After you collect your data, you have several options in regards to the null hypothesis. First, you could fail to reject the null hypothesis.
The data did not provide enough evidence to support the alternative hypothesis, and you accept the null hypothesis as the most likely explanation. Second, you could reject the null hypothesis. This means that your data provided enough evidence to support the alternative hypothesis, and you reject the null hypothesis as the most likely explanation. To neither accept nor reject the null hypothesis. The less common option and occurs when your data does not provide enough evidence to reject the null hypothesis, but also does not provide enough evidence to accept it as the most likely explanation.
The null hypothesis after you collect your data include failing to reject it, rejecting it, or neither accepting nor rejecting it.
To know more about null visit:-
https://brainly.com/question/31031308
#SPJ11
Which of the following is a unit vector perpendicular to the plane determined by the vectors A-2i+ 4j and B=i+j - k? o (-2i+ j - k) ot(+2) 0 1 (-2; - ; -1) -2i+j-k
The vector perpendicular to a plane determined by two vectors A and B can be found by taking their cross product. The unit vector perpendicular to the plane determined by the vectors A and B is (-4/√56)i + (2/√56)j + (-6/√56)k.
A x B = (-2i+4j+0k) x (i+j-k)
= (-4k + 2i + 6j)
To find a unit vector perpendicular to the plane, we need to normalize this vector by dividing it by its magnitude:
|A x B| = sqrt((-4)^2 + 2^2 + 6^2) = sqrt(56)
So, a unit vector perpendicular to the plane determined by A and B is:
(-4k + 2i + 6j) / sqrt(56)
which simplifies to:
(-2i + 3j - k) / sqrt(14)
Therefore, the answer is (-2i + 3j - k).
To find a vector perpendicular to the plane determined by vectors A and B, you need to calculate the cross product of A and B.
A = -2i + 4j
B = i + j - k
Step 1: Calculate the cross product (C) of vectors A and B:
C = (A_y * B_z - A_z * B_y)i - (A_x * B_z - A_z * B_x)j + (A_x * B_y - A_y * B_x)k
Step 2: Plug in the values of A and B:
C = (4 * (-1) - 0 * 1)i - (-2 * (-1) - 0 * 1)j + (-2 * 1 - 4 * 1)k
Step 3: Simplify the expression:
C = -4i + 2j - 6k
Step 4: Find the magnitude of C:
|C| = √((-4)^2 + 2^2 + (-6)^2) = √(16 + 4 + 36) = √56
Step 5: Divide each component of C by its magnitude to find the unit vector:
Unit vector = (-4/√56)i + (2/√56)j + (-6/√56)k
So, the unit vector perpendicular to the plane determined by the vectors A and B is (-4/√56)i + (2/√56)j + (-6/√56)k.
Learn more about vector at: brainly.com/question/24256726
#SPJ11
ASAP HELPPP!
Write an equation for the parabola graphed below.
The equation of the parabola graphed below is given as follows:
x = -1/49(y - 2)² - 1.
How to obtain the equation of the parabola?The parabola in the context of this problem is in horizontal form, hence the equation is given as follows:
x = a(y - k)² + h.
In which the parameters are given as follows:
a is the leading coefficient.(h,k) are the coordinates of the vertex.The coordinates of the vertex are given as follows:
(-1, 2).
Hence:
x = a(y - 2)² - 1.
When x = -2, y = -5, hence the leading coefficient a is obtained as follows:
-2 = a(49) - 1
a = -1/49.
Hence the equation is:
x = -1/49(y - 2)² - 1.
More can be learned about the equation of a parabola at https://brainly.com/question/4061870
#SPJ1
please help my answers are wrong
The proof that shows that sides SP is congruent to side TR is explained below.
How to Prove that Sides SP and TR are Congruent to Each Other?First, using the given information, we have to establish that both triangles are congruent to each other, then state that the two sides are congruent since corresponding parts of congruent triangles are congruent.
Therefore, the correct proof is:
Statement Reason
1. QP ≅ QR; SQ ≅ TQ 1. Given
2. <SQP ≅ <TQR 2. Vertical Angle Theorem
3. ΔSQP ≅ ΔTQR 3. SAS congruence theorem
4. SP ≅ TR 4. Corresponding parts of congruent
triangles are congruent.
