Answers
Using the Poisson and the normal distributions, the probabilities are given as follows:
a) 0.0895 = 8.95%.
b)
Without correction, P(X < 8) = 0.1251 = 12.51%.
With continuity correction, P(X < 8) = 0.0968 = 9.68%.
c)
Without correction, P(16 < X < 24) = 0.1248.
With correction, P(16 < X < 24) = 0.1558 = 15.58%.
What is the Poisson distribution?In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are:
x is the number of successese = 2.71828 is the Euler number[tex]\mu[/tex] is the mean in the given interval.In this problem, the mean is given by:
[tex]\mu = 12[/tex]
Hence the probability that X is less than 8 is given by:
P(X < 8) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7).
In which:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-12}12^{0}}{(0)!} = 0.00001[/tex]
...
[tex]P(X = 7) = \frac{e^{-12}12^{7}}{(7)!} = 0.04368[/tex]
The middle values are found applying the same formula, and adding them, the probability is given by:
P(X < 8) = 0.0895 = 8.95%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The Poisson distribution can be approximated to the normal with [tex]\sigma = \sqrt{\mu}[/tex]Without continuity correction, the probability that X is less than 8 is the p-value of Z when X = 8, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{8 - 12}{\sqrt{12}}[/tex]
Z = -1.15
Z = -1.15 has a p-value of 0.1251.
Hence:
Without correction, P(X < 8) = 0.1251 = 12.51%.
With continuity correction, as the Poisson distribution is discrete and the normal is continuous, the probability is P(X < 7.5), which is the p-value of Z when X = 7.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{7.5 - 12}{\sqrt{12}}[/tex]
Z = -1.3
Z = -1.3 has a p-value of 0.0968.
Hence:
With continuity correction, P(X < 8) = 0.0968 = 9.68%.
For item c, without correction, the probability is the p-value of Z when X = 24 subtracted by the p-value of Z when X = 16, hence:
X = 24:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{24 - 12}{\sqrt{12}}[/tex]
Z = 3.46
Z = 3.46 has a p-value of 0.9997.
X = 16:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{16 - 12}{\sqrt{12}}[/tex]
Z = 1.15
Z = 1.15 has a p-value of 0.8749.
0.9997 - 0.8749 = 0.1248.
Hence:
Without correction, P(16 < X < 24) = 0.1248.
With correction, the probability is the p-value of Z when X = 23.5 subtracted by the p-value of Z when X = 15.5, hence:
X = 23.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{23.5 - 12}{\sqrt{12}}[/tex]
Z = 3.32
Z = 3.32 has a p-value of 0.9996.
X = 15.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{15.5 - 12}{\sqrt{12}}[/tex]
Z = 1.01
Z = 1.01 has a p-value of 0.8438.
0.9996 - 0.8438 = 0.1558.
Hence:
With correction, P(16 < X < 24) = 0.1558 = 15.58%.
More can be learned about the normal distribution at https://brainly.com/question/28576919
#SPJ1
Related Questions
What is the area of the trapezoid shown? Show your work
Answers
The Area of the trapezoid in the image attached below is: 204 units².
How to Find the Area of a Trapezoid?To find the area of a trapezoid, the following formula is used:
Area of trapezoid = 1/2 × (a + b) × h, where h is the height of the trapezoid, and a and b are the length of the two parallel bases of the trapezoid.
Given the trapezoid in the image attached below, we have the following parameters:
a = 10
b = 24
h = 12
Area of trapezoid = 1/2 × (10 + 24) × 12
Area of trapezoid = 1/2 × (34) × 12
Area of trapezoid = 34 × 6
Area of trapezoid = 204 units²
Therefore, the Area of the trapezoid in the image attached below is: 204 units².
Learn more about the area of a trapezoid on:
https://brainly.com/question/1463152
#SPJ1
FREE BRAINLIEST!!! What is the slope of the line?
2
-2
-1/2
1/2
Answers
Answer:
i think its 2
Step-by-step explanation:
Answer: 2.
Step-by-step explanation: Because if you see where the dot of line is you will see that the dot is right next to number 2
6.3 = 2x - 4.5 solve for x
Answers
Answer:
x = 5.4
Step-by-step explanation:
6.3 = 2x-4.5
2x = 6.3 + 4.5 = 10.8
x= 5.4
Answer:
5.4is the value if x
Step-by-step explanation:
6.3=2x-4.5
6.3+4.5=2x
10.8=2x
10.8/2=x
5.4=x
So,x=5.4
Marie ran 5.9 miles on Tuesday. This was 1.9 miles less than she ran on Monday. How many miles did she run on Monday?
