A bank gets an average of 12 customers per hour. Assume the variable follows a Poisson distribution. Find the probability that there will be 10 or more customers at this bank in one hour.
Answers
Answer:
75.76% probability that there will be 10 or more customers at this bank in one hour.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
\(P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}\)
In which
x is the number of sucesses
e = 2.71828 is the Euler number
\(\mu\) is the mean in the given interval.
A bank gets an average of 12 customers per hour.
This means that \(\mu = 12\)
Find the probability that there will be 10 or more customers at this bank in one hour.
Either there are less than 10 customers, or there are 10 or more. The sum of the probabilities of these events is 1. Then
\(P(X < 10) + P(X \geq 10) = 1\)
We want \(P(X \geq 10)\)
Then
\(P(X \geq 10) = 1 - P(X < 10)\)
In which
\(P(X < 10) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9)\)
So
\(P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}\)
\(P(X = 0) = \frac{e^{-12}*12^{0}}{(0)!} \approx 0\)
\(P(X = 1) = \frac{e^{-12}*12^{1}}{(1)!} = 0.0001\)
\(P(X = 2) = \frac{e^{-12}*12^{2}}{(2)!} = 0.0004\)
\(P(X = 3) = \frac{e^{-12}*12^{3}}{(3)!} = 0.0018\)
\(P(X = 4) = \frac{e^{-12}*12^{4}}{(4)!} = 0.0053\)
\(P(X = 5) = \frac{e^{-12}*12^{5}}{(5)!} = 0.0127\)
\(P(X = 6) = \frac{e^{-12}*12^{6}}{(6)!} = 0.0255\)
\(P(X = 7) = \frac{e^{-12}*12^{7}}{(7)!} = 0.0437\)
\(P(X = 8) = \frac{e^{-12}*12^{8}}{(8)!} = 0.0655\)
\(P(X = 9) = \frac{e^{-12}*12^{9}}{(9)!} = 0.0874\)
\(P(X < 10) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) = 0 + 0.0001 + 0.0004 + 0.0018 + 0.0053 + 0.0127 + 0.0255 + 0.0437 + 0.0655 + 0.0874 = 0.2424\)
Then
\(P(X \geq 10) = 1 - P(X < 10) = 1 - 0.2424 = 0.7576\)
75.76% probability that there will be 10 or more customers at this bank in one hour.
Related Questions
Can I get a answer for it please
Answers
Answer:
25%
Step-by-step explanation:
There are 6+8+10 = 24 cookies
P ( chocolate chip) = number of chocolate chip/ total
= 6/24 = 1/4
Changing to percent
1/4 = 25/100 = 25%
Find the domain of the inverse function w-1 (x) . Express your answer as in inequality
Answers
Answer:
ANSWER
Step-by-step explanation:
Without knowing the specific function w(x), it is impossible to determine the domain of the inverse function w^-1(x). However, in general, the domain of an inverse function is the range of the original function, and vice versa.
If we assume that w(x) is a one-to-one function (which is necessary for it to have an inverse function), we can determine the range of w(x) and use it to find the domain of w^-1(x).
For example, if we know that w(x) is a function that takes all real numbers except x=2, then the range of w(x) is (-∞,2) U (2,∞). The domain of w^-1(x) is then the same as the range of w(x), which is (-∞,2) U (2,∞). Therefore, the domain of w^-1(x) is x ≠ 2.
Without more information about w(x), we cannot determine the domain of w^-1(x) more precisely.
Brayden has 7/8 of a candy
bar. He wants to split the
bar into servings that are
3/10 of the bar. How many
servings can he make?
Answers
When 7/8 of the candy bar is split into 3/10 of the bar, the candy bar can make around 2 servings.
What are fractions?In mathematics, a fraction is represented by a number that identifies a portion of a whole. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.
Given that there is 7/8 of the candy bar. The bar is needed to be further divided into 3/10 of the bar, this can be calculated as follows:
\(\frac{\frac{7}{8} }{\frac{3}{10} } = \frac{7}{8} * \frac{10}{3} = 2.91\)
Hence, we can make 2 serving of the required amount, with an extra piece for third serving. Since, the third serving will not be exactly of the required amount it is not counted.
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need help i dont understand
Answers
Answer:
Step-by-step explanation:
it would be "c" because the question asks for the number that makes the inequality true
4x≤ x+3
the graph in c is saying that every number that is 1 or less than 1 makes the inequality true. so lets take -7 as an example
4 x -7=-28
-28+3=-25
-25 is greater than -28 so the inequality is true. the reason why graph d doesnt work is because if we plug in 2 into the equation, then 4x =8 and x+3=5
5 is not greater than 8 so it doesnt work
6 minutes 20 seconds into seconds.
