Answer:
The mean and standard deviation of the number of questions that each student gets correct are 4 and 1.789 respectively.
Step-by-step explanation:
Let the random variable X be defined as the number of correct answers marked by a student.
It is provided that each question has 5 possible choices, 1 of the which is correct.
Then the probability of marking thee correct option is:
[tex]P(X)=\frac{1}{5}=0.20[/tex]
There are a total of n = 20 questions to be answered.
As the students does not the answer to any question, they would be guessing for each question. This implies that for a random question, all the five options has the equal probability of being correct and each of the five options can be correct independently from the other.
All these information above indicates that the random variable X follows a Binomial distribution with parameters n = 20 and p = 0.20.
The mean and standard deviation of a Binomial distribution are:
[tex]\mu=np\\\\\sigma=\sqrt{np(1-p)}[/tex]
Compute the mean and standard deviation of the random variable X as follows:
[tex]\mu=np=20\times 0.20=4\\\\\sigma=\sqrt{np(1-p)}=\sqrt{20\times 0.20\times(1-0.20)}=1.789[/tex]
Thus, the mean and standard deviation of the number of questions that each student gets correct are 4 and 1.789 respectively.
According to the question,
The probability of making 3 correct options will be:
→ [tex]P(X) = \frac{1}{5}[/tex]
[tex]= 0.20[/tex]
Total number of questions,
n = 20As we know,
The mean will be:
→ [tex]\mu = np[/tex]
By substituting the values, we get
[tex]= 20\times 0.20[/tex]
[tex]= 4[/tex]
and,
The standard deviation will be:
→ [tex]\sigma = \sqrt{np(1-p)}[/tex]
[tex]= \sqrt{20\times 0.20\times (1-0.20)}[/tex]
[tex]= 1.789[/tex]
Thus the responses above are correct.
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Automobile racing, high-performance driving schools, and driver education programs run by automobile clubs continue to grow in popularity. All these activities require the participant to wear a helmet that is certified by the Snell Memorial Foundation, a not-for-profit organization dedicated to research, education, testing, and development of helmet safety standards. Snell "SA" (Sports Application)-rated professional helmets are designed for auto racing and provide extreme impact resistance and high fire protection. One of the key factors in selecting a helmet is weight, since lower weight helmets tend to place less stress on the neck. The following data show the weight and price for 18 SA helmets.
W p
64 252
64 283
64 190
64 197
58 291
47 702
49 907
59 341
66 202
58 305
58 477
52 477
63 379
62 377
54 563
63 255
63 286
a. Develop a scatter diagram with weight as the independent variable.
b. Does there appear to be any relationship between these two variables?
There appears to be a - Select your answer -negativepositiveItem 2 linear relationship between the two variables. The heavier helmets tend to be less expensive.
c. Develop the estimated regression equation that could be used to predict the price given the weight.
The regression equation is (to 1 decimal and enter negative values as negative numbers). If your answer is zero enter "0".
Answer:
Step-by-step explanation:
Hello!
Given the variables
X₁: Weight of a safety helmet for racers
X₂: Price of a safety helmet for racers
Note, there is n= 17 observed values for each variable so for all calculations I'll use this number and disregard the 18 mentioned in the text.
a) Scatterplot in attachment.
b) If you look at the diagram it seems that there is a negative linear regression between the price and the weight of the helmets, meaning, the higher the helmet weights, the less it costs.
c) The estimated regression equation is ^Yi= a + bXi
n= 17; ∑Y= 6466; ∑Y²= 3063392; ∑X= 1008; ∑X²= 60294; ∑XY= 367536
Y[bar]= 380.35; X[bar]= 59.29
[tex]b= \frac{sumXY-\frac{(sumX)(sumY)}{n} }{sumX^2-\frac{(sumX)^2}{n} } = \frac{367536-\frac{1008*6466}{17} }{60294-\frac{(1008)^2}{17} } = -30.18[/tex]
[tex]a= Y[bar]- bX[bar]= 380.35-(-30.18)*59.29= 2169.77[/tex]
The estimated regression equation for the price of the helmets as a function of their weight is:
^Yi= 2169.77 -30.18Xi
I hope it helps!
A large company that produces a "fat-burner" pill claims an average loss of 20 pounds in the first month. A consumer advocacy group believes that this claim is actually just "hype" intended to sell more of the compound. The advocacy group would like to obtain statistical evidence about this issue and takes a random sample of 100 consumers who responded that they had purchased the pill but didn't know what the survey was about. They find that these 100 people lost an average of 18 pounds with a standard deviation of 7.5 pounds. What are the null and alternative hypothesis in this situation
The null and alternative hypothesis for the tests are:
H0: μ = 20
Ha: μ < 20
Given data:
In this situation, the null and alternative hypotheses can be formulated as follows:
Null Hypothesis (H0): The average weight loss of consumers who take the "fat-burner" pill is equal to 20 pounds.
