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.
An investment service is currently recommending the purchase of shares of Dollar Department Store selling at $18 per share. The price is approximately normally distributed with a mean of 20 and a standard deviation of 2. What is the probability that in a year the shares will be selling: Between $21 and $24
Answer:
0.2857 = 28.57% probability that in a year the shares will be selling between $21 and $24
Step-by-step explanation:
When the distribution is normal, we use 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.
The price is approximately normally distributed with a mean of 20 and a standard deviation of 2.
This means that [tex]\mu = 20, \sigma = 2[/tex]
What is the probability that in a year the shares will be selling between $21 and $24
This is the pvalue of Z when X = 24 subtracted by the pvalue of Z when X = 21. So
X = 24:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{24 - 20}{2}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a pvalue of 0.9772
X = 21:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{21 - 20}{2}[/tex]
[tex]Z = 0.5[/tex]
[tex]Z = 0.5[/tex] has a pvalue of 0.6915
0.9772 - 0.6915 = 0.2857
0.2857 = 28.57% probability that in a year the shares will be selling between $21 and $24
I’m to lazy to write it so here’s the photo
Answer:
Step-by-step explanation:
Fishman, Goron, Smith, other
:::::
votes for Goron = 35% of 280 = 0.35×280 = 70
:::::
10% of 280 = 0.10×280 = 28 ≠ 40
The estimate was inaccurate
Solve |2x - 5| = 4 Thank you
Answer: x= 2 /9
Step-by-step explanation:
the length of a rectangle garden is 5 m the area is 176 m2 what is the width of the garden
Answer:
Step-by-step explanation:
L = 5 m
area = L×W = 176 m²
5W = 176
W = 176/5 = 35.2 m
Do
xº
470
Find the values of x and y.
In ΔEFG, e = 8.9 cm, f = 7.7 cm and g=2.2 cm. Find the measure of ∠F to the nearest degree.
Answer:
51 degrees
Step-by-step explanation:
gave up on delta math
Write and solve an equation to find Marys. Mary is 6 years older than Ellen. Jim is 5 years older than Mary. If their total combined age is 41. How old is Ellen?
nggkkkb ghjkkjgh
ggjbdfhhkmbssrjokncfd
What is 2/3 divided by 3/4
Answer:
8/9
Step-by-step explanation:
It can sometimes be difficult to divide fractions, such as 2/3 divided by 3/4! When we divide two fractions, such as 2/3 ÷ 3/4, we flip the second fraction and then we simply multiply the numerators with each other and the denominator with each other. We also simplify the answers to fraction problems whenever possible.
Hope This Helps You!
-TheAnimeCatUwU
#LearnWithBrainly
y= -1/2
55 + 3/8 y
.....................................................................
Answer:
55+3/8 -1/2=55-3×2/8=55-3/4=54.25
23 divided by 92 show the steps pls and you get brainliest
Answer:
Just divide 23 by 92 using long division to get a decimal answer, then convert the decimal to a percent by moving the decimal over to the right by 2 places and adding a percent sign.
Step-by-step explanation:
23/92 = x/100
92x = 2300
x = 25
Answer:
i dont c-a-r-e
Step-by-step explanation:
Which is the smallest standard deviation?
Answer:
C
Step-by-step explanation:
Because I'm smart.
HELP ME PLEASE I DONT KNOW WHAT TO DO!!!!!!!!
Answer:
I would have to guess c because it show a decrease in the number line
Step-by-step explanation:
Step-by-step explanation:
ɪᴛs ᴛʜᴇ ʟᴀsᴛ ᴏᴘᴛɪᴏɴ D
ᴀs ᴛʜᴇ ᴅᴏᴛ ɪs ᴘᴏɪɴᴛᴇᴅ ʙᴇᴛᴡᴇᴇɴ -15 ᴀɴᴅ -20
Can someone pls help me
Answer:
e
Step-by-step explanation:
If you divide 36 by 12, you get 3.
For this to work, whatever the white wax is, it needs to be 3 times as more as 5.
5x3=15
Answer:
i’ve done this before
Step-by-step explanation:
E and D
for every 12ml of red wax there’s 5 ml of white wax right? so you just multiply them at the same number to see if it matches.
12 x 5 = 60
5 x 5 = 25
12 x 3 = 36
5 x 3 = 15
fair- sided coin is tossed 18 times . Which of the experimental outcomes is most consistent with theoretical outcomes
A) 4 heads and 14 tails
B) 6 heads and 12 tails
C) 9 heads and 9 tails
D) 10 heads and 8 tails
HELP WILL GIVE BRAINLY
Answer:
C) 9 heads and 9 tails
Step-by-step explanation:
if a fair sided coin is tossed, the probability of obtaining either heads or tails is 50%
If the coin is tossed 18 times, we would expect to see the same probability outcome which is 50% heads and 50% tails.
which corresponds to 9 heads and 9 tails.
Answer:
Step-by-step explanation:
Each throw is independent of any other throw. The probability of getting a head or tail is 1/2, so you should expect to flip as many heads as tails. Answer C shows that even split.
Joy drinks 4.5 bottles of water per day.
Each bottle contains 16.5 fluid ounces.
How many fluid ounces of water does
she drink per day?
A 20.10 fluid ounces
B 64.00 fluid ounces
C 74.25 fluid ounces
D 82.50 fluid ounces
This is math and science.