Learn more about congruent triangles on:
https://brainly.com/question/1675117
#SPJ1
you need to run stats testing on sales data from two different buffalo wild wings stores to see if there's a correlation between number of employees and customer satisfaction. the test you want is a:
If there is a correlation between the number of employees and customer satisfaction in two different Buffalo Wild Wings stores, we need to perform a Pearson's correlation coefficient analysis.
To run stats testing on sales data from two different Buffalo Wild Wings stores, we need to use a correlation analysis. Specifically, we need to use Pearson's correlation coefficient to determine if there is a relationship between the number of employees and customer satisfaction. The Pearson's correlation coefficient ranges from -1 to +1, with -1 indicating a perfect negative correlation and +1 indicating a perfect positive correlation. If the coefficient is close to zero, it indicates that there is no correlation.
The data we need to collect includes the number of employees in each store and the sales data for a specific period. We also need to gather customer satisfaction data, which can be collected through surveys or other feedback mechanisms. Once we have the data, we can use a statistical software program like SPSS or Excel to perform the correlation analysis.
If the correlation coefficient is positive and statistically significant, it means that there is a relationship between the number of employees and customer satisfaction. This could mean that more employees lead to better customer service, which in turn leads to higher customer satisfaction and sales. However, if the correlation is negative or not statistically significant, it means that there is no relationship between the two variables.
In conclusion, to determine if there is a correlation between the number of employees and customer satisfaction in two different Buffalo Wild Wings stores, we need to perform a Pearson's correlation coefficient analysis. Gathering accurate data and using statistical software will allow us to determine if there is a significant relationship between the variables.
To know more about Employees visit:
https://brainly.com/question/29450584
#SPJ11
Fifteen words were randomly selected from a book. The line plot shows the number of letters in each of the 15 words.
What is the mean length of the words?
Just type the number No Units.
The mean length of the words that are given above in a line plot would be = 4
How to calculate the mean length of given words?The total number of words that where selected form the book = 15
The number of letters in each word is represented above in a line plot such as follows;
words with one letter = 3 ×1 = 3 letters
words with two letters = 2×2 = 4
Words with 3 letters = 1×3 = 3
words with four letters =4×4 = 16
words with six letters = 2 × 6 = 12
words with seven letters = 2×7 = 14
Words with eight letters = 1×8 = 8
Total word length = 3+4+3+16+12+14+8 = 60
But mean = total of given data/number of data
= 60/15
= 4
Learn more about permutation here:
https://brainly.com/question/30267292
#SPJ1
out of 550000 given to a school, an amount of 325000 was used.what fraction of the total amount was used
Answer:
Step-by-step explanation:
[tex]\frac{325000}{550000} \\= \frac{325}{550} \\= \frac{65}{110}\\ = \frac{13}{22}[/tex]
In the diagram below, AABC= ADEF. Complete the statement ZA =
C
A
B
F
D
In the diagram, if ΔABC= ΔDEF, then angle A is congruent to angle D.
Option C.
What are similar triangles?Similar triangles are triangles that have the same shape, but not necessarily the same size. In other words, their corresponding angles are equal, and their corresponding sides are proportional in length.
Two triangles are considered similar if they satisfy one of the following conditions:
AA SimilaritySSS SimilaritySAS SimilarityABC ≅ DEF
∠A ≅ ∠ D
Thus, two triangles are similar if their corresponding angles are congruent, and their corresponding sides are in proportion, so angle A of triangle ABC is congruent to angle D of triangle DEF.
Learn more about similar triangles here: https://brainly.com/question/14285697
#SPJ1
What is the freezing point in c of a 0.33 m aqueous solution of Na2so3
The freezing point of a 0.33 m aqueous solution of Na₂SO₃ is -0.077 °C.
To find the freezing point of a solution, we can use the formula:
ΔTf = Kf · m
where ΔTf is the change in freezing point, Kf is the freezing point depression constant (for water, Kf = 1.86 °C/m), and m is the molality of the solution (in moles of solute per kilogram of solvent).
First, we need to calculate the molality of the solution:
m = moles of solute / mass of solvent (in kg)
We are given that the solution is 0.33 m, which means there are 0.33 moles of Na₂SO₃ per kilogram of water. The molar mass of Na₂SO is:
2 Na + 1 S + 3 O = 2(23.0 g/mol) + 32.1 g/mol + 3(16.0 g/mol) = 126.0 g/mol
So, 0.33 moles of Na₂SO₃ is equal to:
0.33 mol × 126.0 g/mol = 41.6 g
Since we have 1 kg of water, the mass of the solvent is 1000 g. Therefore, the molality of the solution is:
m = 41.6 g / 1000 g = 0.0416 mol/kg
Now, ΔTf = Kf · m = (1.86 °C/m) · (0.0416 mol/kg) = 0.077 °C
freezing point = 0 °C - ΔTf = 0 °C - 0.077 °C = -0.077 °C
Therefore, the freezing point of a 0.33 m aqueous solution of Na₂SO₃ is -0.077 °C.
