Answer and Step-by-step explanation: This function is a probability density function of a random variable X:
[tex]f(x)=\frac{3(8x-x^{2})}{256}[/tex]
and to calculate probabilities, we will have to integrate it:
[tex]P(X<x)=\int\limits^x_0 {\frac{3}{256}(8x-x^{2}) } \, dx[/tex]
Solving:
[tex]P(X<x)=\frac{3}{256}(4x^{2}-\frac{x^{3}}{3} )[/tex]
Then:
a. P(X < 5)
[tex]P(X<5)=\int\limits^5_0 {\frac{3}{256}(8x-x^{2}) } \, dx[/tex]
[tex]P(X<5)=\frac{3}{256}(100-\frac{125}{3} )[/tex]
[tex]P(X<5)=\frac{3}{256}(\frac{300-125}{3} )[/tex]
[tex]P(X<5)=\frac{175}{256}[/tex]
P(X < 5) = 0.683
b. P(X < 9)
Since density function's upper limit is 8, probability of x < 9 is 100% or 1.
So, P(X < 9) = 1
c. P(5 < X < 7)
[tex]P(5<X<7)=\int\limits^7_5 {\frac{3}{256}(8x-x^{2}) } \, dx[/tex]
[tex]P(5<X<7)=\frac{3}{256}[4(7)^{2}-\frac{7^{3}}{3}-4(5)^{2}+\frac{5^{3}}{3}][/tex]
[tex]P(5<X<7)=\frac{3}{256}[96-\frac{218}{3} ][/tex]
[tex]P(5<X<7)=\frac{70}{256}[/tex]
P(5 < X < 7) = 0.273
d. P(X > 3)
[tex]P(X>3)=\int\limits^8_3 {\frac{3}{256}(8x-x^{2}) } \, dx[/tex]
[tex]P(X>3)=\frac{3}{256}[256-\frac{512}{3}-36+9 ][/tex]
[tex]P(X>3)=\frac{3}{256}(229-\frac{512}{3} )[/tex]
[tex]P(X>3)=\frac{175}{256}[/tex]
P (X > 3) = 0.683
e. P(X < x) = 0.95
[tex]0.95=\int\limits^x_0 {\frac{3}{256}(8x-x^{2}) } \, dx[/tex]
[tex]\frac{3}{256}[\frac{12x^{2}-x^{3}}{3} ] =0.95[/tex]
[tex]\frac{12x^{2}-x^{3}}{256}=0.95[/tex]
[tex]12x^{2}-x^{3}=243.2[/tex]
[tex]-x^{3}+12x^{2}-243.2=0[/tex]
Solving this cubic equation, we have three values for x:
x₁ = -3.909
x₂ = 8.992
x₃ = 6.917
The value of x will the one between 0 and 8, which are the limits of the function. So, value of x which gives a probability of 0.95 is x = 6.917.
A study showed that 25% of the students drive themselves to school. Based on the suggested probability, in a class of 18 students, what would be the probability that at least 6 students drive themselves to school? (CDF)
A) 0.139
B) 0.283
C) 0.717
D) 0.861
Answer:
B) 0.283
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.
25% of the students drive themselves to school.
This means that [tex]p = 0.25[/tex]
Class of 18 students
This means that [tex]n = 18[/tex]
What would be the probability that at least 6 students drive themselves to school?
This is
[tex]P(X \geq 6) = 1 - P(X < 6)[/tex]
In which
[tex]P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + 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 = 0) = C_{15,0}.(0.25)^{0}.(0.75)^{18} = 0.006[/tex]
[tex]P(X = 1) = C_{15,1}.(0.25)^{1}.(0.75)^{17} = 0.034[/tex]
[tex]P(X = 2) = C_{15,2}.(0.25)^{2}.(0.75)^{16} = 0.096[/tex]
[tex]P(X = 3) = C_{15,3}.(0.25)^{3}.(0.75)^{15} = 0.17[/tex]
[tex]P(X = 4) = C_{15,4}.(0.25)^{4}.(0.75)^{14} = 0.213[/tex]
[tex]P(X = 5) = C_{15,5}.(0.25)^{5}.(0.75)^{13} = 0.199[/tex]
[tex]P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.006 + 0.034 + 0.096 + 0.17 + 0.213 + 0.199 = 0.718[/tex]
[tex]P(X \geq 6) = 1 - P(X < 6) = 1 - 0.718 = 0.282[/tex]
Closest option is B, just a small rounding difference.
Hello Brainly pleas help
Answer:
can you take a better pick
Step-by-step explanation:
Find the equation of a line parallel to the equation y = 5x + 7 through the point (2,7).
Answer:
y = 5x + 7
Step-by-step explanation:
1. Substitue the numbers into their spots.
7 = 5(2)+b
2. Find b by simplifying
7 = 10 + b
-3 = b
3. Substitute it back in since parallel lines have the same slope.
Mr. Voelz estimates that he will spend $10 on concessions at the basketball game, He actually spends $15. What is the percent error?
PLEASE ANSWER
Answer:
.........................................................................................................................................................................