Alternative Hypothesis (Ha): The average weight loss of consumers who take the "fat-burner" pill is less than 20 pounds.
In symbolic notation:
H0: μ = 20
Ha: μ < 20
where μ represents the population mean weight loss of consumers who take the "fat-burner" pill.
The null hypothesis assumes that the claim made by the company is accurate and that the average weight loss is indeed 20 pounds. The alternative hypothesis challenges this claim and suggests that the actual average weight loss may be less than 20 pounds, implying that the "hype" around the pill's effectiveness might be exaggerated.
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-7 2/3 +(-5 I/2) + 8 3/4=
Answer:-53/12
Step-by-step explanation:
-7 2/3+(-5 1/2)+8 3/4
-7 2/3-5 1/2+8 3/4
-23/3 - 11/2 + 35/4
(4x-23 - 6x11 + 3x35)/12
(-92-66+105)/12=-53/12
If you flipped a fair coin 18 times about how many times would you expect heads to appear?
Answer:
9 times
Step-by-step explanation:
hope this helps
Answer:
9
Step-by-step explanation:
Mathematically, 9, although reality wise, you could flip the coin and get heads every time, or the opposite.
I think you mean mathematically though, so yes, it would be 9.
What is the GCF of 45 and 72?
Answer:
The common factors of 45 and 72 are 9, 3, 1
Step-by-step explanation:
Answer:
The GCF of these two numbers is nine.
Step-by-step explanation:
They share three common factors: 1, 3 and 9. The greatest out of all of those is 9. Hope this helps!
Which set of numbers is included in the solution set of the compound inequality? {–7, 5, 18, 24, 32} {–9, 7, 15, 22, 26} {16, 17, 22, 23, 24} {18, 19, 20, 21, 22}
Answer:
{-7,5,18,24,32}
Step-by-step explanation:
Let's verify all cases to determine the solution to the problem.
CASE A) we have
-9,7,15,22,26
The number 22 is not included in the solution set of the compound inequality.
CASE B) we have
-7,5,18,24,32
The number 22 is not included in the solution set of the compound inequality.
CASE C) we have
16,17,22,23,24
The number 22 is not included in the solution set of the compound inequality.
CASE D) we have
18,19,20,21,22
The numbers 19,20,21,22 are not included in the solution set of the compound inequality.
The answer to your question would be A
HELP ME ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing.
Answer:
D. Vertx: (3,-16); Intercepts: x = -1, 7
Step-by-step explanation:
I graphed the equation on the graph below.
Graph-3x2 + 12y2 = 84. What are the domain and range?
Domain (infinity,infinity)
Range (infinity,[tex]\sqrt{7}[/tex])
which is equivalent to sin^-1 ( sqrt 3/2 )? Give your answer
Give your answer in radians.
Answer: pi/3
Step-by-step explanation:
correct on edge 2020
The equivalent value of trigonometric relation sin⁻¹ ( √3/2 ) = π/3
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the trigonometric relation be represented as A
Now , the value of A is
sin⁻¹ ( √3/2 ) = θ
Now , the value of θ is calculated by
In a triangle , sin θ = opposite / hypotenuse
So , sin θ = √3/2
The value of θ = 60°
So , the measure of 60° in radians is θ = π/3
Hence , the value of θ from the trigonometric relation is π/3
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To study the effects of an advertising campaign at a supply chain, several stores are randomly selected with the following observed before‐ and after‐advertising monthly sales revenues: Store number 1 2 3 4 5 Old sales revenue (mil. $) 6.5 4.8 7.9 6.2 7.1 New sales revenue (mil. $) 7.5 6.3 7.1 7.8 8.9 Let μ₁ and μ₂ be the means of old and new sales revenues, both in millions of dollars per month. (a)[7] At α = 0.05, test H₀: μ₂ ≤ μ₁ versus H₁: μ₂ > μ₁. Sketch the test. Interpret your result. (b)[3] Sketch and find the p‐value of the test. Would you reject H₀ if α = 0.01? Hint: Use 5 decimals. Refer to some Excel lookups: αv 0.990 0.990 0.950 0.950
Answer:
Check the explanation
Step-by-step explanation:
Part a
H0: µ2≤µ1 versus H1: µ2>µ1
(Upper tailed test)
WE will consider differences as (New – Old).
From given data, we have
Dbar = 0.70
SD = 0.70
n = 5
Degrees of freedom = df = n – 1 = 5 – 1 = 4
Test statistic = t = (Dbar - µd) /[SD/sqrt(n)]
t = (0.70 – 0)/[0.70/sqrt(5)]
t = 0.70/ 0.3130
t = 2.2361
Critical value = 2.1318
(by using t-table)
P-value = 0.0445
(by using t-table)
P-value < α = 0.05
So, we reject the null hypothesis
There is sufficient evidence to conclude that the average monthly sales revenue increases after the advertising.
