One sample mean t test is used to to check whether the true average is 59k.
Average:
In statistics, average means a mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.
Given,
Here we need to find in what test can you use to check whether the true average is 59k.
While we looking into the given question we have identified the following details,
Number of students = 49
True average = 59k
Sample average = 44k
In this given situation, the perfectly suitable test is one sample t test,
Why we used this because of a statistical hypothesis test used to determine whether an unknown population mean is different from a specific value.
Suppose our student center published data that the average starting salary for college graduates is 59k. You randomly sampled 49 college graduates and calculated the sample average salary is 44k.
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a survey of 1000 students nationwide showed a mean act score of 21.4. a survey of 500 south carolina scores showed a mean of 21.2. if the population standard deviation in each case is 3, can we conclude the national average is greater than the south carolina average? use
The hypotheses for [tex]H_{0}[/tex] is [tex]\µ_{1}[/tex] = [tex]\µ_{2}[/tex] and for [tex]H_{1}[/tex] [tex]\µ_{1} > \µ_{2}[/tex] (claim)
Given:
Nationwide scores as n1=1000, [tex]x_{1}[/tex]` = 21.4 ,σ1 = 3
Carolina scores as n2=500, [tex]x_{2}[/tex]` = 21.2 ,σ2 = 3
So from here we can say
µ represents population mean.
[tex]u_{1}[/tex] represent population mean for nationwide scores.
[tex]u_{2}[/tex] represents population mean for Carolina scores.
[tex]H_{0}[/tex] is [tex]\µ_{1}[/tex] = [tex]\µ_{2}[/tex] and for [tex]H_{1}[/tex] [tex]\µ_{1} > \µ_{2}[/tex] (claim)
Given Question is incomplete, Complete Question here,
a survey of 1000 students nationwide showed a mean act score of 21.4. a survey of 500 south Carolina scores showed a mean of 21.2. if the population standard deviation in each case is 3, can we conclude the national average is greater than the south Carolina average?
use α=0.01 and [tex]\µ_{1}[/tex] for the nationwide mean act score.
State the hypotheses and identify the claim.
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Question 3(Multiple Choice Worth 2 points)
(Theoretical Probability MC)
The probability P(DD) of the letters D and D is 4/9
How to determine the probability?The letters of the alphabets used to generate the word ADD are given as
Sample space (letters) = {A, D, D}
It is assumed that when a card (i.e. letter) is selected, the card is returned to the set
This means that the selection is with replacement
These letters mean that
P(Letter D) = Count of letter D/Number of letters
So, we have the following representation
P(Letter D) = 2/3
Now, the sample space is
Sample space (letters) = {A, D, D}
These letters mean that
P(Letter D2) = 2/3
So, we have the probability equation
P(DD) = P(D) * P(D2)
This gives
P(DD) = 2/3 * 2/3
Evaluate
P(DD) = 4/9
So, the probability is 4/9
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forty teams play a tournament in which every team plays every other team exactly once. no ties occur, and each team has a 50% chance of winning any game it plays. the probability that no two teams win the same number of games is m/n, where m and n are relatively prime positive integers. find log2n
The probability that no two teams win the same number of games is 742.
There are (40/2) = 780 total pairings of teams, and thus 2⁷⁸⁰ possible outcomes. In order for no two teams to win the same number of games, they must each win a different number of games. Since the minimum and maximum possible number of games won are 0 and 39 respectively, and there are 40 teams in total, each team corresponds uniquely with some k, with 0 ≤ k ≤ 39, where k represents the number of games the team won. With this in mind, we see that there are a total of 40! outcomes in which no two teams win the same number of games. Further, note that these are all the valid combinations, as the team with 1 win must beat the team with 0 wins, the team with 2 wins must beat the teams with 1 and 0 wins, and so on; thus, this uniquely defines a combination.The desired probability is thus 40!/2⁷⁸⁰ . We wish to simplify this into the form m/n , where m and n are relatively prime. The only necessary step is to factor out all the powers of 2 from 40!, the remaining number is clearly relatively prime to all powers of 2.The number of powers of 2 in 40! is
= (40/2) + (40/4) + (40/8) + (40/16) + (40/32)
= 20 + 10 + 5 + 2 + 1
= 38.
