Answer:
a) 0.001 = 0.1% probability that she will get five questions correct.
b) 0.0156 = 1.56% probability that she will get at least four questions correct.
c) 0.2373 = 23.73% probability that she will get no questions correct.
d) 0.8965 = 89.65% probability that she will get no more than two questions correct.
Step-by-step explanation:
For each question, there are only two possible outcomes. Either she gets it correct, or she does not. The probability of getting a question correct is independent of any other question, which means that the binomial probability distribution is used to solve this question.
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.
There are five multiple choice questions on the exam.
This means that [tex]n = 5[/tex]
She has decided on a strategy in which she will place four balls (marked A, B, C, and D) into a box. She randomly selects one ball for each question and replaces the ball in the box.
This means that [tex]p = \frac{1}{4} = 0.25[/tex]
a. Five questions correct?
This is [tex]P(X = 5)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{5,5}.(0.25)^{5}.(0.75)^{0} = 0.001[/tex]
0.001 = 0.1% probability that she will get five questions correct.
b. At least four questions correct?
This is:
[tex]P(X \geq 4) = P(X = 4) + P(X = 5)[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 4) = C_{5,4}.(0.25)^{4}.(0.75)^{1} = 0.0146[/tex]
[tex]P(X = 5) = C_{5,5}.(0.25)^{5}.(0.75)^{0} = 0.001[/tex]
[tex]P(X \geq 4) = P(X = 4) + P(X = 5) = 0.0146 + 0.001 = 0.0156[/tex]
0.0156 = 1.56% probability that she will get at least four questions correct.
c. No questions correct?
This is P(X = 0). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{5,0}.(0.25)^{0}.(0.75)^{5} = 0.2373[/tex]
0.2373 = 23.73% probability that she will get no questions correct.
d. No more than two questions correct?
This is:
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{5,0}.(0.25)^{0}.(0.75)^{5} = 0.2373[/tex]
[tex]P(X = 1) = C_{5,0}.(0.25)^{1}.(0.75)^{4} = 0.3955[/tex]
[tex]P(X = 2) = C_{5,2}.(0.25)^{2}.(0.75)^{3} = 0.2637[/tex]
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2373 + 0.3955 + 0.2637 = 0.8965[/tex]
0.8965 = 89.65% probability that she will get no more than two questions correct.
Three airlines serve a small town in Ohio. Airline A has 48% of all scheduled flights, airline B has 26% and airline C has the remaining 26%. Their on-time rates are 81%, 61%, and 40%, respectively. A flight just left on-time. What is the probability that it was a flight of airline A?
Answer:
0.5969 = 59.69% probability that it was a flight of airline A
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Left on time.
Event B: From airline A.
Probability of a flight leaving on time:
81% of 48%(airline A).
61% of 26%(airline B)
40% of 26%(airline C). So
[tex]P(A) = 0.81*0.48 + 0.61*0.26 + 0.40*0.26 = 0.6514[/tex]
Probability of leaving on time and being from airline A:
81% of 48%. So
[tex]P(A \cap B) = 0.81*0.48 = 0.3888[/tex]
What is the probability that it was a flight of airline A?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.3888}{0.6514} = 0.5969[/tex]
0.5969 = 59.69% probability that it was a flight of airline A
Balu had a collection of coins1/2 of the coins were from Asian countries,1/3
of them from European countries and the remaining 36 from America.
How many coins were from ASIAN countries?
A)18
B)30
C)108
D)216 step by step explanation please
Step-by-step explanation:
[tex] \frac{1}{2} = asian \\ \frac{1}{3} = european \\ 36 = american \\ \frac{1}{2} + \frac{1}{3} = \frac{3 + 2}{6} = \frac{5}{6} \\ \frac{6}{6} - \frac{5}{6} = \frac{1}{6} = 36 \\ \frac{1}{6} = 36 \: so \\ \frac{6}{6} =6 \times 36 = 216 \\ \frac{1}{2} \times 216 = asian \\ \frac{1}{2} \times 216 = 108asian \\ please \: mark \: brainliest[/tex]
There are total 108 coins belonging to Asian countries.
What is equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, Balu had a collection of coins 1/2 of the coins were from Asian countries, 1/3 of them from European countries and the remaining 36 from America.
Let the total number of coins be x,
Establishing the equation, we get,
x/3+x/2+36 = x
Multiplying the equation by 6, we get,
2x+3x+216 = 6x
6x-5x = 216
x = 216
Therefore, the total numbers of coins are 216,
Since, there are 1/2 of total coins are Asian coins,
Therefore, number of Asian coins = 216 / 2 = 108
Hence, There are total 108 coins belonging to Asian countries.
For more references on equations, click;
https://brainly.com/question/29657983
#SPJ2
A driver works 40 hours a week for the first two months on the job. How much more per week does the driver make after 28 days?