Learn more about Freezing Point here:
https://brainly.com/question/3121416
#SPJ1
Answer: -1.84
Step-by-step explanation:
3x1.86x0.33=1.84
0.00-1.84= -1.84
late answer but hope it helps someone!
Of the 95children in 6th grade 3/5 went to holiday parties how many students went to holiday parties in all?
Answer:
57
Step-by-step explanation:
95/5 x 3 = 57
Packs of 14 juice boxes are on sale for $11. 34. Packs of 16 juice boxes are on sale for $12. 64. Which is the better buy?
To determine which option is the better buy between packs of 14 juice boxes for $11.34 and packs of 16 juice boxes for $12.64, we need to compare the cost per juice box for each option. The better buy is the one that offers a lower cost per juice box.
To calculate the cost per juice box for each option, we divide the total cost of the pack by the number of juice boxes in the pack.
For the pack of 14 juice boxes priced at $11.34, the cost per juice box is:
$11.34 / 14 = $0.81 per juice box
For the pack of 16 juice boxes priced at $12.64, the cost per juice box is:
$12.64 / 16 = $0.79 per juice box
Comparing the two options, we find that the pack of 16 juice boxes offers a lower cost per juice box ($0.79) compared to the pack of 14 juice boxes ($0.81).
Therefore, the better buy is the pack of 16 juice boxes for $12.64, as it provides a lower cost per juice box.
To learn more about cost click here : brainly.com/question/14566816
#SPJ11
To determine which option is the better buy between packs of 14 juice boxes for $11.34 and packs of 16 juice boxes for $12.64, we need to compare the cost per juice box for each option. The better buy is the one that offers a lower cost per juice box.
To calculate the cost per juice box for each option, we divide the total cost of the pack by the number of juice boxes in the pack.
For the pack of 14 juice boxes priced at $11.34, the cost per juice box is:
$11.34 / 14 = $0.81 per juice box
For the pack of 16 juice boxes priced at $12.64, the cost per juice box is:
$12.64 / 16 = $0.79 per juice box
Comparing the two options, we find that the pack of 16 juice boxes offers a lower cost per juice box ($0.79) compared to the pack of 14 juice boxes ($0.81).
Therefore, the better buy is the pack of 16 juice boxes for $12.64, as it provides a lower cost per juice box.
To learn more about cost click here : brainly.com/question/14566816
#SPJ11
Given 6 email addresses and 6 distinct passwords. Each password is entered once and can give access to only one email address. In how many ways can the passwords be entered to that no password matches its email address?
Please show steps!
20. Graph the absolute value function f(x) = |x – 2| on the coordinate plane someone please answer showing work on how to do this problem
The absolute value function f(x) = |x – 2| takes a non-negative value for all real numbers x, and it returns 0 only when x = 2.
The graph of f(x) is symmetric about the vertical line x = 2 and has a vertical asymptote at x = 2.
We have,
The absolute value function f(x) = |x – 2| is a piecewise function that returns the positive distance between the input value x and the number 2.
Geometrically,
It represents the distance of a point on the number line from point 2.
On the coordinate plane,
The graph of the absolute value function is V-shaped, with its vertex at the point (2, 0).
The two arms of the V extend indefinitely in opposite directions, passing through the points (-∞, 2) and (2, +∞) on the positive and negative sides of the x-axis, respectively.
Thus,
The absolute value function f(x) = |x – 2| takes a non-negative value for all real numbers x, and it returns 0 only when x = 2.
The graph of f(x) is symmetric about the vertical line x = 2 and has a vertical asymptote at x = 2.
Learn more about functions here:
https://brainly.com/question/28533782
#SPJ1
ANSWER BY THE CHOICE IN THE BOTTOM NOT BY WHAT YOU WANT
The stem-and-leaf plot displays the distances that a heavy ball was thrown in feet.
2 0, 2, 5
3 1, 3, 4
4 1, 1, 5
5 0, 6
6 7
Key: 3|1 means 3.1
What is the mean, and what does it tell you in terms of the problem?
3.1 feet; The value means the furthest the ball went.