780-38 = 742.
Hence, the probability that no two teams win the same number of games is 742.
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the summary of the percent of times each and every category appears for the entire sample is called the:
The summary of the percent of times each and every category appears for the entire sample is called the frequency distribution , the correct option is (d) .
In the question ,
it is asked about what is The summary of the percent of times each and every category appears for the entire sample is called ,
it is called frequency distribution ,
Frequency distribution : it lists all categories of data and number of occurrences for each data category and
it is also the summary of percent of times each and every category appears for entire sample .
Therefore , the correct option is (d) .
The given question is incomplete , the complete question is
The summary of the percent of times each and every category appears for the entire sample is called the ,
(a) mode
(b) categorical percentage rate
(c) percentage distribution
(d) frequency distribution
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d • r = r • d what is the property
Answer:
Commutative Property of Multiplication
Step-by-step explanation:
Hope it helps!
A 7 ft tall person is walking away from a 20 ft tall lamppost at a rate of 5 ft/sec. Assume the scenario can be modeled with right triangles. At what rate is the length of the person's shadow changing when the person is 16 ft from the lamppost?In similar triangles, both the two triangles must satisfy the two properties. One is the side proportional, and the other is equal in angles. There are three criteria in similarity. They are AA similarity, SSS similarity, and SAS similarity. The below one satisfies the AA similarity.
The change in rate of length of shadow is 2.692 ft/sec.
Given,
Height of tall person =7 ft
Height of tall lamp post = 20 ft
Rate at which tall person walks = 5 ft/sec
Let,
Distance between tall person and lamp post be x ft
the length of shadow be y ft
From similar triangles,
[tex]\frac{x+y}{20}=\frac{y}{7}\\\\7(x+y)=20y\\\\7x+7y=20y\\\\13y=7x\\\\y=\frac{7x}{13}[/tex]
Differentiating on both sides with respect to time 't'
[tex]\frac{dy}{dt}=\frac{7}{13}\frac{dx}{dt}[/tex]
here, [tex]\frac{dx}{dt}[/tex] is nothing but the change in distance between tall person and lamppost it means rate at which tall person walks=5 ft/sec
[tex]\frac{dy}{dt}=\frac{7}{13}*5\\\\\frac{dy}{dt}=\frac{35}{13}=2.692\ ft/sec[/tex]
Thus, the change in rate of length of shadow is 2.692 ft/sec.
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A certain type of mango that weighs over 425 grams is considered to be large in size. the weights for this type of mango, x grams, are normally distributed with a mean of 400 and a standard deviation of 25. find the probability that a randomly selected mango of this type will not be considered as large size. round your answer to four decimal places.
The probability that a randomly chosen mango of this type won't be deemed to be large in size is 26.43%.
Explain the term z-distribution/normal distribution?The statistics field is where z-distribution probability is most frequently employed. It is used to determine a person's height, weight, and pay. The graph produced by these measurements is symmetrical.For the stated question;
The formula for the z-score is;
z = (x - μ)/σ
x < 425 gram
mean μ = 400,
standard deviation σ = 40:
Thus,
z = (425 - 400)/40
z = 0.625
P(X < 425) = 1 - P(z = 0.625)
P(X < 425) = 1 - 0.7357
P(X < 425) = 0.2643
Thus, there is a 26.43% chance that a randomly chosen mango of this sort will not be regarded as being huge in size.
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Answer:0.8413
Step-by-step explanation:
0.8413
The mean is μ=400, and the standard deviation is σ=25.
Open Excel. Click on an empty cell. Type =NORMDIST(425,400,25,1) and press ENTER.
The probability, rounded to four decimal places, is P(X<425)≈0.8413.
Victoria purchased 0.6 lbs of deli ham for $4.71. What would it cost to purchase 1.4 lbs of the same ham? please and they solve asap and correct answer please
Using proportions and ratios, the cost of 1.4lbs is $10.96
ProportionsProportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.
