Calculate the mean, the variance, and the standard deviation of the following discrete probability distribution. (Negative values should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places. Round your final answers to 2 decimal places.)
x −36 −26 −15 −4
P(X = x) 0.32 0.36 0.21 0.11
Mean
Variance
Standard deviation
Answers
Mean = 24.47
Variance = 108.31
Standard deviation = 10.41
Step-by-step explanation:The probability distribution table has been attached to this response.
(1) To calculate the mean (m)
(a) First multiply each of the values of x by their corresponding probability values.
This is shown in the third column of the table.
(b) The sum of the results in the third column gives the mean of the distribution. i.e
m = ∑xP(x) = 11.52 + 9.36 + 3.15 + 0.44
m = 24.47
(2) To calculate the variance (σ²).
(a) First find the square of the difference between the values of x and the mean (m) calculated in (1b) above. i.e
(x - m)²
The result is shown in the fourth column of the table.
(b) Next, multiply each of the results in the fourth column (x - m)², by their corresponding probability values P(X = x). i.e
(x - m)²(P(X = x))
The result is shown in the fifth column of the table.
(c) Now find the variance (σ²) which is the sum of the results in the fifth column. i.e
σ² = ∑(x - m)²(P(X = x)) = 42.5411 + 0.8427 + 18.8330 + 46.0923
σ² = 108.3091
σ² = 108.31 [to 2 decimal places]
(3) To calculate the standard deviation (σ)
The standard deviation is the square root of the variance of the distribution. Calculate this by finding the square root of the result in (2c) above.
σ = √σ²
σ = [tex]\sqrt{108.31}[/tex]
σ = 10.4072
σ = 10.41 [to 2 decimal places]
Related Questions
Ivan runs a cake shop. Renting the
shop costs him $1600 per month,
and he makes a profit of $16 on each
cake he sells. Ivan wants a profit of at
least $2000 a month.
Answers
With the help of a diagram a boy starts at a and walks 3km east to b he then walk 4km north to c find the distance and bearing of c from a
Answers
Answer:
t=3
Step-by-step explanation:
sorry if its incorrect i got it right on edgy.
A random sample of 21 desktop PCs is selected. The mean life span is 6.8 years with a standard deviation of 2.4 years. Construct a 95% confidence interval for the mean life span of all desktop PCs. Assume that the life spans of all desktop PCs are approximately normally distributed (a) (5.85, 7.75) (b) (1.68, 3.12) (c) (5.60, 8.00) (d) (5.71, 7.89) (e) (5.77, 7.83)
Answers
Answer:
(d) (5.71, 7.89)
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 21 - 1 = 20
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 20 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.086
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.086\frac{2.4}{\sqrt{21}} = 1.09[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 6.8 - 1.09 = 5.71 years
The upper end of the interval is the sample mean added to M. So it is 6.8 + 1.09 = 7.89 years
So the confidence interval is (5.71, 7.89), and the correct answer is given by option b.
A jacket costs $154.85. There is a 45% discount. What is the new price of the jacket.
A.) $68.68
B.) $85.17
C.) $224.53
Answers
Answer:
B) $85,167
Step-by-step explanation:
u got discount 45% so u just have to pay 55% of it
cost = 55% x $154,85 = $85,1675
Intravenous fluid bags are filled by an automated filling machine. Assume that the fill volumes of the bags are independent, normal random variables with a standard deviation of 0.08 fluid ounces.
(a)What is the standard deviation of the average fill volume of 22 bags?
(b)The mean fill volume of the machine is 6.16 ounces, what is the probability that the average fill volume of 22 bags is below 5.95 ounces?
(c)What should the mean fill volume equal in order that the probability that the average of 22 bags is below 6.1 ounces is 0.001?
Answers
Answer:
a) 0.0171 fluid ounces.
b) 0% probability that the average fill volume of 22 bags is below 5.95 ounces
c) The mean should be of 6.153 fluid ounces.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Standard deviation of 0.08 fluid ounces.
This means that [tex]\sigma = 0.08[/tex]
(a)What is the standard deviation of the average fill volume of 22 bags?
This is s when n = 22. So
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
[tex]s = \frac{0.08}{\sqrt{22}}[/tex]
[tex]s = 0.0171[/tex]
(b)The mean fill volume of the machine is 6.16 ounces, what is the probability that the average fill volume of 22 bags is below 5.95 ounces?
We have that [tex]\mu = 6.16[/tex]. The probability is the p-value of Z when X = 5.95. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{5.95 - 6.16}{0.0171}[/tex]
[tex]Z = -12.3[/tex]
[tex]Z = -12.3[/tex] has a p-value of 0.
0% probability that the average fill volume of 22 bags is below 5.95 ounces.