The time for Speedy Pizza to deliver a pizza has a mean of 10 minutes, and a standard deviation of 2.8 minutes. Speedy guarantees that all pizzas will be delivered within 15 minutes or the customer will receive the pizza free. If delivery time follows a normal distribution, use a random number of .961 to simulate one pizza delivery time. Give your answer to 3 decimal places.
Answer:
14.9336
Step-by-step explanation:
Given that :
Mean = 10
Standard deviation = 2.8
To simulate a pizza delivery time with a random z - value of 0.961
Using the Z - probability calculator :
To find the x value corresponding to Z = 0.961
P(Z < x) ; P(Z < x) = 0.961 = 1.762
Simulated delivery time for the random number generated :
Mean + (Zscore * standard deviation)
10 + (1.762 * 2.8)
10 + 4.9336
= 14.9336
Help fast quick fast fast emergency
A school with 340 students produces trash that fills 1,190 tall trash cans per week. If each student produces the same amount of trash, approximately how many trash cans does each student fill per week, written as a decimal?
Answer:
3.5 trash cans
Step-by-step explanation:
I divided 1,190 by 340 and got 3.5 trash cans
select repeating or nonrepeating to correctly classify each decimal
Answer:
You Need To add a picture
Step-by-step explanation:
But if the decimal is before a number and has a line then its repeating if not its nonrepeating
Please help I dont get this
Answer: The commutative property
Step-by-step explanation: The commutative property is where an equations can be swapped and not change the answer. The following is true with that problem.
How many kilograms are equivalent to 14,000 grams?
Answer:
14
Step-by-step explanation:
the answer for this question is 14
Answer:
14 kiligrams
Step-by-step explanation:
PLEASE HELP ASAP 10+ PTS!!
Answer:
(x,y) = (25,15)
Step-by-step explanation:
In a parallelogram, alternate angles are equal, so
[tex]\left \{ {{3x-8=4y+7} \atop {4x+13=5x-12}} \right.[/tex]
From the latter equation we obtain [tex]x= 13 + 12 = 25[/tex]. So substituting in the former equation gives
[tex]75-8 = 4y + 7\\4y = 60\\y = 15[/tex]
What is it ????????????????????????
Answer:
1/8 or 8/64
Step-by-step explanation:
its 1/8 you just times them both by 8 it ez
EEEEEEEE I NEED HELP ASAP THESE 3 QUESTIONS ARE ON MY DBA AND I NEED TO GET A A+ ON MY DBA SO I CAN GET THE CODES FOR MY OTHER ASSIGNMEENNTSSS SO PLSSS HELP I WILL GIVE 30 POINTS AND IF U PUT JIBBERISH PLEASE DONT BECAUSE THATS NOT NICE AT ALL D:
1( Explain how to use the Order of Operations to calculate: 32 + 2(8) = ______
2( How do you write the Algebraic Expression for “5 less than the product of three and a number”
3( Write an equivalent expression for 3(3x + 5). Explain what property you used to write your equivalent expression.
I WILL ALSO GIVE BRAINLIEST AND STARTS A THANKS AND A COMMENT!! I WILL DO IT ON ALL 3 OF MY ACCOUNTS TO PLEASEEEEE HELP
Answer:
1) 2(8) +32 = 48 2) 5-3x 3) 9x+15
Step-by-step explanation:
For the first equation, you do PEMDAS which is parenthesis, exponents, multiplication/division, addition/subtraction. So, you multiply first. For the second problem, you subtract 5 because you see that in the equation, and product of 3 and a number which would be x since it is unknown. For the last equation, you would use the distributive property to do 3(3x) and 3(5) to get 9x+15.
A collection of dimes and nickels is worth $6.70. There are 76 coins in all. How many dimes and how many nickels are there?
please help
Answer:
58 dimes and 18 nickels
Step-by-step explanation:
Rank the following values from largest to smallest
Answer:
Number of blades of grass on a football field.
Number of Pages in the novel.
Number of members in your immediate family.
Number of musicians.
Step-by-step explanation:
¯\_(ツ)_/¯
Answer: (largest to smallest) Number of blades of grass on a football field, Number of pages in the novel "MobyDick", Number of musicians in a school marching band, Number of members in your immediate family
Step-by-step explanation:
M∠LON = 7x-92 and m∠MON = 6x+12
Answer:
[tex]M∠LOM = \boxed{48}[/tex]
Step-by-step explanation:
[tex]M∠LOM + m∠MON = 180 \\ 7x-92 + 6x+12 = 180 \\ 13x - 80 = 180 \\ 13x = 180 + 80 \\ 13x = 260 \\ \boxed{ x = 20} \\ (7x - 92 )= 140 - 92 = \boxed{48} \\ [/tex]
8р - 15 = 49
8р=
p =
Answer:
8
Step-by-step explanation:
Help&EXPLAIN
Don’t use for points or will be reported and I’ll take the points back
Answer:
105
Step-by-step explanation:
A straight line is 180 degrees so 180-75=105
Answer:
x= 105 degrees
Step-by-step explanation:
We know that the sum of x and 75 degrees is equal to 180 degrees.
So that means that x= 180-75 or x=105 degrees
Solve for w.
6w=-12
Simplify your answer as much as possible.
Answer:
-2
Step-by-step explanation:
Rearrange for w
-12/6 = -2
Have a great day :)
-2
Step-by-step explanation:
6w = -12
w = -12/6
w = -2
hope u will happy forever