This is basically the process of comparing two ratios with one another.
In this problem, we will compare the two ratios and solve for the unknown cost of 1.4lbs
0.6 / 4.71 = 1.4 / x
Cross multiply both sides
x = (4.71 * 1.4) / 0.6
x = 10.96
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At what point do the curves and intersect? find their angle of intersection correct to the nearest degree.
The intersection of two curves is important because it marks the spot where the values of the two curves coincide. There are numerous applications for this.
What are angles?When two lines meet at a point, an angle is created. An "angle" is the measurement of the "opening" between these two rays. It is symbolized by the character.
The circularity or rotation of an angle is often measured in degrees and radians. Angles are a common occurrence in daily life. Angles are used by engineers and architects to create highways, structures, and sports venues.
When two rays are linked at their ends, they create an angle in geometry.
The sides or arms of the angle are what are known as these rays. Read on to learn about the various components of an angle.
Hence, The intersection of two curves is important because it marks the spot where the values of the two curves coincide. There are numerous applications for this.
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A professor wants to estimate how many hours per week her students study. A simple random sample of 65 students had a mean of 16 hours of studying per week. Construct a 98% confidence interval for the mean number of hours a student studies per week. Assume that the population standard deviation is known to be 2.4 hours per week. Round to two decimal places. Answer 2 Points Keypad Keyboard Shortcuts Lower Endpoint Upper Endpoint: Prev
98% confidence Interval for the mean number of hours a student studies per week is (21.0208,18.9792)
mean x = 16
standard deviation σ = 2.4
sample size n = 65
z score for 98% = 2.576
Interval = x±z*s/
= 16±2.576*2.4/
= 16±2.576*0.39629
= 16±1.0208
Interval = (21.0208,18.9792)
Therefore 98% confidence Interval for the mean number of hours a student studies per week is (21.0208,18.9792).
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on the grid draw the graph of y= 1- 3x for values of x from -2 to 3
Answer:
see solution
Step-by-step explanation:
equation: y = 1 - 3x
when x is -2:
y = 1 -3 * -2 = y = 1+6 = y = 7
coordinates = (x,y) = (-2,7)
when x is -1:
y = 1-3*-1 = y = 1+3 = y = 4
coordinates = (x,y) = (-1,4)
when x is 0:
y = 1 - 3 * 0 = y = 1-0 = y =1
coordinates = (x,y) = (0,1)
when x is 1
y = 1-3*1 = y = 1-3 = y = -2
coordinates = (x,y) = (1,-2)
When x is 2
y = 1-3*2 = y = 1-6 = y = -5
coordinates = (x,y) = (2,-5)
when x is 3
y = 1-3*3 = y = 1-9 = y = -8
coordinates = (x,y) = (3,-8)
Plot these points on the graph and join up the dots to see the line.
bye
given are five observations collected in a regression study on two variables. xi 2 6 9 13 20 yi 7 18 9 26 23 which of the following scatter diagrams accurately represents the data?
The regression equation is y = 0.9x+ 7.5
given that
xi: 2 6 9 13 20
Yi : 7 18 9 26 23
from the given data we have:
∑x = 2+6+9+13+20 = 50
∑y = 7+18+9+26+23 = 83
Also, we need to calculate:
∑xy = 2 × 7+ 6 × 18+ 9× 9+ 13 × 26+ 20×23 = 1001
∑[tex]x^{2}[/tex] = [tex]2^{2}[/tex] + [tex]6^{2}[/tex] + [tex]9^{2}[/tex] + [tex]13^{2}[/tex] + [tex]20^{2}[/tex] = 690
∑[tex]y^{2}[/tex]= [tex]7^{2}[/tex] + [tex]18^{2}[/tex] + [tex]9^{2}[/tex] + [tex]26^{2}[/tex] + [tex]23^{2}[/tex] = 1659
the slope b is calculated:
b = ∑xy - ∑x × ∑y/n ÷ ∑[tex]x^{2}[/tex] - (∑x)^2 /n
now we need to substitute above values in the equation:
b = 1001 - 50×83 /5 ÷ 690 - (50)^2/5
b= 0.9
the y-intercept (a) is :
a = y - bx
where
y = ∑y/n = 83/5 = 16.6
x = ∑x/n = 50/5 = 10
now substitute these values
a = 16.5 - 0.9 × 10
a = 7.5
the regression equation:
y = bx + a
now ,
y = 0.9x+ 7.5
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Convert 4,300 kilometers into miles round your answer to the nearest whole number
4300 km to miles:
[tex]{ \red{ \tt{2671.896}}}[/tex]
2671.896 in nearest whole number :
[tex]{ \blue{\boxed{ \tt{2672}}}}[/tex]
under what circumstances is a score that is 5 points above the mean considered a central value--meaning it is relatively close to the mean?
