Answer:
Since [tex]n(1-p) = 3.6 < 5[/tex], the normal distribution cannot be used as an approximation to the binomial probability to approximate the probability.
Using the binomial distribution, 100% probability that more than 97 out of 120 people will get the flu this winter.
Step-by-step explanation:
Binomial probability 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.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
Assume the probability that a given person will get the flu this winter is 97%.
This means that [tex]p = 0.97[/tex]
120 people
This means that [tex]n = 120[/tex]
Verifying the necessary conditions.
[tex]np = 120*0.97 = 116.4[/tex]
[tex]n(1-p) = 120*0.03 = 3.6[/tex]
Since [tex]n(1-p) = 3.6 < 5[/tex], the normal distribution cannot be used as an approximation to the binomial probability to approximate the probability. Thus, the binomial distribution has to be used.
Probability using the binomial distribution:
[tex]P(X > 97) = P(X = 98) + ... + P(X = 120)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 98) = C_{120,98}.(0.97)^{98}.(0.03)^{22} \approx 0[/tex]
Probability close to 0, but below the mean, which means that the probability of the number being above this is 100%.
Using the binomial distribution, 100% probability that more than 97 out of 120 people will get the flu this winter.
If a=120° , find the measure of angles b, c and d.
Explain your reasoning.
Answer:
b=120°
c=60°
d=60°
SEE THE IMAGE FOR SOLUTION
A bag of 31 tulip bulbs contains 13 red tulip bulbs, 9 yellow tulip bulbs, and 9 purple tulip bulbs. Suppose two tulip bulbs are randomly selected without replacement from the bag. (a) What is the probability that the two randomly selected tulip bulbs are both red? (b) What is the probability that the first bulb selected is red and the second yellow? (c) What is the probability that the first bulb selected is yellow and the second red? (d) What is the probability that one bulb is red and the other yellow?
Answer:
36% on first
Step-by-step explanation:
A circular fence is being placed to surround a tree. The diameter of the
fence is 4 feet. How much fencing is used? *
Answer:
12.6 ft
Step-by-step explanation:
[63-(-3) (-2-8-3}] = 3{5+(-2) (-1)}
63-(-3)(-2-8-3) = 3(5+(-2)(-1))
63-(6+24+9) = 3(5+(2))
63-(39) = 3(7)
24 ≠ 21
Answered by Gauthmath must click thanks and mark brainliest
let a function F:A➡️B be defined by f(x)=x+1÷2x-1 with A={-1,0,1,2,3,4} and B= {-1,0,4/5,5/7,1,2,3,}.Find the range of f. plzzzz help
Answer:
Range: {-1, 0, 5/7, 4/5, 1, 2}
Step-by-step explanation:
We know that:
f(x) = (x + 1)/(2x - 1)
And:
f: A ⇒ B
where:
A={-1,0,1,2,3,4}
B= {-1,0,4/5,5/7,1,2,3,}
We want to find the range of f(x).
The range of f(x) will be the set of the outputs of f(x) (and because f goes from A to B, we will only take the outputs that belong to B).
Then we only need to evaluate all the values of A in f(x), and see if the output belongs to B.
we have:
f(x) = (x + 1)/(2x - 1)
f(-1) = (-1 + 1)/(2*-1 - 1) = 0 (this does belong to B)
f(0) = (0 + 1)/(2*0 - 1) = -1 (this does belong to B)
f(1) = (1 + 1)/(2*1 - 1) = 2 (this does belong to B)
f(2) = (2 + 1)/(2*2 - 1) = 1 (this does belong to B)
f(3) = (3 + 1)/(2*3 - 1) = 4/5 (this does belong to B)
f(4) = (4 + 1)/(2*4 - 1) = 5/7 (this does belong to B)
So the range of f(x) is the set with all these outputs, which is:
Range: {-1, 0, 5/7, 4/5, 1, 2}
The data show the traveler spend- ing in billions of dollars for a recent year for a sample of the states. Find the range, variance, and standard deviation for the data.
20.1 33.5 21.7 58.4 23.2 110.8 30.9
24.0 74.8 60.0
Solution :
Given data :
20.1 33.5 21.7 58.4 23.2 110.8 30.9
24.0 74.8 60.0
n = 10
Range : Arranging from lowest to highest.