Answers
Answer:
380 seconds
Step-by-step explanation:
Convert 6 minutes to seconds by multiplying 6 times 60, because there are 60 seconds per minute.
6 x 60 = 360
Now add the 20 seconds.
360 + 20 = 380
6 minutes and 20 seconds are equal to 380 seconds.
WHAT is the power of 10*5 well is 100*5
Answers
Answer:
So, 100 to the 5th power is 10,000,000,000 (or say 10 billion) in words.
Now, look at the explanation below.
Step-by-step explanation:
100 powers are the following:
100 1 = 100
100 2 = 10,000
100 3 = 1,000,000
100 4 = 100,000,000
100 5 = 10,000,000,000
100 6 = 1,000,000,000,000
If this helped you, you should thank me a lot. :)
If this didn't, try rereading the power table.
Please help ASAP
In the diagram, line a and b are parallel. Line is the transversal.
Given that the measure of angle POQ is 114° determine the measure of angle QON
In your explanation be sure to include the key terms corresponding angles ,supplementary Angles, parallel lines ,and transversal computational slep in complete sentences
Answers
The measure of angle QON is 66 degrees
What are transversal lines ?
In geometry, a transversal is any line that intersects two straight lines at distinct points
In geometry, two lines in the same plane are transversed by a line at two different locations. The parallelism of two or more additional straight lines in the Euclidean plane is established via transversals. Two lines cross it at separate locations. Transversal intersection creates a number of angles. These include co-interior, alternate interior, alternate exterior, and matching angles.
From the figure,
∠POQ + ∠QON = 180 degrees
114 + ∠QON = 180
=> ∠QON = 180 - 114 = 66 degrees
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QUESTION FOUR
A. Use Excel to prepare an appropriate type of chart (bar, line, pie, scatter) to display
the U.S. energy consumption data. You may modify the default colors, fonts, etc., as
you judge appropriate to make your display effective. (15 pts)
B. What type of chart did you choose, and why did you choose this chart? (5 pts.)
pts.).
3. Explain why you chose each chart; be as thorough as you can on why the selected cha
the type of data (Part B- 5 pts)
4. Note: there may be more than one type of chart that is appropriate. You only need to c
however, if you like, you may also create a second chart for the same question (optiona
URGENT
Answers
The most appropriate chart to depict US energy consumption would be a pie chart since a pie chart helps to see the composition of different proportions representing total consumption.
How to explain the chartsChart A is not appropriate because a line graph is used to depict information to analyze changes over time or over a period. However, to show the energy consumption, the line graph is not an accurate depiction since the type of energy source is a categorical variable.
Chart B is also appropriate because it is a column graph and such type of graphs are used to represent categorical variables. The US energy consumption can be represented well through a column graph as it well depicts the highest consumption source and the lowest consumption source.
Yes more than one kind of display would therefore be acceptable as we can use to show the information through both a pie chart and a column graph.
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the measures of ABD is (0.2x+52) and the measures of CBD is (0.2x+42) find the value of x
Answers
The value of x in the triangle is determined as 45.
What is the value of x?The value of x in the triangle is calculated by applying the following formula,.
The measure of angle ABD = 0.2x + 52
The measure of angle CBD = 0.2x + 42
From the diagram, we can set-up the following equations;
x + 16 = 0.2x + 52
Simplify the equation above, by collecting similar terms;
x - 0.2x = 52 - 16
0.8x = 36
Divide both sides of the equation by " 0.8 "
0.8x / 0.8 = 36/0.8
x = 45
Thus, the value of x in the triangle is calculated by equating the appropriate values to each other.
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What is the value of n? A) 41° B) 139° C) 141°D) 180°
Answers
In the diagram we can see that
\(n_2=139^{\circ}\)because they are vertically opposite angles.
And
\(n_2=n\)because they are alternate interior angles, so
\(n^{\circ}=139^{\circ}\)Letter B.
PLEASE HELP ME FAST I NEED HELP PLEASE
Answers
Answer:
The first one
Step-by-step explanation:
You You need to make it 5 lb of crawfish so 6$ for 4 pounds is 12$
1 pound is 3$
4 pounds + 1 pound is 15$
Shop a and b is 15$
The graph shows the distribution of the lengths (in seconds) of videos on a popular video-streaming site. The distribution is approximately Normal, with a mean of 264 seconds and a standard deviation of 75 seconds.
A graph titled Streaming Videos has length (seconds) on the x-axis, going from negative 36 to 564. The highest point of the curve is at 264.
What percentage of videos on the streaming site are between 264 and 489 seconds?
0.15%
49.85%
95%
99.7%
Answers
According to the properties of the standard normal distribution, approximately 99.7% of the values lie within three standard deviations of the mean. Therefore, the answer is 99.7%.