Answers
Answer:
7.8 miles
Step-by-step explanation:
5.9 + 1.9 = 7.8miles
the length of a rectangle is 6 m longer than its width. of the perimeter of the rectangle is 36 m, find its area
Answers
The length of a rectangle is 6 m longer than its width. of the perimeter of the rectangle is 36 m, its area is 72 m².
Any polygon's area is the amount of space it takes up or encloses. The amount of square units that make up the polygon. Because the area is a two-dimensional object, it has both length and width. Typically, the area is expressed in square meters, square feet, or square inches. Acres, hectares, and square kilometers are used to measure the size of larger shapes like cities and farms.
Let l be the length of the rectangle
And w be the width of the rectangle.
Given, l=6+w
Perimeter,p =36m
We know that, p= 2(l+w)
p =36=2(6+w+w)
36/2= 6 +2w
18-6=2w
w=6m
Therefore, l=6+w
l=12m
Area of rectangle= lw
A = 12×6
A=72 m².
To learn more about area of rectangle refer the link:
https://brainly.com/question/14383947
#SPJ9
There are $13.30 worth of nickels and dimes in a piggy bank. There are 5 more nickels than dimes. How
many of each are in the piggy bank? You must solve this problem algebraically (no guess and check). Show
each step for full credit. Circle your final answer. (4 points)
Answers
Answer:
92 nickels87 dimesStep-by-step explanation:
You want the number of nickels and dimes that make up $13.30 when there are 5 more nickels than dimes.
SetupLet d represent the number of dimes. Then (d+5) is the number of nickels. The total value in cents is ...
10d +5(d+5) = 1330
SolutionSimplifying the equation, we get ...
15d +25 = 1330
15d = 1305 . . . . . . . . subtract 25
d = 87 . . . . . . . . . . . divide by 15
(d+5) = 92 . . . . . . the number of nickels
[tex]\boxed{\text{There are 92 nickels and 87 dimes in the piggy bank.}}[/tex]
The grid above shows the graph of the parent function f(x) = |x| and a translated functions graph.
Write the equation for the translated graph.
Answers
The equation of the translated graph is g(x) = |x + 2| + 1
How to write the equation of the translated graph?The parent function is given as
f(x)= |x|
From the graph, we can see that the parent function f(x) is translated as follows:
2 units left1 unit upThis is represented as
(x, y) = (x + 2, y + 1)
So, we have
g(x) = |x + 2| + 1
Hence, the equation of the translated graph is g(x) = |x + 2| + 1
Read more about transformation at
https://brainly.com/question/4289712
#SPJ1
please answer as soon as possible
Answers
Step-by-step explanation:
the answer is, if it's correct y=4
IM TIMED PLEASE HELP
Find the value of x if U is between T and V, TU=7x+35,UV=4(x+7),and TU≅UV .
Multiple choice questions.
A)
−3
B)
−7/3
C)7/3
D)
3
Answers
The value of x if U is between T and V is -7/3
How to determine the value of x?The given parameters are:
U is between T and V,
TU = 7x + 35
UV = 4(x + 7)
TU ≅ UV
The above means that
7x + 35 = 4(x + 7)
Open the brackets
7x + 35 = 4x + 28
Evaluate the like terms
3x = -7
Divide both sides by 3
x = -7/3
Hence, the value of x if U is between T and V is -7/3
Read more about line segments at
https://brainly.com/question/2437195
#SPJ1
Help I need the answer to this question
Answers
The Density of the given plank with dimensions is; 33.82 kg/m³
How to calculate the density of an Object?We are given;
Length of plank = 2.3 meters
Width of plank = 30 cm = 0.3 m
Height of Plank = 3 cm = 0.03 m
Mass of plank = 0.7 kg
Now, formula for density = mass/volume
Volume of the plank is gotten from the formula;
Volume = Length * width * height
V = 2.3 * 0.3 * 0.03
V = 0.0207 m³
Thus;
Density = 0.7/ 0.0207
Density = 33.82 kg/m³
Thus, we can conclude that the Density of the given plank with dimensions is 33.82 kg/m³
Read more about Density formula at; https://brainly.com/question/952755
#SPJ1
A ball is thrown up in the air from the top of a building. The function h(t) = -5t²+10t + 80 models the height of the ball, in feet, after t seconds. Graph this function.