20.1, 21.7, 23.2, 24.0, 30.9, 33.5, 58.4, 60.0, 74.8, 110.8
Range = low highest value - lowest value
= 110.8 - 20.1
= 90.7
Mean = [tex]$\frac{\sum x}{n}$[/tex]
[tex]$=\frac{20.1+21.7+23.2+24.0+30.9+33.5+58.4+60.0+74.8+110.8}{10}$[/tex]
[tex]$=\frac{457.4}{10}$[/tex]
[tex]$=45.74$[/tex]
Sample standard deviation :
[tex]$S=\sqrt{\frac{1}{n-1}\sum(x-\mu)^2}$[/tex]
[tex]$S=\sqrt{\frac{1}{10-1}(20.1-45.74)^2+(21.7-45.74)^2+(23.2-45.74)^2+(24.0-45.74)^2+(30.9-45)^2}$[/tex]
[tex]\sqrt{(33.5-45.74)^2+(58.4-45.74)^2+(60.0-45.74)^2+(74.8-45.74)^2+(110.8-45.74)^2}[/tex]
[tex]$S=\sqrt{\frac{1}{9}(657.4+577.9+508.0+472.6+220.2+149.8+160.2+203.3+844.4+4232.8)}$[/tex][tex]$S=\sqrt{\frac{1}{9}(8026.96)}$[/tex]
[tex]$S=\sqrt{891.88}$[/tex]
S = 29.8644
Variance = [tex]S^2[/tex]
[tex]=(29.8644)^2[/tex]
= 891.8823
I need help on this math problem
Answer:
for the first one, simply add g(x) and h(x) :
x+3 + 4x+1 = 5x + 4
the second one, you would multiply them :
(x+3)(4x+1) = 4x^2 + 13x + 3
the last one, you would subtract :
(x+3)-(4x+1) = -3x + 2
and then substitute 2 for 'x' :
-3*2 + 2 = -6 + 2 = -4
Answer:
1. 5x+4
2. [tex]4x^2+13x+3[/tex]
3. -4
Step-by-step explanation:
1. (x+3)+(4x+1)
Take off the parentheses and Add.
5x+4
2. (x+3)(4x+1)
Use the FOIL method to multiply.
[tex]4x^2+x+12x+3[/tex]
[tex]4x^2+13x+3[/tex]
3. First, set up the equation as (g-h)(x)
(x+3)-(4x+1)
x+3-4x-1
Solve.
-3x+2
Substitute in 2 for x.
-3(2)+2
-6+2
-4
Give two Examples of workers targeted for by minimum waged
Answer:
Minimum wage refers the smallest wage an employee can make per hour for all hours he or she works on the job. ... For example, New York has a higher minimum wage than Maine, as the cost of living is higher in New York.
if my answer helps you than mark me as brainliest.
please help me with this
——/———————-////—————-
Answer:
"C"
Step-by-step explanation:
-B means the B is in the opposite direction
This table gives a few (x,y) pairs of a line in the coordinate plane.
Answer:
The x-intercept of the line will be (10, 0)
Step-by-step explanation:
start from -12
get to -2...
-12 + (10) = -2
-2 + (10) = 8
therefore, the x-intercept is (10, 0)
Find the least whole number that can replace
to make the statement true.
110< =47
Answer:
it is false
Step-by-step explanation:i cant explain but trust
Find the sum of -3x^2-4x+3 2x^2+3
A ladder 10m long is set against a vertical wall, Calculate the height of the wall where the ladder reached a foot of the ladder is 6m away from the wall.
Answer:
8m
Step-by-step explanation:
If x+y=
= 12 and x = 2y, then x =
O
2
06
08
10
Answer:
2y + y = 12
3y = 12
y = 4
now , x = 2y
x = 2 ( 4 )
x = 8
hope that helps ✌
find an odd natural number x such that LCM (x,40)= 1400
The odd natural number x such that the LCM of x and 40 is 1400 is 35
Lowest Common MultipleThe least common multiple the lowest multiple of two or more numbers.
From the question, we need to determine the value of x of the LCM of the numbers is 1400
LCM (x,40) = 1400
Find a possible value of x
x = 1400/40
x = 35
Hence the odd natural number x such that the LCM of x and 40 is 1400 is 35
Learn more on LCM here: https://brainly.com/question/233244
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If g(x) = x^2 + 8x - 24 find the value of g(6)
Answer:
hope it helps you..........
Answer:
60
Step-by-step explanation:
g(x)= x^2 +8x - 24
Substitute x for 6 in the equation
g(6)= 6^2 + 8(6) - 24
= 36+48-24
= 60
WILL GIVE BRAINLIEST!!!!!!! A boy had 20 cents. He bought x pencils for 3 cents each. If y equals the number of pennies left, write an equation showing the dependence of y on x. What is the domain of the function?But it says that x is a whole number for the domain. PLS HELP.
Answer:
Hey there!!
