5+15=z²
10+15=z²
25=z²
/25=z
5=z
If a 6 pound bag of oranges costs $5.46 and an 8 pound bag of oranges costs
$7.44, what is the unit prices of each bag?
Answer:
its food, eat it.
Step-by-step explanation:
just get the cheaper bag. why do we care about unit pricing?
add the Expression 3 y + 5 + y + 24
Answer:
29+4y
Step-by-step explanation:
Answer:
4y + 29
Step-by-step explanation:
Group all like terms together so variables are on one side and regular numbers are on the other, add all similar elements, then add all numbers together to form another expression.
3y + y + 5 + 24
3y + y = 4y
5 + 24 = 29
Answer: 4y + 29
What is 14/15 over 4/7 equal to
Answer:
[tex]\frac{0.93}{0.57}[/tex]
Step-by-step explanation:
Simplify both of the fractions so [tex]\frac{14}{15}[/tex] to get 0.93 and [tex]\frac{4}{7}[/tex] to get 0.57.
Then you put them back into fraction form.
11/12 3/6 3/12 what is the odd one out?
Answer:
11/12 is odd
Step-by-step explanation:
as it contain many decimal places
Please answer this correctly without making mistakes
9514 1404 393
Answer:
35 gallons 0 quarts
Step-by-step explanation:
There are 4 quarts per gallon, so this is ...
1 gallon 1 quart = 1 1/4 gallons
Then the product is ...
(1 1/4 gallons) × 28 = (5/4 gallons)×28 = 35 gallons (and 0 quarts)
PlZ help pleased I need an answer now
Answer:
1/12
Step-by-step explanation:
Can someone please solve this for me.
y= 50x+150
Answer:
Step-by-step explanation:
Y=25
Expanded Multiplication
563 x 3=
Answer:
1689
Step-by-step explanation:
563 x 3
1
5 6 3
x
3
-----------
1689 so you do 3x3 put ur answer then you do 6x3 = 18 carry the one and put it above the 5 do 5x3 = 15 and add that 1 you carried.
A waiter claims he made tips that were 221% more than his wage for the day. If he made $25 for his wage, how many tips did he make? $78.50 $78.00 0 $20.65 $68,50 None of the above
Answer: None of.the above
Step-by-step explanation:
From the question, we are informed that a waiter claims he made tips that were 221% more than his wage for the day.
Assuming the waiter made $25 for his wage, the number of tips that he made would be calculated as:
= $25 + (221% × $25)
= $25 + (2.21 × $25)
= $25 + $55.25
= $80.25
Since the answer isn't given in the option, the answer will be None of the above
pls help me on this
A lighthouse is located on an island 350 feet from the shore of the mainland as shown. If x=0.41 rad, what is D?
Now, let X= 0.41
Answer: d = 382
===========================================
Work Shown:
d = 350*sec(x)
d = 350*(1/cos(x))
d = 350*(1/cos(0.41))
d = 381.62910632113
d = 382
Make sure your calculator is in radian mode.
help me plzzzzzzz i will give u 50 points
Balanced means both sides are equal.
Add the left side: there are 7 1's which equal 7
Adding the right side you have 2 + r
They have to equal each other so the equation is 7 = 2 + r
which equation matches the table
Answer:
( B ) definitely .. try each choice and you will see .
Answer:
b
Step-by-step explanation:
How do I do this problem? My teacher isn’t good at explaining things...Thank you
Answer:
i cant read it cuz its sideways can you flip the picture plz i want to help
Step-by-step explanation:
Ice cubes trays each contain 12 cubes of ice. If t represents the number of trays, and c
represents the number of cubes, find an equation that relates t and c.
Answer:
c = 12 * t
Step-by-step explanation:
The only equation that relates t and c would be the following...
c = 12 * t
This is because the total number of cubes that exist depends on how many available trays exist. Therefore, creating a positive correlation relationship between these two variables. Since each tray contains 12 cubes, 12 is therefore multiplied by the number of trays to get the total number of cubes. This means that the more trays available the more cubes that are created.
2. (4a - 8b + 12c) (-5/2) Simply using distributive property and combining like terms
Answer:
-10a + 20b - 30c
Step-by-step explanation:
(4a - 8b + 12c)(-5/2)
=(4a + - 8b + 12c)(-5/2)
=(4a)(-5/2) + (-8b)(-5/2) + (12c)(-5/2)
=-10a + 20b -30c
(Also Mathpapa is great for this kind of problems and Mathw*y is also a good one I use those two all the time they both saved me so many times)