What is the maximum height reached by the ball?
Answers
Answer:
Step-by-step explanation:
h(t)=-5t²+10t+80=-5(t²-2t+1-1)+80
=-5(t²+2t+1)+5+80
=-5(t-1)²+85
maximum height reached=85 ft
Which of the following could be the equation of the graph shown below? Check all that apply.
(Picture included)
Answers
The equations that could represent the graph shown are:
A. -4x + 2y = -6
C. y = 3x - 2
How to Determine the Equation of a Graph?The equation of a linear graph, in slope-intercept form, can be written as y = mx + b, where:
b is the point on the y-axis that the line intercepts, which is called the y-intercept of the graph.m is the slope of the graph, which is the rise/run along the line.Given the graph in the diagram, it would have a positive slope and a negative y-intercept.
A. -4x + 2y = -6
Rewrite in slope-intercept form
2y = 4x - 6
y = 4x/2 - 6/2
y = 2x - 3 [positive slope and negative y-intercept]
B. 2x - 3y = -9
Rewrite in slope-intercept form
-3y = -2x - 9
y = 2/3x + 3 [positive slope and positive y-intercept]
C. y = 3x - 2 [positive slope and negative y-intercept]
D. y = -10 is a horizontal line.
Therefore, the equations that could represent the graph shown are:
A. -4x + 2y = -6
C. y = 3x - 2
Learn more about equation of a graph on:
https://brainly.com/question/19040584
#SPJ1
Two trains leave towns 900 miles apart at the same time and travel toward each other. One train travels 20mi/h slower than the other. If they meet in 6 hours, what is the rate of each train?
Answers
Answer:
Hello,
Step-by-step explanation:
The time they travel is t=6 hours
v is rate of the fastest train
v-2 the slower one.
v*t+(v-20)*t=900
2vt-20t=900
12v-120=900
12v=900+120
v=1020/12
v=85 (mi/h)
v-20=65 (mi/h)
the general solution to
Sin2x = Cosx+l
Answers
Answer:
Step-by-step explanation:
sin2x = cosx + l
This can be written as:
2 sinxcosx = cosx + 1
One way would be to draw graphs of sin2x and cosx + 1 and see where they intersect.
Another way is to use y = tan(x/2), then sinx = 2y/(y^2+1) and cos x
= (-y^2 + 1) / (y^2 + 1) to substitute into the given equation and solve for y.
The algebra will be pretty challenging in this method.
. A caterer in Florida is making fresh
orange juice, the official state beverage.
Four oranges make 1 cup of juice. How
many oranges will the caterer need to
use to make 58 cups of juice? HELPPP
Answers
Step-by-step explanation:
58 multiple 4
..................
Jordan jogs 6.9 miles each day. How many miles does he jog in 8 days
Answers
Based on the given conditions, formulate: 6.9 * 8 Calculate the product or quotient:55.2get the result
Answer:
55.2 miles
Step-by-step explanation:
6.9 x 8 = 55.2
Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day :)
Exercise
Squats
Crunches
Lunges
Curls
Time (h)
0.08
0.03
0.04
0.05
Javier likes to work out for 1 hour. If he
doesn't use the full hour on his exercises, he
runs on a treadmill for the remaining time. If
he completed 3 repetitions of each exercise,
how long did he run on the treadmill on
Monday? (Example 1)
Answers
By addition of all the exercise and substracting it from 1 hourJavier runs on treadmill on Monday is 0.40 hour.
Now According to the question javier completed 3 repetitions of each exercise so by multiplication time taken by javier to complete each exercise is as follow;
Squats = 0.8*3= 0.24 hour
Crunches = 0.03*3 = 0.09 hour
Lunges = 0.04*3 = 0.12 hour
curls = 0.05*3 = 0.15 hour
we can calculate total time taken to complete all exercise by Addition is,
0.24 + 0.09 + 0.12 + 0.15
0.60 hour
time taken on treadmill by javier;
1 hour - 0.60 hour
0.40 hour
Read more about Addition here:
https://brainly.com/question/20658817
#SPJ4
13. A large group of 30 people attended a hockey game. Each person ordered a hotdog or a slice of pizza from the concession stand. Hot dogs cost $2.50 each and a slice of pizza costs $3.25 each. If the total bill for these items was $81.75, how many of each type was purchased?