When the population standard deviation is much greater than 5.
What is the standard deviation?
The term "standard deviation" refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
Here, we have
The circumstance is a score that is 5 points above the mean considered a central value.
We have to find under what circumstances is a score that is 5 points above the mean considered a central value--meaning it is relatively close to the mean.
We concluded from the above statement that when the population standard deviation is much greater than 5.
Hence, when the population standard deviation is much greater than 5 then, the score that is 5 points above the mean is considered a central value.
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use the value of the linear correlation coefficient r to find the coefficient of determination and the percentage of the total variation that can be explained by the linear relationship between the two variables.
The coefficient of determination is 0.588 and the percentage of the total variation is 58.8%.
The coefficient of determination (r^2) refers to a measurement used to explain how much variability of one variable can be caused by its relationship to another related variable. It is the fit of goodness and measures how well a statistical model fits the observed data and is a number between 0 and 1. When the value of linear correlation coefficient r is known, the coefficient of determination can be computed simply by squaring r.
Hence if r = 0.767, then the coefficient of determination = r^2 = 0.588
As percentage of the total variation is same as the coefficient of determination (given in percentage) and is given by the R² value = 58.8%. Hence, about 58.8% of variation is explained by the linear relationship between the two variables.
Note: The question is incomplete. The complete question probably is: Use the value of the linear correlation coefficient r to find the coefficient of determination and the percentage of the total variation that can be explained by the linear relationship between the two variables. r = 0.767.
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find two positive numbers that satisfy the given requirements. the sum of the first number squared and the second number is 51 and the product is a maximum. (first number) (second number)
The two positive numbers that satisfy the given requirements are √17 and 34
Given the sum of the first number squared and the second number
is 51.
Let's assume first number is x.
second number is y.
Square of first number is [tex]x^2[/tex].
sum of the first number squared and the second number = [tex]x^2 + y[/tex].
[tex]x^2 + y = 51[/tex]
subtract [tex]x^2[/tex] from both side of equal sign.
[tex]x^2 + y- x^2 = 51 - x^2[/tex]
[tex]y = 51 - x^2[/tex]
Product of both numbers p = x*y.
[tex]p = x*(51 - x^2)[/tex]
[tex]p = 51*x - x^3.[/tex]
Given the product is a maximum.
so derivative of p with respect to x will be = 0.
derivative of p with respect to x is [tex]51-3*x^2[/tex]
[tex]51-3*x^2 = 0[/tex]
[tex]3*x^2=51[/tex]
[tex]x^2 = 17[/tex]
x = √17.
put value of x in [tex]y = 51 - x^2[/tex]
[tex]y = 51 - (\sqrt17)^2[/tex] = 51 - 17 = 34
So the value of x and y is √17 and 34 respectively.
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how do the results compare to your hypothesis? explain why your hypothesis was/was not supported by the results?
Based on the results from your experiment, rank the antibiotics from the most effective to the least in controlling epidermidis. These aid by halting bacterial growth and infection spread.
A Gram-positive bacterium called S. epidermidis is a component of the flora of humans. Anaerobic bacteria are what it is. It promotes the growth of pathogens that are present in medical equipment. These may enter the bloodstream. Based on the results from your experiment, rank the antibiotics from the most effective to the least in controlling s. epidermidis.
Molds produce a class of antibiotics known as penicillium. Actinomycetes produce the antibody known as novobiocin, which has antibacterial characteristics. Gentamicin is one of the antibodies that can treat infections and aid in halting bacterial development.