The total number of cents - 20
Cost for each pencil - 3 cents
Number of pencils bought - ' x '
y = number of pennies left
What is the domain ?
Show how y is dependent on x ..
Let's get this into an equation :
... The total cost for x pencils bought = 3x
... Number of pennies left = 20 - 3x
... y = number of pennies left
... y = 20 - 3x
Notice : If the x value changes, the y value changes too
... If x = 1 , then , y = 17; If x = 2 , then , y = 14
Hence, we could say y is dependent upon x
Domain = ?
... Remember - The total number of pennies = 20 ; hence, the total cost cannot go above 20 cents.
Hence, we will have to work with inequalities
The equation :
... 20 ≥ 3x
Divide 3 on both sides
20 / 3 ≥ x
x ≥ 6.667
Let's take this as 6
Hence , the domain will be :
D : { 1 , 2 , 3 , 4 , 5 , 6 }
Hope my answer helps!
What is the measure of ∠x?
Angles are not necessarily drawn to scale.
∠x= ____∘
Please help me!
Answer:
hey mate ...
105 + JID = 180 ( STRAIGHT LINE )
JID = 75
NOW APPLY ANGLE SUM IN TRIANGLE JID
75 + 39 + IJD = 180
IJD = 66
x = IJD by vertically opposite angles
x = 66
A superhero can fly from New York to Los Angeles in 30 minutes. The distance from New York to Los Angeles is approximately 2,450 miles.
How many miles per hour is the superhero flying?
Work Shown:
30 min = 30/60 = 0.5 hours
distance = rate*time
rate = distance/time
rate = (2450 miles)/(0.5 hours)
rate = (2450/0.5) mph
rate = 4900 mph
For the sake of comparison, a typical commercial passenger jet can reach max speeds of about 600 mph.
additive inverse of 2/8
Answer:
-2/8is it's answer
Step-by-step explanation:
mark as Brainlist
Study the scatterplot and trend line. Which two points can be used to find the equation of the trend line?
Which points are on the trend line?
(1, 30) and (9, 95)
(2, 30) and (6, 70)
(2, 45) and (8, 90)
(3, 50) and (7, 65)
Answer:
C
Step-by-step explanation:
Just trust
Answer:
C
Step-by-step explanation:
I did the assignment in edge and got it right.
Proof:
Please help me. I don't understand fractions here is my problem.
Add:
5/24+9/20
Answer:
79/120
Step-by-step explanation:
5/24+9/20
to add the fractions the denominator (bottom part) has to be the same. ex you can add one third and one third to make two thirds. but you wont know what 1/2 + 1/3 is.
convert to same denominator. to do this, the fractions themselves need to stay the same value but the bottom number needs to change. ex 1/2=2/4 and 1/3= 2/6. when you multiply and divide the top and bottom part of the fraction by the same number, the value of the fraction stays the same. ex 3/6 divide both parts by 3 you get 1/3. so 3/6=1/3
to get the common denominator we have to find the least common multiple, or LCM (since 5 and 9 dont share any common factors.)
24 and 20 LCM
=120
convert both 5/24+9/20 to x/120 and y/120
5/24 multiply by 5 on top and bottom
=25/120
9/20 multiply by 6 on top and bottom
=54/120
25/120+54/120
=(25+54)/120
=79/120
Alice, Bob, and Carol play a chess tournament. The first game is played between Alice and Bob. The player who sits out a given game plays next the winner of that game. The tournament ends when some player wins two successive games. Let a tournament history be the list of game winners, so for example ACBAA corresponds to the tournament where Alice won games 1, 4, and 5, Caroll won game 2, and Bob won game 3.
Required:
a. Provide a tree-based sequential description of a sample space where the outcomes are the possible tournament histories.
b. We are told that every possible tournament history that consists of k games has probability 1/2k, and that a tournament history consisting of an infinite number of games has zero prob- ability. Demonstrate that this assignment of probabilities defines a legitimate probability law.
c. Assuming the probability law from part (b) to be correct, find the probability that the tournament lasts no more than 5 games, and the probability for each of Alice, Bob, and Caroll winning the tournament.
Answer:
I don't know what you think about it is not going to be a great day of school and I don't know what you think about it is not going to be a great day of school
Please help me! Thank you!