(c)What should the mean fill volume equal in order that the probability that the average of 22 bags is below 6.1 ounces is 0.001?
[tex]X = 6.1[/tex] should mean that Z has a p-value of 0.001, so Z = -3.09. Thus
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]-3.09 = \frac{6.1 - \mu}{0.0171}[/tex]
[tex]6.1 - \mu = -3.09*0.0171[/tex]
[tex]\mu = 6.153[/tex]
The mean should be of 6.153 fluid ounces.
rational numbers.
Example 6: Write any 3 rational numbers between –2 and 0.
-20
0
ondas
-
Answers
Answer:
my firnd coli
Step-by-step explanation:
In a plain, robust, conversational style, the author known as “Elena Ferrante” has captivated readers worldwide with her chronicle of a complicated friendship between two women.
what are the adjectives in this sentence: the class cheered when Sonia had finished reading her funny poem.
Answers
2. How to find the variance and standard deviation of a discrete
random variable?
Answers
Answer:
To find the variance just take the second moment and subtract that from the first moment squared
To find the standard deviation just take the square root of the variance
Step-by-step explanation:
HELP PLEASE! What is BD??
Answers
Answer:
[tex]BD=13[/tex]
Step-by-step explanation:
Note that Ray AC bisects ∠A. Therefore, we can use the Angle Bisector Theorem shown below.
Hence:
[tex]\displaystyle \frac{27}{x+5}=\frac{12}{x}[/tex]
Solve for x. Cross-multiply:
[tex]12(x+5)=27(x)[/tex]
Distribute:
[tex]12x+60=27x[/tex]
Subtract 12x from both sides:
[tex]15x=60[/tex]
Divide both sides by 15. Thus:
[tex]x=4[/tex]
BD is the sum of BC and CD:
[tex]BD=BC+CD[/tex]
Substitute:
[tex]BD=x+(x+5)[/tex]
Substitute and evaluate:
[tex]BD=(4)+(4+5)=13[/tex]
Therefore, BD is 13.
(08.07 MC)
A polynomial function is shown below:
f(x) = x3 − 3x2 − 4x + 12
Which graph best represents the function? (5 points)
Answers
Answer:
Graph A (first graph from top to bottom)
Step-by-step explanation:
Given [tex]f(x)=x^3-3x^2-4x+12[/tex], since the degree of the polynomial is 3, the function must be odd and will resemble the shown shape in the graphs. The degree of 3 indicates that there are 3 zeroes, whether distinct or non-distinct. Therefore, the graph must intersect the x-axis at these three points.
Factoring the polynomial:
[tex]f(x)=x^3-3x^2-4x+12,\\f(x)=(x+2)(x-2)(x-3),\\\begin{cases}x+2=0, x=-2\\x-2=0, x=2\\x-3=, x=3\end{cases}[/tex]
Thus, the three zeroes of this function are [tex]x=-2, x=2, x=3[/tex] and the graph must intersection the x-axis at these points. The y-intercept of any graph occurs when [tex]x=0[/tex]. Thus, the y-coordinate of the y-intercept is equal to [tex]y=0^3-3(0^2)-4(0)+12,\\y=12[/tex] and the y-intercept is (0, 12).
The graph that corresponds with this is graph A.
a trader borrowed 2500$ at a sumple interest at the end of 8 months he paid back $2500 find the rate
Answers
Answer:
8%
Step-by-step explanation:
Rate = 100×Interest ÷ Principal× Time
100× 2500/ 2500 × 8 = 800
800/100 = 8%
I hope this helps
Three bags contain 3 red, 7 black; 8 red, 2 black, and 4 red & 6 black balls
respectively. 1 of the bags is selected at random and a ball is drawn from it. If the ball
drawn is red, find the probability that it is drawn from the third bag.
Answers
Answer:
[tex]Probability = \frac{4}{15}[/tex]
Step-by-step explanation:
B1 = first bag
B2= second bag
B3 = third bag
Let A = ball drawn is red
Since, there are three bags.
Probability of choosing one bag= P(B1) = P(B2) = P(B3) = 1/3.
From B1: Total balls = 10
3 red + 7 black balls.
Probability of drawing 1 red ball from it , P(A) = 3/10.
From B2: Total balls = 10
8 red + 2 black
Probability of drawing 1 red ball is, P(A) = 8/10
From B3 : Total Balls = 10
4 red + 6 black
Probability of drawing 1 red ball, P(A) = 4/10 .
To find Probability given that the ball drawn is red, that the ball is drawn from the third bag by Bayes' rule.
That is , P(B3|A)
[tex]=\frac{\frac{1}{3} \times \frac{4}{10}} { \frac{1}{3} \times \frac{3}{10} + \frac{1}{3} \times\frac{8}{10} + \frac{1}{3} \times \frac{4}{10}}[/tex]
[tex]=\frac{4}{30} \times \frac{30}{15}\\\\=\frac{4}{15}[/tex]
Therefore, the probability that it is drawn from the third bag is 4/15.