Answers
Answer:
21 hot dogs
9 pizza slices
Step-by-step explanation:
Given information:
Group = 30 peopleCost of a hot dog = $2.50Cost of a slice of pizza = $3.25Total bill = $81.75Define the variables:
Let x = the number of hot dogs purchased.Let y = the number of pizza slices purchased.Create two equations from the given information:
[tex]\textsf{Equation 1}: \quad x + y = 30[/tex]
[tex]\textsf{Equation 2}: \quad 2.5x+3.25y=81.75[/tex]
Rewrite Equation 1 to make x the subject:
[tex]\implies x=30-y[/tex]
Substitute this into Equation 2 and solve for x:
[tex]\implies 2.5(30-y)+3.25y=81.75[/tex]
[tex]\implies 75-2.5y+3.25y=81.75[/tex]
[tex]\implies 75+0.75y=81.75[/tex]
[tex]\implies 0.75y=6.75[/tex]
[tex]\implies y=9[/tex]
Substitute the found value of y into the rewritten form of Equation 1 and solve for x:
[tex]\implies x=30-9[/tex]
[tex]\implies x=21[/tex]
Solution
Hot dogs purchased = 21Pizza slices purchased = 9Learn more about systems of equations here:
https://brainly.com/question/28281431
https://brainly.com/question/27034625
Answer:
Number of hot dogs purchased = 21
Number of pizza slices purchased = 9
Step-by-step explanation:
Let the number of people buying hot dogs be represented by the variable H and the number of people buying pizzas be represented by the variable P
Since H hot dogs were purchased and each hot dog costs $2.50, total amount spent on hot dog purchase = $2.50H
Since P slices of pizza were purchased and each slice of pizza costs $3,25, total amount spent on hot dog purchase = $3,25P
Total amount spent (in $) = 2.50H + 3.25P and we are given that this total amount is $81.75
So we have an equation in two variables
2.50H + 3.25P = 81.75 (1)
We know the number of people is 30 and that should equal the number of hot dogs and pizza slices purchased
So
H + P = 30 (2)
Multiply Equation (2) on both sides by 2.50
==> 2.50(H + P) = 2.50 x 30
2.50H + 2.50P = 75 (3)
Subtract equation (3) from equation (1) to eliminate the H terms
(1) - (3):
2.50H + 3.25P - (2.50H + 2.50P) = 81.75 -75
2.50H + 3.25P - 2.50H - 2.50P = 6.75
Collect like terms and simplify
==> (2.50H -2.50H) + (3.25P - 2.50P) = 6.75
==> 0.75P = 6.75
Divide both sides by 0.75
==> 0.75P/0.75 = 6.75/0.75
==> P = 9
So number of people who bought pizza slices = 9
This is the same as the number of pizza slices that were bought
Substitute for P in Eq (2) H + P = 30
==> H + 9 = 30
Subtract 9 from both sides
==> H + 9 - 9 = 30 - 9
==> H = 21
So number of people who bought hot dogs = 21
This is the same as the number of hot dogs purchased
Can someone tell me if this is right if not can u help me
Answers
Answer:
It is incorrect. It is supposed to be set at -8 to 9 but instead it is at -8 to 7.
The decimal should go up 2 places higher!
Step-by-step explanation:
Consider the line y = 6x-9.
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line?
Slope of a parallel line:
Slope of a perpendicular line:
Answers
Answer:
Gradient of parallel line: 6
Gradient of perpendicular line: -1/6
Step-by-step explanation:
The gradient is the value of m in the equation format y = mx + c.
Parallel lines share the same gradient, with just the y-axis intercept (c value) changing.
The gradient of a line perpendicular to a line is found by taking the negative reciprocal of the original line's gradient. A reciprocal is a essentially fraction flipped over. For example 3/2 becomes 2/3. 6 can be expressed as 6/1 (as every whole number can be divided by 1), so the reciprocal of that is 1/6. The negative version of 1/6 is -1/6.