Step-by-step explanation:
if someone could explain this to me :((
Answer:
A) (0,2)
Step-by-step explanation:
The Y-Intercept is where the line on the coordinate plane meets the y axis which in this case is 2
Answer:
A. (0, 2)
Step-by-step explanation:
So first things first, you will want to either put the line on a graph by hand or, in a graphing calculator, I recommend DESMOS
the table is a set of coordinates so
(-4, -18) (-2.5, -10.5) (-.4, 0) (0, 2) (2, 12)
Then you'll put these coordinates into a graph and the point you see touching the y-line is your answer, (0, 2)
hope this helps!!
help please (will mark brainliest or however you spell it)
PLEASE HELP I'LL GIVE BRAINLIEST!!!!!!!!! According to the Census Bureau, in 2014 California had an estimated population of 3.88 × 107 and Wyoming had a population of 5.84 × 105. Complete the following sentences.
3.8216 × 107 0.38216 × 107 3.8216 × 106 38.216 × 107 0.66 × 101
66.4 × 101 6.64 × 101
The population of California is __________ more than the population of Wyoming
Alternatively, the population of California is _________ times the population of Wyoming.
Answer:
The population of California is [tex]3.3216 * 10^{7}[/tex] more than the population of Wyoming.
Alternatively, the population of California is [tex]6.64 * 10^{1}[/tex] times the population of Wyoming.
Step-by-step explanation:
The first part is to take the numbers out of the scientific notation. The estimated population of California is 38,800,000, and the population of Wyoming is 584,000.
Not that we've done that, let's start with the first part of the problem.
"The population of California is __________ more than the population of Wyoming."
This is a statement of subtraction, because it's not asking how many TIMES more. So, we subtract Wyoming's population from California's population.
[tex]38,800,000 - 584,000 = 38,216,000.[/tex]
Putting that number into scientific notation is easy: move the decimal to the place in the number where there will only be one number in front of the decimal: 3.3216. How many number slots until you have only one number in front of the decimal? 7. So, we know that the power of 10 is going to be 7. So, the first part of the question answers to:
[tex]3.8216 * 10^{7} .[/tex]
Now for the second part.
"Alternatively, the population of California is _________ times the population of Wyoming."
This is a problem of division. The question is asking us to divide California's population by Wyoming's population.
[tex]\frac{38,800,000}{584,000} = 0.664383562 * 10^{2} .[/tex]
We need to have one number in front of the decimal point, so we move it behind the first 6, giving us 6.64. Because we did this, we need to bump the exponent from 2 to 1, leaving us with:
[tex]6.64 * 10^{1}.[/tex]
So, the answer to the question is:
1. [tex]3.8216 * 10^{7}.[/tex]
2. [tex]6.64 * 10^{1}.[/tex]
Hope this helped you, and I hope you get a perfect score!! :)
Answer:
The population of California is ( 3.8216 x 10⁶ ) more than the population of Wyoming.
Alternatively, the population of California is ( 6.64 x 10¹ ) times the population of Wyoming.
Step-by-step explanation:
I'm pretty sure this is what the other person was trying to say it was just very confusing.
Anyway I got this right on my mastery test.
so thx for the points
If a1 = 4 and an = -3an-1 then find the value of a4.
Answer:
[tex]a_4 = -108[/tex]
Step-by-step explanation:
Given
[tex]a_n = -3a_{n-1}[/tex]
[tex]a_1 = 4[/tex]
Required
Find [tex]a_4[/tex]
[tex]a_4 = -3a_{4-1}[/tex]
[tex]a_4 = -3a_3[/tex]
We calculate for a3
[tex]a_3 = -3a_{3-1}[/tex]
[tex]a_3 = -3a_2[/tex]
Calculate for a2
[tex]a_2 = -3a_{2-1[/tex]
[tex]a_2 = -3a_1[/tex]
Substitute 4 for a1
[tex]a_2 = -3*4[/tex]
[tex]a_2 = -12[/tex]
Substitute -12 for a2 in [tex]a_3 = -3a_2[/tex]
[tex]a_3 = -3 * -12[/tex]
[tex]a_3 = 36[/tex]
Substitute 36 for a3 in [tex]a_4 = -3a_3[/tex]
[tex]a_4 = -3*36[/tex]
[tex]a_4 = -108[/tex]
6. Find the ICM of 60 and 400
Answer: it's 1200
Step-by-step explanation: please give me brainliest
400x3=1200
60x20=1200
At the City Zoo, of the zoo is set aside for the monkeys. There are 4 different monkeys, each
with an equal-sized area. What fraction of the zoo is set aside for one monkey area?
Can someone plz answer me...
A.1/4
B.4/15
C.1/13
D.1/36
i think part of this question is missing between “at the city zoo” and “of the zoo.”
but i think the answer could be a.
because if there are 4 different monkeys, and they all got 1/4 of space, it would be equal.
Which fraction is equivalent to (7-3)*3/10^4-10^2
A. 16/25
B. 1/25
C. 8/1125
D. 16/2475
Answer:
C.8/1125 is the answer......
Find the equation of the line with slope –5/2
and y-intercept (0,0).
Answer:
y= -5/2X
.....................