Answer:
4/15
Step-by-step explanation:
Solution of conditional probability problem:
Given:
Bags (3R,7B), (8R,2B), (4R,6B)
Let
P(R,i) = probability of drawing a red AND from bag i
P(R, 1) = 3/10 * (1/3) = 3/30
P(R, 2) = 8/10 * (1/3) = 8/30
P(R, 3) = 4/10 * (1/3) = 4/30
Let
Let P(R) = probability of drawing a red from any bag
P(R) = sum P(R,i) for i = 1 to 3 using the addition rule
= 3/30 + 8/30 + 4/30
= 15/30
= 1 / 2
Conditional Probability of drawing from the third bag GIVEN that it is a red
= P(3 | R)
= P(R, 3) / P(R)
= 4/30 / (1/2)
= 8/30
= 4 / 15
(Since all bags contain 10 balls, by intuition, 4 red from third / 15 total red = 4/15)
Write the following equation in the general form Ax + By + C = 0.
y - x - 1 = 0
2x - 3y + 6 = 0
2x - 3y - 6 = 0
-2x + 3y - 6 = 0
Answers
Answer:
C. -2x +3y-6=0
this is the answer
the probability that a customer of a network operator has a problem about you needing technical staff's help in a month is 0.01. This operator installs internet for 500 households in a residential area a, Calculate the average number of households in this residential area having internet problems in a certain month
b, Calculate the probability that in 6 consecutive months there is only one month that no customer in this area has a network problem that needs the help of technical staff
Answers
Answer:
(a) average calls = 5
(b) probability that there is exactly one call in 6 consecutive monts = 0.038
Step-by-step explanation:
Let event of a customer requiring help in a particular month = H
and event of a customer not requiring help in a particular month = ~H
Given
p= 0.01, therefore
Number of households, n = 500.
Binomial distribution:
x = number of households requiring help in a particular month
P(x,n,p) = C(x,n)*p^x*(1-p)^(n-x)
where
C(x,n) = n!/(x!(n-x)!) is the the number of combinations of x objects out of n
(a) Average number of households requiring help = np = 500*0.01 = 5
(b)
Probability that there are no calls requiring help in a particular month
P(0), q= C(0,n)*p^0(1-p)^(n-0)
= 1*1*0.99^500
= 0.006570483
Applying binomial probability over six months,
q = 0.006570483
n = 6
x = 1
P(x,n,q)
= C(x,n)*q^x*(1-q)^(n-x)
= 6!/(1!*5!) * 0.006570483^1 * (1-0.006570483)^5
= 0.038145
Therefore the probability that in 6 consecutive months there is exactly one month that no customer has called for help = 0.038
Is triangle XYZ = ABC ? If so, name the postulate that applies. A. Congruent - ASA B. Congruent - SAS C. Might not be congruent D. Congruent - SSS
Answers
Malachy rolls a fair dice 720 times.
How many times would Malachy expect to roll a five?
Answers
Answer:
120 times
Step-by-step explanation:
On a dice, there are 6 sides.
Since one of these sides is a 5, the chance of rolling a five is 1/6.
Find how many times Malachy can expect to roll a five by multiplying 720 by 1/6:
720(1/6)
= 120
So, Malachy can expect to roll a five 120 times
Whoever helps gets Brainliest!!! PLEASE HELP!!!
Answers
Find the volume of this rectangular pyramid.
Be sure to include the correct unit in your answer.
6 m
3 m
9 m
Answers
Answer:
54 m^3
Step-by-step explanation:
this is the answer = 54 m^3
Volume of the rectangular pyramid will be 54[tex]m^{3}[/tex].
What is Rectangular Pyramid?Rectangular pyramid has 5 faces where one face is rectangular which is at bases and other 4 faces are triangular which is connected at the one point .
How to calculate the volume of the rectangular pyramid?If we assume that l is the length of the base and b is the width of the base and h is height of the rectangular pyramid then we can calculate the volume of the rectangular pyramid using the formula stated below
Volume of the rectangular pyramid = V= (1/3)×l×b×h
According to the asked question
l = 6m
b = 3m
h = 9m
then we can calculate the volume of the rectangular pyramid by using the above formula
= V= (1/3)×l×b×h
= (1/3)×6m×3m×9m
= 54[tex]m^{3}[/tex]
Learn more about volume of the rectangular pyramid
Here:https://brainly.com/question/924442
#SPJ2
which elements in the following set are integers -8,3/4,-0.18,0,0.16,5,-2/7,6
Answers
Answer:
345
Step-by-step explanation:
The product of three consecutive numbers is divisible by
Answers
Answer:
6
Step-by-step explanation:
The product of three consecutive numbers is divisible by 6
Let us say the numbers are x, x+1 , x+2
if x = 1,
Product of the three consecutive numbers,
(1)(2)(3)
=> 6, which is divisible by 6
if x = 2,
Product of the three consecutive numbers,
(2)(3)(4)
=> 24, which is divisible by 6
Similarly if we take any 3 consecutive numbers their product will be divisible by 6.