To determine the percentage of videos on the streaming site that are between 264 and 489 seconds, we need to calculate the area under the normal curve within that range. Since the distribution is approximately normal with a mean of 264 seconds and a standard deviation of 75 seconds, we can use the properties of the standard normal distribution to find the desired percentage.
First, we need to convert the values 264 and 489 to z-scores, which represent the number of standard deviations a particular value is away from the mean. The z-score formula is given by:
z = (x - μ) / σ
where x is the value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get:
z1 = (264 - 264) / 75 = 0
z2 = (489 - 264) / 75 = 3
Next, we can use a standard normal distribution table or a calculator to find the area under the curve between z = 0 and z = 3. The area represents the percentage of videos falling within that range. The answer is 99.7% .
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Ullany TVd How much 20k stamps can #2.00 buy
Answers
Answer: 4000
Step-by-step explanation:
Find the area of the composite figure below.
2 ft
2 ft
6 ft
4 ft
8 ft
22 ft2
30 st²
36 ft²
38 ft
Answers
Answer:
A = 139.25
Step-by-step explanation:
24) Janet takes home 800 a week. She always tries to set aside
of her pay. Of the
1
money she sets aside, Janet puts into her savings account. How much does she
2
add to her savings account each week?
Answers
Which expression represents twice the sum of a number and six
Answers
Answer:
2(x + 6)
Step-by-step explanation:
If we let the number be "x", then the sum of the number and six is x + 6. To find twice the sum, we multiply this expression by 2:
2(x + 6)
Therefore, the expression that represents twice the sum of a number and six is 2(x + 6)
Find the volume of the rectangular prism.
Answers
Answer:
Q9:
\(\boxed{V = \dfrac{7}{96}\;cubic\;feet}}\)
Q10
\(\boxed{V = \dfrac{64}{125}\;cubic\;yards}\)
Step-by-step explanation:
For a rectangular prism, the volume = length x width x height
Given these 3 dimensions simply multiply them to get the volume
Q9
\(V = \dfrac{7}{8} \cdot \dfrac{2}{3} \cdot \dfrac{1}{8}\\\\\)
\(V = \dfrac{7\cdot 2\cdot 1}{8\cdot 3 \cdot 8}\\\\V = \dfrac{14}{192}\\\\\)
Divide numerator and denominator to reduce to lowest fraction
\(V = \dfrac{14 \div 2}{192\div 2}\\\\\boxed{V = \dfrac{7}{96}\;cubic\;feet}}\)
Q10
This is a cube since each side is the same length
For a cube of side a, the volume = a³
So for this particular cube
\(V = \left(\dfrac{4}{5}\right)^3\\\\\\\boxed{V = \dfrac{64}{125}\;cubic\;yards}\)
Alegbra- How can I solve #5?
Answers
Answer:
3
9
21
Step-by-step explanation:
For the first one use the law of total probability
B=A∩B+A'∩B
12=9+A∩B
A∩B= 3
For this one you should use demorgans law and the union formula
(A'∩B')=(AUB)'
AUB= A+B-A∩B
6+12-3=15
15'= 24-15 = 9
For this one use demorgans law again
(A'UB')=(A∩B)'
(A∩B)'= 24-A∩B= 24-3= 21
I WILL GIVE U
THE BRAINLEST!!!!!
I WILL GIVE U THE BRAINLEST!!!!!
If a circle has a diameter of 3 cm, what is the circumference? Enter a numerical value
only. Round all answers to the nearest hundredth.
Answers
Answer:
C≈9.42cm
Step-by-step explanation:
This is the correct answer for your question
Answer:
3.71
Step-by-step explanation:
Robin can make 8 puppets with the material she already has. For each additional sheet of felt she buys, she can make 5 more puppets. What is an equation that shows how the total number of puppets she can make, y, depends on the number of sheets of felt she buys?
Answers
Therefore the equation is
y = 5x + 8
Hope it helps
Use the distributive property to identify the equivalent expression.
8x + 10
Answers
Answer:
36
Step-by-step explanation:
8squared+10=18
18x2=36
Answer:
ummmmmmmmmmmmmmmmmmmmmmmm
Suppose that a single die with 9 sides (numbered 1, 2, 3, ... , 9) is rolled twice. What is the probability that the sum of the two rolls equals 3
Answers
Answer:
2/81Step-by-step explanation:
Probability is defines as the likelihood or chance that an event will occur.
Probability = expected outcome of event/total outcome.
Since a single die with 9 sides was rolled, the total event outcome will be 9*9 = 81
Expected outcome will be the event that the sum of the two rolls equals 3. The possible outcomes are {(1,2), (2,1)}. The expected outcome is 2
Probability that the sum of the two rolls equals 3 = 2/81
The probability that the sum of the two rolls equals 3 is \(\dfrac{2}{81}\).