Diana and Michael, who are taking different classes, are arguing about who did better on their most recent test. Diana received a score of 92 on her History test and Michael received a 688 on his Math test. The mean test score for the History class is 71 with a standard deviation of 15.The mean test score for the Math class is 493 standard deviation of 150. Who did better, relative to other students in the same class? Justify your answer.
Answer:
Diana's score is better.
Step-by-step explanation:
In Diana case :
Score = 92
Mean score , μ = 71
Standard deviation σ = 15
So,
P( x ≥ 92 ) = 1 - P( x ≤ 92 )
= 1 - P(z ≤ [tex]\frac{x - u}{\sigma}[/tex] )
= 1 - P( z ≤ [tex]\frac{92 - 71 }{15}[/tex] )
= 1 - P( z ≤ 1.4 )
= 1 - 0.9192
= 0.0808 = 8.08 %
⇒P( x ≥ 92 ) = 8.08%
∴ we get
Diana score is > 91.92% other students in the class.
In Micheal case :
Score = 688
Mean score , μ = 493
Standard deviation σ = 150
So,
P( x ≥ 688 ) = 1 - P( x ≤ 688 )
= 1 - P(z ≤ [tex]\frac{x - u}{\sigma}[/tex] )
= 1 - P( z ≤ [tex]\frac{688 - 493 }{150}[/tex] )
= 1 - P( z ≤ 1.3 )
= 1 - 0.9032
= 0.0968 = 9.68 %
⇒P( x ≥ 688 ) = 9.68%
∴ we get
Micheal score is > 90.32% other students in the class.
From both scores , we can conclude that
Diana's score is better.
Is a coin flip random? Why or why not, in your opinion?
Choose the correct answer below.
A.
Yes. You will get heads on every other flip.
B.
Yes. You cannot predict the outcome beforehand.
C.
No. You must run numerous trials before you can tell.
D.
No. You can predict the outcome beforehand.
Answer:
B
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
50 points! I only want mhanifa to help me so no one else answer unless you actually know how to do it
Answer:
Bbc
Step-by-step explanation:
its something about cookies
Answer:
huh????
Step-by-step explanation:
Answer:
cool. i like cookies.
Select three ratios that are equivalent to
8
:
20
8:208, colon, 20.
Choose 3 answers:
Choose 3 answers:
(Choice A)
A
1
:
4
1:41, colon, 4
(Choice B)
B
4
:
10
4:104, colon, 10
(Choice C)
C
24
:
60
24:6024, colon, 60
(Choice D)
D
2
:
5
2:52, colon, 5
(Choice E)
E
10
:
24
10:24
Answer:
Its b,c,d
Step-by-step explanation:
What does the enlargement look like and what are the coordinates?
Answer:
(-6, -3) (-3,-3) (-3,-6)
Step-by-step explanation:
Multiple all of the vertices by 1.5.
(-6, -3) (-3,-3) (-3,-6)
Hope I helped!
[enlargment will still be a triangle]
F(t)=212-6t
what is the value of t when F (t) = 140?
Answer: -628
Step-by-step explanation:
F(140) = 212 - 6(140)
F(140) = 212 - 840
F(140) = -628
What is the quotient of 33.288 and 7.6?
Answer:
219/50 or 4.38
Step-by-step explanation:
divide
How much is 20% off of $90.75?
(This is fundamental Counting principle) choosing from 35 different flavors of ice cream; one, two or three scoops; and sugar or waffle cone.
Answer:
210
Step-by-step explanation:
35x3x2=210
3/8x5/4 Helpppppp pls
Answer:
9/25 or .36
Step-by-step explanation:
I SUCK AT THIS. PLEASE HELP! Factor x^2-11x+24x.
Answer: I think it is (x+3) (x+8)
[tex]x^{2} +13[/tex]
Step-by-step explanation: can u gimme brain plz!
Cuanto es 1+2:
pOrFa NoSe
Answer:
3
Step-by-step explanation:
es hora de comer
Pls help I need a good grade
Answer:
f= -14
Step-by-step explanation:
Answer:
f= -14
Step-by-step explanation:
A cone has a base area of 20 m and a volume of 160 m. Find the height of the cone
Given:
Base area of cone =20 m²
Volume of the cone = 160 m³
To find:
The height of the cone.
Solution:
We know that, the volume of a cone is
[tex]V=\dfrac{1}{3}Bh[/tex]
Where, B is the base area and h is the height of the cone.
Putting V=160 and B=20, we get
[tex]160=\dfrac{1}{3}(20)h[/tex]
[tex]480=20h[/tex]
[tex]\dfrac{480}{20}=h[/tex]
[tex]24=h[/tex]
Therefore, the height of the cone is 24 m.
Which of the following is a rational number?
square root of 79, square root of 80, square root of 81, square root of 82
Answer:
square root of 81.
Step-by-step explanation:
solving the systems of linear equations by substitution.
x+2y=6
5x+2y=18
Simplify: 10 divided by 1/4
1) 40
2) 1/40
3) 2 and 1/2
4) 20
Answer:
1
Step-by-step explanation:
10*4=40
so 1