3.875 feet; The value means that a typical throw of the ball results in 3.875 feet.
4.1 feet; The value means this measurement had the most occurrences.
4.65 feet; The value means that a typical throw of the ball results in 4.65 feet.
The mean distance that the heavy ball was thrown in feet is 4.65 feet. This value tells us that on average, a typical throw of the ball results in a distance of 4.65 feet.
To find the mean, we need to first list all the distances and then find the sum of the distances. Finally, we will divide the sum by the number of distances.
Distances: 2.0, 2.2, 2.5, 3.1, 3.3, 3.4, 4.1, 4.1, 4.5, 5.0, 5.6, 6.7
Sum of distances: 2.0 + 2.2 + 2.5 + 3.1 + 3.3 + 3.4 + 4.1 + 4.1 + 4.5 + 5.0 + 5.6 + 6.7 = 51.5
Number of distances: 12
Mean = Sum of distances / Number of distances
Mean = 51.5 / 12 = 4.29 (rounded to two decimal places)
The closest answer to our calculated mean is:
4.65 feet; The value means that a typical throw of the ball results in 4.65 feet.
For more such questions on average , Visit:
https://brainly.com/question/20118982
#SPJ11
What is y=4/5x+2 written in standered form
Answer Immeditely Please
Answer:
9
Step-by-step explanation:
This situation creates 3 similar triangles, so the lengths of corresponding sides are proportional.
1/3 = 3/x
x = 3 × 3
x = 9
Maricopa's Success scholarship fund receives a gift of $ 145000. The money is invested in stocks, bonds, and CDs. Stocks pay 6. 7 % interest, bonds pay 2. 5 % interest, and CDs pay 5. 75 % interest. Maricopa Success invests $ 10000 more in bonds than in CDs. If the annual income from the investments is $ 6977. 5 , how much was invested in each account?
Maricopa Success invested $ in stocks. Maricopa Success invested $ in bonds. Maricopa Success invested $ in CDs
Please answer as soon as possible!
The triangle ABC has its coordinates as shown below.
A:(3,3)
, B:(−2,−2)
, and C:(4,−4)
Triangle ABC is translated 2 units up, 3 units left and then dilated by a scale factor of 4 about the origin to form triangle A' B' C'. What are the coordinates of the vertex B' ? Enter your answer in the box below.
The coordinates of the vertex B' are (-20, 0).
What is a translation?In Mathematics and Geometry, the translation of a graph to the left simply means subtracting a digit from the numerical value on the x-coordinate of the pre-image;
g(x) = f(x + N)
Based on the information provided about triangle ABC, we have the following translation:
(x, y) → (x - 3, y + 2)
Point B (-2, -2) → (-2 - 3, -2 + 2) = point B (-5, 0)
Next, we would dilate point B by a scale factor of 4 about the origin:
point B (-5, 0) → (-5 × 4, 0 × 4) = point B' (-20, 0).
Read more on function and translation here: brainly.com/question/31559256
#SPJ1
Choose the representation that is INCORRECT and does NOT match the others.
Answer:
The table is the incorrect representation.
This graph represents an exponential function.
Complete the sentences.
The function's y-intercept is ___ , and the equation of its asymptote is ___. The graph shows that the function ____ by a factor of ____ each time x increases by 1. This function can be represented by the equation _____ .
The function's y-intercept is 4, and the equation of its asymptote is y = 0. The graph shows that the function increases by a factor of [tex]\frac{3}{2}[/tex] each time x increases by 1. This function can be represented by the equation [tex]y = 4(\frac{3}{2})^x[/tex].
What is an exponential function?In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:
[tex]f(x) = a(b)^x[/tex]
Where:
a represents the initial value or y-intercept.x represents x-variable.b represents the rate of change, common ratio, base, or constant.Based on the graph, we would calculate the value of a and b as follows;
[tex]f(x) = a(b)^x[/tex]
4 = a(b)⁰
a = 4
Next, we would determine value of b as follows;
6 = 4(b)¹
6 = 4b
b = 6/4
b = 3/2
Therefore, the required exponential function is given by;
[tex]y = 4(\frac{3}{2})^x[/tex]
In conclusion, the graph shows that the exponential function increases by a factor of [tex]\frac{3}{2}[/tex] or 1.5 each time x increases by 1.
Read more on exponential equation here: brainly.com/question/28939171
#SPJ1
What is the y-intercept the equation y=(x+4)2? The equation you wrote to answer the last question should help you. (Only enter the y-coordinate.)