Important information:
A single die with 9 sides is rolled twice.We need to find the probability that the sum of the two rolls equals 3.
Probability:If a die with 9 sides is rolled twice, then the number of total possible outcomes is:
\(9\times 9=81\)
The sum of the two rolls equals 3, if we get 1, 2 and 2, 1. It means the number of favorable outcomes is 2.
\(P=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}\)
\(P=\dfrac{2}{81}\)
Therefore, the probability that the sum of the two rolls equals 3 is \(\dfrac{2}{81}\).
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SOLVE FOR T
t+3/2 = -2
T =
Answers
Answer:\(t= -\frac{7}{2}\)
Step-by-step explanation:
\(=t+\frac{3}{2}=-2\\=t=-2-\frac{3}{2} \\=t=-\frac{7}{2}\)
Which of the following are solutions to the equation below?
Check all that apply.
4x2 - 81 = 0
Answers
What we should do now to 136 x 27 = 3672, to get back to 1.36 x 2.7.
Use your answer to explain the placement of the decimal point in 1.36 x 2.7.
Answers
Answer:
Step-by-step explanation:
8.008.009
Need answer asap, will give brainliest.
Answers
Answer:
(-2,3)
Step-by-step explanation:
You can see that the purple is the new triangle. So look at the coordinate of the D. You can see that it is plotted at (-2, 3)
Answer:
(-2, 3)
to find the point of something you first find where uts standing on the x-axis (vertical line) and then where its standing on the y-axis (horizontal line)
Please help solve 3m/2/3 = 7
Answers
Answer:
the solution to the equation is m = 28/3, or approximately 9.3333
Step-by-step explanation:
To solve this equation, you need to get the variable, in this case "m," by itself on one side of the equation. To do this, you can start by isolating the fraction on the left side of the equation. You can do this by multiplying both sides of the equation by 2/3, which will cancel out the 2/3 on the left side:
3m/2/3 = 7
(2/3) * (3m/2/3) = (2/3) * 7
3m/2 = 7 * (2/3)
3m/2 = 14/3
Next, you can multiply both sides of the equation by 2 to get rid of the fraction on the left side:
(2) * (3m/2) = (2) * (14/3)
3m = 28/3
Finally, you can simplify the right side of the equation by dividing both sides by 3 to get the final solution:
(3m) / 3 = (28/3) / 3
m = 28/3
Therefore, the solution to the equation is m = 28/3, or approximately 9.3333.
Answer:
Maybe m = 14/9
Maybe m = 14
Step-by-step explanation:
It is not clear what you mean by the fraction on the left side.
Do you mean
3m/(2/3) = 7 ?
If so:
3m = 7 × 2/3
3m = 14/3
m = 14/9
Do you mean
(3m/2)/3 = 7 ?
If so:
3m/2 = 21
m = 21 × 2/3
m = 14
Do you mean something else?
When something is refracted, it changes
direction
volume
size
Answers
Refraction is an effect that occurs when a light wave, incident at an angle away from the normal, passes a boundary from one medium into another in which there is a change in velocity of the light. Light is refracted when it crosses the interface from air into glass in which it moves more slowly.
y=x^2-2x+7
i need help finding the axis of symmetry,the domain, the y-intercept and x intercept
Answers
The axis of symmetry is at x = 1, the domain is (-∞, +∞), the y-intercept c is at 7 and x intercept is not applying .
Explain about the features of parabolic function?A parabolic function is one that satisfies the formula f(x) = ax2 + bx + c and, when represented graphically in two dimensions, has the shape of a parabola. Any quadratic equation with just a second degree in x is the equation for a parabolic function.
The following characteristics define a basic parabola:
The y-axis, a symmetry axis, is where it is symmetric.At the origin, marking the minimal turning point, y has its minimum value. It is sometimes referred to as the parabola's vertex.The parabola's arms are infinitely long.Thus, from the given graph the value are obtained as:
the axis of symmetry is at x = 1, the domain is (-∞, +∞), the y-intercept c is at 7 and x intercept is not applying .Know more about parabolic function
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What is the image point of (-7,-8)after the transformation D1/2oT-1,0?
Answers
The image point of (-7,-8) after the transformation D1/2oT-1,0 is (-4,4).
First, we apply the translation T-1,0, which moves every point 1 unit to the right (since the x-coordinate is decreased by 1) and leaves the y-coordinate unchanged. Therefore, the image of (-7,-8) under T-1,0 is (-7-1,-8) = (-8,-8).
Next, we apply the dilation D1/2, which scales every distance from the origin by a factor of 1/2. Therefore, the image of (-8,-8) under D1/2 is (-8/2,-8/2) = (-4,-4).
Thus, the image point of (-7,-8) after the transformation D1/2oT-1,0 is (-4,4).
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