Find the length of BC
A. 27.22
B. 11.62
C. 22.02
D. 19.78
Answer:
B
Step-by-step explanation:
Since we know the measure of ∠B and the side opposite to ∠B and we want to find BC, which is adjacent to ∠B, we can use the tangent ratio. Recall that:
[tex]\displaystyle \tan\theta = \frac{\text{opposite}}{\text{adjacent}}[/tex]
The angle is 54°, the opposite side measures 16 units, and the adjacent side is BC. Substitute:
[tex]\displaystyle \tan 54^\circ = \frac{16}{BC}[/tex]
Solve for BC. We can take the reciprocal of both sides:
[tex]\displaystyle \frac{1}{\tan 54^\circ} = \frac{BC}{16}[/tex]
Multiply:
[tex]\displaystyle BC = \frac{16}{\tan 54^\circ}[/tex]
Use a calculator. Hence:
[tex]\displaystyle BC \approx 11 .62\text{ units}[/tex]
BC measures approximately 11.62 units.
Our answer is B.
Solve the following system of equations using the elimination method.
5x - 5y = 10
6x - 4y= 4
A) (-3,5)
B) (2-7)
C) (-1,-5)
D) (-2,-4)
Answer:
D. (-2,-4)
Step-by-step explanation:
When given multi-choice questions like these and you're time bound, substitute the provided answers into the question and see if you'll get the figure beside the '='.
So, using D answers as example 1.
let -2 be x and -4 be y
Substitute these answers into the question.
5(-2)-5(-4)=10
-10+20=10 (+20 because when 2 negative values multiply each other, the operator becomes positive and so is the answer)
10=10
This means the answers provided for D(-2,-4) is the right answer.
PS: Please use or adopt this strategy to solve such questions ONLY when you've been provided with multiple answers to choose from. Plus, it also helps save time.
Thanks
In 2012 your car was worth $10,000. In 2014 your car was worth $8,850. Suppose the value of your car decreased at a constant rate of change. Define a function f to determine the value of your car (in dollars) in terms of the number of years t since 2012.
Answer:
The function to determine the value of your car (in dollars) in terms of the number of years t since 2012 is:
[tex]f(t) = 10000(0.9407)^t[/tex]
Step-by-step explanation:
Value of the car:
Constant rate of change, so the value of the car in t years after 2012 is given by:
[tex]f(t) = f(0)(1-r)^t[/tex]
In which f(0) is the initial value and r is the decay rate, as a decimal.
In 2012 your car was worth $10,000.
This means that [tex]f(0) = 10000[/tex], thus:
[tex]f(t) = 10000(1-r)^t[/tex]
2014 your car was worth $8,850.
2014 - 2012 = 2, so:
[tex]f(2) = 8850[/tex]
We use this to find 1 - r.
[tex]f(t) = 10000(1-r)^t[/tex]
[tex]8850 = 10000(1-r)^2[/tex]
[tex](1-r)^2 = \frac{8850}{10000}[/tex]
[tex](1-r)^2 = 0.885[/tex]
[tex]\sqrt{(1-r)^2} = \sqrt{0.885}[/tex]
[tex]1 - r = 0.9407[/tex]
Thus
[tex]f(t) = 10000(1-r)^t[/tex]
[tex]f(t) = 10000(0.9407)^t[/tex]
I just need Primitive function
Answer:
?????
Step-by-step explanation:
In what do you need primitive function?
Which equation has the same solution as 10(x) - x + 5 = 41
Step-by-step explanation:
if that is truly the full problem description, then we have
10x - x + 5 = 41
=>
9x = 36
our simply
x = 4
so, I am not sure, what your teacher wants to see as result.
there is an infinite number of equations I could find, all with the solution x = 4.
need help asap
what is the value of f(3) in the function below
Answer:
Step-by-step explanation:
The given function is :
Here , x= independent variable where we place the input value and f(x) = dependent variable where we get the output value.
Now , when we put x= 3 , we get
That means , the value of f(3) in the given function is 8.
Hence, the correct answer is B=8.
A local grocery store receives strawberries from suppliers in Florida and California. Currently there are 18 strawberry containers on the shelf and 11 of them are from Florida. A shopper selects three containers to purchase. What is the probability that exactly one of the containers is from the Florida supplier
Using the hypergeometric distribution, it is found that there is a 0.2831 = 28.31% probability that exactly one of the containers is from the Florida supplier.
The containers are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. N is the size of the population. n is the size of the sample. k is the total number of desired outcomes.In this problem:
There are 18 containers, hence [tex]N = 18[/tex]11 of those are in Florida, hence [tex]k = 11[/tex].A sample of 3 containers is taken, hence [tex]n = 3[/tex]The probability that exactly one of the containers is from the Florida supplier is P(X = 1), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 1) = h(1,18,3,11) = \frac{C_{11,1}C_{7,2}}{C_{18,3}} = 0.2831[/tex]
0.2831 = 28.31% probability that exactly one of the containers is from the Florida supplier.
A similar problem is given at https://brainly.com/question/24826394