Answer:
x-intercepts: (-4,0)
y-intercepts: (0,16)
Step-by-step explanation:
To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.
have a great day and thx for your inquiry :)
i need this now in 5 mins please
Answer:
6x + 9 + 13x - 95 = 180
19x - 86 = 180
19x = 266
x = 14
z = 6(14) + 9 = 84 + 9 = 93
Annie has $9,000 in an account that earns 5% interest compounded annually.
To the nearest cent, how much interest will she earn in 2 years?
Use the formula B=p(1+r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
$
Answer:
B=$18900.00
Step-by-step explanation:
B=?
P=9000
r=5%=0.05
t=2
B=p(1+r)t
B=9000×(1+0.05)×2
B=9000×(1.05)×2
B=9000×2.1
B=18900
912 is what percent of 1900
48%
912 of 1900 can be written as:
912
1900
To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100
912
1900
×
100
100
= (
912 × 100
1900
) ×
1
100
=
48
100
Therefore, the answer is 48%
If you are using a calculator, simply enter 912÷1900×100 which will give you 48 as the answer.
Answer: 912 is what percent of 1900, the percent is 48%
when we draw small and large samples from the same population, small samples group of answer choices produce a more peaked and narrower distribution. vary more from the population mean result in more degrees of freedom
When we draw small and large samples from the same population, small samples produce a more peaked and narrower distribution.
This phenomenon is due to the presence of fewer degrees of freedom associated with the small samples. Variations between sample and population mean result in fewer degrees of freedom, which results in a greater variation between samples and the population mean.
Degrees of freedom (df) is a statistical measure that quantifies the number of values in the final calculation of a statistic that are free to vary. When we sample data from a population, we calculate the sample mean, standard deviation, and other statistics
Learn more about sample distribution at:
https://brainly.com/question/31483266
#SPJ11
Solve using substitution method. 9x -y +7=0 13x - 4y +5 = 0.
The value of x = -1 and y = -2 by solving the system of equation by using the substitution are 9x - y + 7 = 0 and 13x - 4y + 5 = 0
Given that,
The system of equation are 9x - y + 7 = 0 and 13x - 4y + 5 = 0
We have to solve the system of equation by using the substitution method.
We know that,
Take the system of equation
9x - y + 7 = 0 --------->equation(1)
13x - 4y + 5 = 0 ---------> equation(2)
From the equation (1)
9x - y + 7 = 0
y = 9x + 7
Substitute y = 9x + 7 in equation(2)
13x - 4y + 5 = 0
13x - 4(9x + 7) + 5 = 0
13x - 36x - 28 + 5 = 0
- 23x - 23 = 0
-23x = 23
x = -1
Now, Substitute x = -1 in equation(1)
y = 9(-1) + 7
y = -9 + 7
y = -2
Therefore, The value of x=-1 and y=-2
To know more about substitution visit:
https://brainly.com/question/29754636
https://brainly.com/question/377302
10.8.5: assigning bedrooms to daughters. (a) a family has four daughters. their home has three bedrooms for the girls. two of the bedrooms are only big enough for one girl. the other bedroom will have two girls. how many ways are there to assign the girls to bedrooms?
Answer: 12 different ways.
Step-by-step explanation:
For a set of M elements, the number of combinations of N elements (N ≤ M) is given by:
In this case, we know that there is a room that can hold two of the girls, then the number of combinations of the two girls that can be in that room is:
So these are the different combinations for the larger room.
So we assume that two girls already have a room, then we have two girls left and two rooms left.
For the first room, there are two possible girls that can be in, let's choose one of them.
For the last room, we have only one girl left, so we have one option.
The total number of combinations will be equal to the product between the number of options for each event (where the events are assigning the girls to the rooms)
Then the number of different outcomes is:
C = 6*2*1 = 12
There are 12 different ways.
let f be the function defined by f(x)=2x^2 + 7x -2. Find the following
a. f(-3)
b. f(a+3)
c. f(3a)
d. f(a+h)
The values are a. f(-3) = 7, b. f(a+3) = 2a² + 19a + 37, c. f(3a) = 18a² + 21a - 2, d. f(a+h) = 2a² + 4ah + 2h² + 7a + 7h - 2
What is a function?
A function is a mathematical relationship or rule that assigns a unique output value to each input value. It is a fundamental concept in mathematics and plays a central role in various branches, including calculus, algebra, and analysis.