Hence the answer is Based on the results from your experiment, rank the antibiotics from the most effective to the least in controlling epidermidis. These aid by halting bacterial growth and infection spread.
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What is the value of x?
Enter your answer in the box.
Answer:
x=36
Step-by-step explanation:
An airline finds that 5% of the persons making reservations on a certain flight will not show up for the flight. if the airline sells 155 tickets for a flight that has only 150 seats, what is the probability that a seat will be available for every pe?
The probability that a seat will be available for every person holding a reservation and planning to fly is 0.8980.
What is probability?
Probability is a branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely a proposition is to be true. The probability of an event is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty.
Given:
The probability that a person who makes reservations on a certain flight and does not show up for the flight is p=0.05.
The probability that a person who makes reservations on a certain flight and does show up for the flight is 1-p=1-0.05=0.95.
The airlines sell 160 tickets for a flight with only 155 seats.
Let X be a random variable that denotes the number of persons who show up for the flight and it follows a binomial distribution with parameters n = 160 and p = 0.95.
Hence, X~ Binom (n = 160, p = 0.95).
Here,
np=160×0.95=152>5
n(1-p)=160×0.05 = 8.1>5
Hence, both np and n(1-p) are greater than 5, the binomial distribution can be approximated to normal distribution.
The probability that a seat will be available for every person holding a reservation and planning to fly is calculated as follows:
P(X ≤ 155) = (P < 155 + 0.5)
[tex]=P(x < 155.5)\\\\=P(\frac{X-np}{\sqrt{np(1-p)}} < \frac{155.5 - (160 \times 0.95}{\sqrt{160\times 0.95 \times 0.05}})\\\\=P(Z < \frac{155.5-152}{2.7568})\\\\=P(Z < 1.27)\\\\=0.8980[/tex]
Hence the probability that a seat will be available for every person holding a reservation and planning to fly is 0.8980.
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Donald bought an old truck for $500
did a full restoration over the course of a
summer. When he had finished the
restoration, he sold it for $2,375. What was
the percent of increase on the truck?
The percent of increase on the truck was 375%.
Select the correct answer from each drop-down menu. Timothy purchased a computer for $1,000. The value of the computer depreciates by 20% every year. This situation represents. The rate of growth or decay, r, is equal to. So the value of the computer each year is % of the value in the previous year. It will take years for the value of the computer to reach $512.
It will take 3 years for the value of the computer of initial value $1000 to reach $512.
Given, Timothy purchased a computer for $1,000.
The value of the computer depreciates by 20% every year.
we have to find the number of years value of computer will take to reach $512.
Let, the function representing this situation be,
V(t) = AB^t
where, A is the initial value of the computer and B is the depreciating rate.
So, V(t) = (1000)(1 - 20/100)^t
V(t) = (1000)(0.8)^t
Now, the value will be, 512
512 = 1000(0.8)^t
0.512 = (0.8)^t
t = 3
So, it will take 3 years for the value of the computer of initial value $1000 to reach $512.
Hence, it will take 3 years for the value of the computer of initial value $1000 to reach $512.
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Olaf has 11 more than triple the amount of customers as when he started selling newspapers. He now has 71
customers. Write an equation that can be used to solve for how many customers Olaf had originally, then solve
your equation to find the answer.
The equation representing the situation is written as
3x + 11 = 71the number of customers Olaf had originally is 80
How to write the equationFrom the given information the following is deduced
Olaf has 11 more than triple the amount of customers as when he started selling newspapers
let the amount be x
3x + 11 = ?
He now has 71 customers
3x + 11 = 71
solving the equation
3x = 71 - 11
3x = 60
x = 20
Olaf had 80 customers
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4. Identify each of the following polygons:
Answer:
H
Step-by-step explanation:
question content area top part 1 it is believed that gpa (grade point average, based on a four point scale) should have a positive linear relationship with act scores. attached below is the technology output for predicting gpa using act scores based on a data set of 8 randomly chosen students from a big-ten university. what are the decision and conclusion on testing whether there is any linear relationship at 1% level of significance between gpa and act scores?