Answer:
is there something missing in this question. i cant understand
Step-by-step explanation:
please tell me if there is more to this
this distance-time graph represents a journey made by Jo
a) At 10 minutes the line is at y - 1, which means she reached 1 km in 10 minutes.
b) The last 30 minutes would be 30 minutes to 60 minutes.
at 30 minutes she was at 0km at 60 minutes she was at 4 km, so in 30 minutes she traveled 4 km. 30 minutes is a half hour, so multiply distance by 2: 4 x 2 = 8, she was traveling at 8 km per hour.
Given the equation Y-4=3/4(x+8) in point-slope form, identify the equation of the same line in standard form
Answer:
3x-4y=-40
Step-by-step explanation:
Hi there!
We're given the equation of the line, y-4=3/4(x+8) in point-slope form (y-[tex]y_{1}[/tex]=m(x-[tex]x_{1}[/tex]), where ([tex]x_{1}[/tex],[tex]y_{1}[/tex]) is a point and m is the slope)
We need to convert y-4=3/4(x+8) into standard form (ax+by=c, where a, b, and c are integer coefficients; a CANNOT be 0, and CANNOT be negative).
So we need to get y-4=3/4(x+8) out of point-slope form
We can do this by converting the equation into slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept
to do this, we need to isolate y by itself in the equation
first, do the distributive property and distribute 3/4 on the right side
y-4=3/4x+6
add 4 to both sides
y=3/4x+10
now the equation is in slope-intercept form, but remember, we want it in standard form
x and y are on the same side in standard form, so let's subtract 3/4 x from both sides
-3/4x+y=10
however we aren't done; in standard form, the coefficients need to be integers (whole numbers), and a (the coefficient in front of x) CANNOT be negative
so let's multiply both sides by -4 to clear the fraction and change the sign of a
-4(-3/4x+y)=-4(10)
do the distributive property
3x-4y=-40
Hope this helps! :)
Which pair of expressions below are equivalent?
a. 7(2n) and 9
b. 3n + 5n and 15n
c. 4(2n-6) and 8n - 24
d. 7(2n) and 72n
Answer:
The answer is C
Hope this helped!
Classify each angle of the degrees
Answer:
acute
right angle or obtuse
obtuse
Step-by-step explanation:
those are the answers
Laura, David, and Carlos served a total of 115 orders Monday at the school cafeteria. David served 3 times as many orders as Carlos. Laura served 10 more orders than Carlos. How many orders did they each serve?
Answer:
Step-by-step explanation: ts 6 11 19 56
Laura, David, and Carlos served a total of 115 orders
David served 3 times as many orders as Carlos. David = 3x
Laura served 10 more orders than Carlos. let Carlos = x
How many orders did they each serve? Laura = x + 10
Carlos + David + Laura = 115
x + 3x + x+10 = 115
5x + 10 = 115
5x = 115 - 10
5x = 105
x = 21 Carlos
63 Davide
31 Laura
add then up 115 Total
Why is it useful to factor out the GCF first when factoring?
Answer:
Because it makes factoring easier because the coefficient are smaller requiring less step
WILL GIVE BRAINLIEST
4
3
2x + 4
x+7
Answer:
x = 8
Step-by-step explanation:
[tex]\frac{x+7}{3} =\frac{2x+4}{4}[/tex]
do cross multiplication
[tex]3(2x+4) = 4(x+7)\\6x + 12 = 4x + 28\\6x - 4x = 12 - 16\\2x = 16\\x = 16/2\\x = 8[/tex]
Assume that Y is normally distributed with mean μ and standard deviation σ. After observing a value of Y, a mathematician will construct a rectangle with length L = |Y|and width W = 3 |Y|. Let A denote the area of the resulting rectangle. What is E(A)?
A phone company offers two packages of service. Package A is $35.00 per month with an additional charge of $0.15 per minute for long distance. Package B is $50.00 per month with an additional charge of $0.10 per minute for long distance. How many minutes have to be used for the costs of both plans to be the same?
Answer:
at 300 minutes, the cost of both plans are equal
Step-by-step explanation:
Package A: f(c) = 35 + .15c
Package B: f(c) = 50 + .10c
to answer the question we can set both expressions equal to each other and solve for 'c'
35 + .15c = 50 + .10c
35 + .05c = 50
.05c = 15
c = 15/.05
c = 300
The following data represent the number of loaves of bread, in thousands, which were sold by various grocery stores in the month of June. Construct a dot plot for the given data.