PLEASE HELP!! graph the circle whose equation is (x-6)^2 + (y+2)^2 =4
Answers
Answer:
Y= -x^2+12x-36
Step-by-step explanation:
15 friends want to order pizza for dinner. If each friend can eat 1/3 of a pizza, how many pizzas should they order?
Answers
Answer:
5
Step-by-step explanation:
[tex]\frac{15}{3} =5\\3 friends=1 pizza\\15 friends=5 pizzas\\[/tex]
Find the percent of decrease from 46 songs to 41 songs. Round to the nearest tenth of a percent if necessary.
percent of decrease
%
Answers
Answer:
10.9 %
Step-by-step explanation:
46 - 41 = 5
5/46 * 100% = 10.8695652174%
Rounded
10.9 %
The volume of a rectangular prism is given by 24x3+78x2+49x+10. The height of the prism is given by 2x+5. Find an expression for the area of the base of the prism
Answers
Answer:
?
Step-by-step explanation:
i cant not explian that
How tall is the table?
120cm
90cm
I
Answers
The values of variables, such as the height of the table can be found by writing equations of their relationships
The height of the table is 105 cm
The reason the above height value is correct is as follows;
Known parameters:
The diagram shows a table, a cat and a mice
Let x, represent the height of the table, let y represent the height of the cat, and let z represent the height of the mice
From the given diagram, we have;
Height of the table + Height of the cat - Height of the mice = 120 cm
∴ x + y - z = 120...(1)
Height of the table + Height of the mice - Height of the cat = 90 cm
∴ x + z - y = 90...(2)
Adding equation (1) to equation (2) gives;
x + y - z + (x + z - y) = 120 + 90 = 210
x + y - z + (x + z - y) = 210
However;
x + y - z + (x + z - y) = x + x + y - y - z + z = 2·x
∴ x + y - z + (x + z - y) = 2·x = 210
x = 210/2 = 105
Therefore;
The height of the table, x = 105 cm
Learn more about word problems leading on simultaneous equations here:
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GUIDE QUESTIONS:
1. What is the idea or theme of the play?
2. How do you feel after watching the performance?
3. Does the integration of musical sound, songs, dialogue, and dance affect the
overall mood of the play?
Answers
Answer:
1.sowwy I dunno
2.its so good and it's perfect
3.i dunno ulet hehe
Step-by-step explanation:
Sorry walang matino na sagot.
What is the inverse function of y = 2x - 8
Answers
Answer:
Step-by-step explanation:
y = 2x-8
2x = y+8
x = 0.5y+4
inverse function: y = 0.5x+4
Which expression is equivalent to -6(-⅔+2x)?
O-4-12x
O-4+ 2x
O 4-12x
O 4+ 12x
Answers
Answer:
4-12x
Step-by-step explanation:
opening the brackets;
(-6×-2/3)- 12x
-2×-2 -12x
4-12x
Answer:
4 - 12x
Step-by-step explanation:
We can find an equivalent expression by distributing
-6(-⅔+2x)
Distribute by multiplying -6 times what's inside of the parenthesis ( -2/3 and 2x )
-6 * -⅔ = 4
-6 * 2x = -12x
We would be left with 4 - 12x
Please help please guys how are you doing
Answers
Answer:
the answer of the the triangle is 6
Answer:
6
Step-by-step explanation:
First row:
8 ÷ 2 = 4. → Square: 4
Second row:
14 - 4 = 10.
[two circles] = 10. So, 10÷2 = 5.
Circle = 5
Third Row:
[triangle] + 5 = 11
11 - 5 = 6
Triangle = 6
One evening Papa John’s sold a total of 33 pizzas topped with pepperoni, sausage, or pepperoni and sausage. There were 29 pizzas that had pepperoni. Of these, 15 also had sausage. How many more pizzas had pepperoni only than had sausage only?
Answers
Answer:
10
Step-by-step explanation:
Total pizza topped with pepperoni, sausage or pepperoni and sausage = 33
Number of pizzas with pepperoni = 29
Number of pizzas with pepperoni and sausage = 15
Pizza with pepperoni only = 29 - 15 = 14
Pizza with sausage only = 33 - 29 = 4
Pepperoni only than sausage only :
14 - 4 = 10