The p-value is greater than the significance level, so we do not reject the null hypothesis for the significance level is 0.01 (1%)
What is significance level?
"Significance" in statistics refers to something that is "not by chance" or "likely true." We can infer that when a statistician claims that a finding is "very significant," he or she is implying that it may very well be true. It does not imply that the finding is very significant, but it does imply that it is highly likely. The fixed likelihood of incorrectly eliminating the null hypothesis when it is, in fact, true is what is referred to as the level of significance. The probability of type I error is defined as the degree of significance, and the researcher sets it based on the results of the error. The statistical significance is measured by its level of significance. It specifies whether the null hypothesis is thought to be accepted or rejected.
The p-value for ACT is 0.0286
The significance level is 0.01 (1%)
Hence, the p-value is greater than the significance level, so we do not reject the null hypothesis. We conclude that there is insufficient evidence to conclude that there is any linear relationship at a 1% level of significance between GPA and ACT scores.
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you want to estimate the mean sat score of all georgia students. you know the mean score for a random sample of georgia students is 1050. what number is your best guess as to the mean score for all georgia students?
The best guess for the mean score for all the Georgia students would be 1050 number here.
Given that:
The mean score for a random sample of Georgia students is 1050.
Assuming,
1) X-bar = 42; µ = 44; standard deviation (sigma) = 10; N = 64. Calculate the standard error.
1) The standard error is computed as:
[tex]\sigma_{\bar X} = \frac{\sigma}{\sqrt{n}} = \frac{10}{\sqrt{64}} = 1.25[/tex]
2) You know that X-bar = 42, mu = 44, sigma-sub-X = 10, and N = 64, Calculate z-obtained.
2) The Z-value is computed as:
[tex]Z = \frac{\bar X - \mu}{\frac{\sigma}{\sqrt{N}}} = \frac{42- 44}{\frac{10}{\sqrt{64}}} = -1.6[/tex]
3) The mean score on most IQ tests is 100 with a standard deviation of 15. If Sally has a score of 110 on an IQ test, what is her z-score.
3) The Z -score here is computed as:
[tex]Z = \frac{X -\mu}{\sigma} = \frac{110-100}{15} = 0.6667[/tex]
The best point estimate for the population mean score is equal to the sample mean which is 1050 in this case. Therefore the best guess for the mean score for all the Georgia students would be 1050 here.
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3 times x plus 4 is no less than 4 times the sum of x and 1
There isn't a ton of information regarding exactly what you are looking for to answer this question. However, if you are trying to simply convert the following word phrase to an expression, here you go:
3 Times x - Since there is an unknown variable (x), we can simply write the multiplication as 3x. "Plus 4" is also mentioned, so we write the first part as (3x + 4).No Less Than - This simply means "<". 4 Times the Sum of X and 1 - We can write this as 4(x + 1), considering we are adding an x variable to 1, however also multiplying. To organize this, we add parenthesis.
Hence, the final expression would be written as:
[tex](3x+4) < 4(x+1)[/tex]
Hope this helps!
Find AD . CD = 5x-1 and AD = 4x+8
The numerical side length of length AD is 44 units
How to determine the length AD?From the question, we have the following lengths that can be used in our computation:
AD= 4x + 8
CD = 5x - 1
Also, from the complete question (added at the end of the solution), we understand that
The lengths AD and CD are congruent
These parameters and statements above mean that
AD = CD
Substitute the known values in the above equation, so, we have the following representation
4x + 8 = 5x - 1
Collect the like terms
5x - 4x = 1 + 8
Evaluate the like terms
x = 9
Substitute x = 9 in AD= 4x + 8
AD= 4 x 9 + 8
Evaluate
AD= 44
Hence, the length is 44 units
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Complete question
Given that lengths AD and CD are congruent.
Find AD
CD = 5x-1 and AD = 4x+8
How do u make 630 into 6.3?