8,282 in verbal form
Answers
Eight thousand two hundred and eighty two
I need help with add and sub poly
Answers
Answe[tex]10c^{2} +5c+4[/tex]
Step-by-step explanation:
Step 1 -(((6•(c2))-2c)-1)+((22c2+7c)+5)
Step 2-(((2•3c2) - 2c) - 1) + (4c2 + 7c + 5)
in conclusion, you get [tex]10c^{2} +5c+4[/tex]
I hoped i have helped u have a wonderful day or night !
a) Find The rate of change of f.
b) Express f in the form f(x) = ax + b
Answers
Answer:
this is hard , I suggest you see a tutor
Use the figure below to complete the following problem.
Given:
ZH=2x+60
LT=x+ 30
HALT is a
H
ZA =
O 30
045
O 60
Answers
The value of angle A is 60.
In Euclidean geometry, a parallelogram is a simple quadrilateral having two sets of parallel sides. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.
We have the angles as:
∠H = 2x + 60
∠T = x + 30
Now, HALT is a parallelogram.
Therefore, angles H and T are supplementary.
So,
∠H + ∠T = 180
2x + 60 + x + 30 = 180
3x + 90 = 180
3x = 180 - 90
3x = 90
x = 90 / 3
x = 30
Substituting the value of x in the angles, we get:
∠H = 2x + 60
∠H = 2(30) + 60
∠H = 60 + 60 =120
∠T = x +30
∠T = 30 + 30
∠T = 60
Now, angles T and A are congruent angles.
Therefore, ∠T = ∠A
∠A = 60
Learn more about angles here:
https://brainly.com/question/12919120
#SPJ9
HELP ASSAPP PLSASEEE
Answers
Answer:
(-2,-2)
Step-by-step explanation:
For a cartesian plane, the solutions to 2 lines is where the 2 lines intercept.
Where this interception point is put into a coordinate (x,y)
Which in this case, the point of intersection is found to be (-2,-2) (Read from the graph)
Joni worked 14 hours more than Dominic last month. If Joni worked 7 hours for every 3 hours that Dominic worked, how many hours did they each work?
Answers
Answer:
look at the multiple of 3 and seven and find which number in the 7 multiple equal 14 more.
3/2(6x+2)=-3(x-1) need help with this
Answers
Answer:
x=0
Step-by-step explanation:
:)
Answer:
[tex]{ \tt{ \frac{3}{2}(6x + 2) = - 3(x - 1) }} \\ \\ { \tt{3(3x + 1) = - 3(x - 1)}} \\ { \tt{3x + 1 = - (x - 1)}} \\ { \tt{3x + 1 = - x + 1}} \\ { \tt{3x + x = 0}} \\ { \tt{x = 0}}[/tex]
Evaluate.
Remember Order of Operations!
(PEMDAS)
-5 × (-7+2) - 13
Answers
Answer:
the answer is 12 just =12
3 to the 4th power minus -6 to the 2nd power
Answers
Answer:
45
Step-by-step explanation:
3 to the 4th power is the same as 3 x 3 x 3 x 3
3 x 3 x 3 x 3 = 81
-6 x -6 = 36 (a negative times a negative is always positive)
81 - 36 = 45
11. Lucretia, who works part-time as a substance abuse counselor, earns $18.15
per hour and works 20 hours per week. She is single and claims one withholding
allowance. She lives in a state with no state income tax. (2.1)
Answers
Using proportions, it is found that the weekly amounts are given as follows:
Federal Withholding: $33Social Security Tax: $22.51.Medicare Tax: $10.53.State income tax: $134.31.What is the missing information?We have to determine for Lucretia these following weekly amounts:
Federal Withholding.Social Security Tax.Medicare Tax.State income tax.The rates are given as follows:
Withholding allowance: $33 (for someone earning $363 a week).Medicare tax: 2.9%.Social Security: 6.2%.State tax: 37%, as she lives on a state with no tax, hence pays only the Federal rate.What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
Lucretia's weekly salary is given as follows:
20 x 18.15 = $363.
The withholding allowance is fixed at $33 for a person earning her amount, while the tax rate is of 37%, as she lives in a state with no income tax, hence she only pays the federal tax rate.
The other amounts are given as follows:
Medicare Tax: 0.029 x 363 = $10.53.Social Security Tax: 0.062 x 363 = $22.51.State tax: 0.37 x 363 = $134.31.More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1