4, 8, 11, 10, 10, 4, 5, 13,
6, 13, 8, 14, 8, 1, 10, 9
Select any value to see the controls for increasing or decreasing the frequency.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Answer:
Following are the solution to these question:
Step-by-step explanation:
The frequency of the data value will be the same in dot plots for the number of dots. The frequency table is following:
[tex]X \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Frequency \\\\1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1\\\\2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0\\\\3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0\\\\4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2\\\\5\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1\\\\6\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1\\\\7\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0\\\\8\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3\\\\9\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1\\\\10\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3\\\\11\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1\\\\[/tex]
[tex]12\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0\\\\13\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2\\\\14\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1\\\\[/tex]
Need help quick! Will give brainliest
ABCD is a quadrilateral such that the measures of three of its interior angles are given as B=122 degrees, C= 75 degrees, D= 51 degrees, find m=A
please help me with explanation
Answer:
angle A is 112 degree.
Step-by-step explanation:
quadilateral have 4 angles .
sum of the interior angles of a quadilateral is 360 degree
Here,
angle A = be x
angle B = 122
angle C = 75
angle D = 51
Now,
angle A + angle B + angle C + angle D =360 degree
x + 122 + 75 + 51 = 360
x + 248 = 360
x = 360 - 248
x = 112
(05.01 MC) choose the systems of equations which matches the following graph
Answer:
a
Step-by-step explanation:
x+2y=-10
-x -x
2y=-10-x
y=(1/2)x-5
This is one of the lines and reduces the options to a or c.
3x-y=12
-3x -3x
-y=12-3x
y=3x-12
This is the line with the positive slope and since both lines match, the answer is a.
A farmer needs to calculate the number of liters in 90 cubic meters of fertilizer. How many liters are equivalent to 90 cubic meters?
Answer:
Answer is 90,000
Step-by-step explanation:
Hope this helps!
NO LINKS NO FILES. Write the next two integers: -48, -24, -12, _, _
Answer:
-6,-3
hope this helps
have a good day :)
Step-by-step explanation:
NEED HELP ASAP!!! please!!
Is the graph of the function shown in the graph below one-to-one? why?
Item 21
Subtract.
7,342−2,667
Answer:
4675
Step-by-step explanation:
Help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
9
Step-by-step explanation:
Length * Width = 43 * 36 = 1548 sq ft
1548 / 172 (sq ft per can of wood stain covered) = 9
seven more than the quotient of a number and 2 is equal to 3 equation
Answer:
Step-by-step explanation:
seven more than the quotient of a number and 2 is 10
7+n/2=10 n=6 check 7+3=10 ok
What’s the value of X????
What’s the answer?!!
Answer:
6x+10mm=p is the answer
brainlest plz
170 lbs to kg round to nearest tenth
Assume X is normally distributed with a mean of 5 and a standard deviation of 2. Determine the value for x that solves each of the following.
a. P(X > x) = 0.5
b. P(X > x) = 0.95
c. P(x < X < 9) = 0.2
d. P(3 < X < x) = 0.95
e. P(-x < X - 5 < x) =0.99
Answer:
U = 5
S = 4
1.) P(X>x) = 0.5
Prob = 1-0.5 = 0.5
We have z = 0, that is the z score with the probability of 0.5
X = u + z(s)
= 5+0*4
= 5
2.) 1-0.95 = 0.05
Z score having this probability
Z = -1.64
X = 5-1.64*4
= 5-6.56
= -1.56
3.) P(z<1.0) - p(X<x) = 0.2
0.841345-0.2 = .641345
We find the z score given this probability
Z= 0.36
X = 5+0.36*4
= 5+1.44
= 6.44
4.) P(X<x)-P(Z<-.5)
0.95 = p(X<x)-0.308538
p(X<x) = 0.308538 + 0.95
= 1.258538
There is no x value here, given that the probability is more than 1.
5. 1-0.99/2 = 0.005
We get the z score value
= -2.58
U - 5 = 5-5 = 0
-x = 0-2.58(4)
X = 10.32
A children's inflatable pool takes 17 minutes to fill with an electric air pump. It takes 53 minutes to let the air out of the pool. If the pool's vale is accidentally left open, how long will ot take to fill the pool?
Answer:
less than 17 minutes
Step-by-step explanation:
Hi :), im really struggling with this. Just wanted to know if anyone can explain step by step for me please?
Answer:
314 m²
Step-by-step explanation:
the surface area of a sphere (As) = 4×pi×r²
our radius r (half the diameter) here is 5m.
=>
As = 4×pi×5² = 4×3.14×25 = 100×3.14 = 314 m²
12(5x+10x^2)=480+60x
(^ = exponents)(show work)
x=−2 is the aswer to this problem i was wrong before
need help very bad :((
Answer:
Step-by-step explanation:
First of all, I can't think of a single exception to this, but when you rotate a figure, the two figures are congruent If all you do is rotate it.
2y/2 = 5/2 Divide both sides by 2
y = 5/2
y = 2.5
2x = 67 degrees Divide both sides by 2.
2x/2 = 67/2 x = 33.5
3w + 3 =12 Subtract 3 from both sides
3w + 3 -3 = 12-3 Combine
3w = 9 Divide by 3
w = 9/3
w = 3