Answer:
by dividing by 100
Step-by-step explanation:
630 ÷ 100 = 6.3
Given the following probability distributions:
Distribution A Distribution B x p(x) x p(x)
0 .50 0 0.05
1 .20 1 0.10
2 .15 2 0.15
3 .10 3 0.20
4 .05 4 0.50
a. Compute the expected value for each distribution.
b. Compute the standard deviation for each distribution.
c. Compare the results of distributions A and B.
The expected value of distribution A is 1 and distribution B is 3. The standard deviation for both distributions is the same which is 1.225. In conclusion, distribution B is better than distribution A.
Events with countable or finite outcomes are counted in a discrete probability distribution. This includes the probability values for the discrete random variable. The expected value for this type of distribution is calculated by E(X)=μ=ΣxP(x). And the standard deviation is calculated by σ=√(E(X²)-(E(X))²).
a) Expected value for the distributions A and B is calculated as follows,
The expected value for distribution A,
[tex]\begin{aligned}E(X)&=\sum x P(x)\\&= (0\times0.50)+(1\times0.20)+(2\times0.15)+(3\times0.10)+(4\times0.05)\\&=1\end{aligned}[/tex]
The expected value for distribution B,
[tex]\begin{aligned}E(X)&=\sum x P(x)\\&= (0\times0.05)+(1\times0.10)+(2\times0.15)+(3\times0.20)+(4\times0.50)\\&=3\end{aligned}[/tex]
b) The standard deviation for the distributions A and B is calculated as follows,
First, find E(X²) for distribution A and B to substitute in the standard deviation formula.
The E(X²) for distribution A is,
[tex]\begin{aligned}E(X^2)&=\sum x^2P(x)\\&=(0^2\times0.50)+(1^2\times0.20)+(2^2\times0.15)+(3^2\times0.10)+(4^2\times0.05)\\&=2.5\end{aligned}[/tex]
The E(X²) for distribution B is,
[tex]\begin{aligned}E(X^2)&=\sum x^2P(x)\\&=(0^2\times0.05)+(1^2\times0.10)+(2^2\times0.15)+(3^2\times0.20)+(4^2\times0.50)\\&=10.5\end{aligned}[/tex]
Then, the standard deviation for distribution A is,
[tex]\begin{aligned}\sigma_A&=\sqrt{2.5-1^2}\\&=1.225\end{aligned}[/tex]
The standard deviation for distribution B is,
[tex]\begin{aligned}\sigma_B&=\sqrt{10.5-3^2}\\&=1.225\end{aligned}[/tex]
Distribution A and B have the same standard deviation.
c) The standard deviation values are the same for both distributions. But the expected value of distribution A is lesser than the expected value of distribution B. So distribution B looks better than distribution A.
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Select the correct answer from each drop-down menu. Consider the following polynomials equations. A = 3 x 2 ( x − 1 ) B = − 3 x 3 + 4 x 2 − 2 x + 1 Perform each operation and determine if the result is a polynomial. Is the result of A + B a polynomial? Is the result of A - B a polynomial? Is the result of A · B a polynomial?
Carrying out the operations on the polynomials shows that
A + B - polynomial
A - B - polynomial
A * B - polynomial
How to determine the result of the operationsThe given polynomials are
A = 3x²( x − 1 )
B = -3x³ + 4x² − 2x + 1
A + B
= 3x²( x − 1 ) + (-3x³ + 4x² − 2x + 1)
= 3x³ - 3x² - 3x³ + 4x² − 2x + 1
= x² − 2x + 1
This is a polynomial
A - B
= 3x²( x − 1 ) - (-3x³ + 4x² − 2x + 1)
= 3x³ - 3x² + 3x³ - 4x² + 2x - 1
= 6x³ - 7x² + 2x - 1
This is a polynomial
A * B
= 3x²( x − 1 ) * (-3x³ + 4x² − 2x + 1)
= (3x³ - 3x²) * (-3x³ + 4x² − 2x + 1)
= -9x^6 + 12x^5 - 6x⁴ + 3x³ + 9x^5 - 12x⁴ + 6x³- 3x²
= -9x^6 + 21x^5 - 18x⁴ + 9x³- 3x²
This is a polynomial
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