To evaluate the given function at various values, we substitute the given values into the function and simplify the expression.
a. To find f(-3), we substitute -3 into the function: f(-3) = 2(-3)² + 7(-3) - 2 = 18 - 21 - 2 = 7.
b. To find f(a+3), we substitute a+3 into the function: f(a+3) = 2(a+3)² + 7(a+3) - 2. Expanding and simplifying the expression yields 2a² + 12a + 18 + 7a + 21 - 2 = 2a² + 19a + 37.
c. To find f(3a), we substitute 3a into the function: f(3a) = 2(3a)² + 7(3a) - 2. Simplifying the expression gives 18a² + 21a - 2.
d. To find f(a+h), we substitute a+h into the function: f(a+h) = 2(a+h)² + 7(a+h) - 2. Expanding and simplifying the expression yields 2a² + 4ah + 2h² + 7a + 7h - 2.
learn more about Expression here:
https://brainly.com/question/29176690
#SPJ4
Write a recursive formula for the sequence an = (5)(3)n-1
This formula says that the nth term in the sequence is equal to three times the (n-1)th term in the sequence. By starting with a1 = 5 and applying the recursive formula repeatedly
A recursive formula is a mathematical expression that defines a sequence in terms of previous values in the sequence. For the given sequence an = (5)(3)n-1, we can create a recursive formula using the following steps:
First, we define the base case for the sequence. In this case, the base case is a1 = 5.
Next, we define the recursive formula for the sequence. This formula uses the previous term in the sequence to calculate the next term. For this sequence, we can use the formula an = (5)(3)n-1 = 3an-1.
Using these steps, we can write the recursive formula for the sequence as follows:
a1 = 5
an = 3an-1 for n > 1
To learn more about : formula
https://brainly.com/question/29797709
#SPJ11
The midpoint of a segment is (4, 3) and one endpoint is (10, 8). Find the coordinates of the other endpoint
The coordinates of the other endpoint of the segment, given the midpoint (4, 3) and one endpoint (10, 8), are (-2, -2).
To find the coordinates of the other endpoint of a segment given its midpoint and one endpoint, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint between two points (x1, y1) and (x2, y2) are given by:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
In this case, we are given the midpoint as (4, 3) and one endpoint as (10, 8). Let's assume the coordinates of the other endpoint are (x, y).
Using the midpoint formula, we can set up the following equations:
((10 + x)/2, (8 + y)/2) = (4, 3)
From the first equation, we can solve for x:
(10 + x)/2 = 4
10 + x = 8
x = 8 - 10
x = -2
From the second equation, we can solve for y:
(8 + y)/2 = 3
8 + y = 6
y = 6 - 8
y = -2
Therefore, the coordinates of the other endpoint are (-2, -2).
To know more about Endpoint .
https://brainly.com/question/29164764
#SPJ11
A bank manager wishes to provide prompt service for customers at the bank's drive-up window. The bank currently can serve up to 10 customers per 15-minute period without significant delay. The mean arrival rate is 7 customers per 15-minute period. Let X denote the number of customers arriving per 15-minute period. Assume X has a Poisson distribution.
a. Find the probability that 10 customers will arrive in a particular 15-minute period.
b. Find the probability that 10 or fewer customers will arrive in a particular 15-minute period.
c. Find the probability that there will be a significant delay at the drive-up window. That is, find the likelihood that more than 10 customers will arrive during a particular 15-minute period.
To find the probability that 10 customers will arrive in a particular 15-minute period, we can use the Poisson distribution formula:
P(X = k) = (e^(-λ) * λ^k) / k!
Where λ is the mean arrival rate, which is 7 in this case, and k is the number of customers we're interested in, which is 10.
P(X = 10) = (e^(-7) * 7^10) / 10!
Calculating this expression will give us the probability that exactly 10 customers will arrive in a particular 15-minute period.
b. To find the probability that 10 or fewer customers will arrive in a particular 15-minute period, we need to sum up the probabilities of different arrival counts from 0 to 10.
P(X ≤ 10) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 10)
We can use the Poisson distribution formula for each value of k and sum them up to find the cumulative probability.
c. To find the probability of more than 10 customers arriving during a particular 15-minute period, we can calculate the complement of the probability of 10 or fewer customers.
P(X > 10) = 1 - P(X ≤ 10)
This will give us the probability of there being a significant delay at the drive-up window due to more than 10 customers arriving.
Know more about probability here:
https://brainly.com/question/32004014
#SPJ11