Kindly check the first attached image for the graphical table.
Part b
P-value = 0.0445
α = 0.01
P-value > α = 0.01
So, we do not reject the null hypothesis
There is insufficient evidence to conclude that the average monthly sales revenue increases after the advertising.
Kindly check the second attached image for the graphical table.
6. A golfer is standing at the tee,
looking up to the green on a hill. If the
tee is 36 yards lower than the green
and the angle of elevation from the tee
to the hole is 12º, find the distance from
the tee to the hole.
Answer:
173.15 yards is the distance from tee to hole.
Step-by-step explanation:
Please refer to the image attached.
Let A is the position of tee and where the golfer is standing.
C is the position of hole.
CB is the vertical distance between greens and tee.
Angle of elevation, [tex]\angle BAC = 12^\circ[/tex]
To find: side AC.
Using trigonometric functions, we know that value of sine is:
[tex]sin\theta = \dfrac{\text{Perpendicular}}{\text{Hypotenuse}}[/tex]
Here [tex]\theta = \angle BAC = 12^\circ[/tex]
Perpendicular is side CB.
Hypotenuse is side AC.
[tex]sin12^\circ = \dfrac{\text{CB}}{\text{AC}}\\\Rightarrow \text{CB} = \dfrac{36}{sin12^\circ}\\\Rightarrow \text{CB} = 173.15\ yards[/tex]
Hence, 173.15 yards is the distance from tee to hole.
Finding the work done in stretching or compressing a spring.
Hooke's Law for Springs.
According to Hooke's law, the force required to compress or stretch a spring from an equilibrium position is given by F(x)=kx, for some constant k. The value of k (measured in force units per unit length) depends on the physical characteristics of the spring. The constant k is called the spring constant and is always positive.
In this problem we assume that the force applied doesn't distort the metal in the spring.
A 2 m spring requires 11 J to stretch to 2.4 m. Find the force function, F(x), for the spring described.
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached images below to see the step by step explanation to the question above.
A coin is tossed and a fourth section spinner is spun once a tree diagram shows the possible outcomes for the two events what is the probability of flipping tails on a coin and spinning a two on the spinner
Answer:
2/6 or 1/3 I think
Step-by-step explanation:
you have a 1 out of 2 chances to land tails and 1 out of 4 chance to role a 2 on the spinner. so in total there is 6 chances for rolling and flipping the coin. and there is only 1 chance for both in the odds.
therefore I believe that its is 1/3 or 2/6. I do not know if I am right exactly but that is my thought process.
What do you have to know before you can round a number
Answer:
if it ends in 5 then you round up but if it's less than 5 you round down
Step-by-step explanation:
You first have to locate the digit in the rounding place and this digit can be in the ones place, tens place,
hundreds place, thousands place, and so on.
After you locate the digit, look at the
digit to the right of the rounding place.
If the digit to the right of the rounding place is less than 5, we round down and if the digit is greater than or equal to 5, we round up.
The length of time it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of 7 minutes and a standard deviation of 3 minutes. Based upon the above information and numerically justified, would you be surprised if it took less than one minute to find a parking space?
a. Yes
b. No
c. Unable to determine.
Answer:
a. Yes
Step-by-step explanation:
Problems of normally distributed samples can be solved using 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.
If the absolute value of the z-score is 2 or larger, X is considered a surprising outcome.
In this question:
[tex]\mu = 7, \sigma = 3[/tex]
Would you be surprised if it took less than one minute to find a parking space?
We have to find the z-score when X = 1. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1 - 7}{3}[/tex]
[tex]Z = -2[/tex]
Since Z = -2, the correct answer is:
a. Yes
I need the answer ASAP giving 20 points!
Answer: a makes the most sense
Step-by-step explanation:
Fernando factored 45y^6 as (9y^3)(5y^3).
Salma factored 45y as (3y)(15y^5).
Which of them factored 45y^6 correctly?
Answer:
They both factored it correctly
Step-by-step explanation:
To find the one that was factored correctly, we expand the two of them and compare with [tex]45y^6[/tex].
Fernando
[tex](9y^3)(5y^3)[/tex]
= [tex]9 * 5 * y^3 * y^3[/tex]
= [tex]45y^6[/tex]
Salma
[tex](3y)(15y^5)[/tex]
= [tex]3 * 15 * y * y^5[/tex]
= [tex]45y^6[/tex]
As we can see, they both factored it correctly.
Answer:
both are correct in their factoring
Step-by-step explanation:
A regular deck of cards has 52 cards with 4 aces. Carl asked a friend to pick a card from the deck three times, replacing the card each time. His friend picked three aces. Which expression will give the probability of that event?
(StartFraction 4 over 52 EndFraction) (StartFraction 4 over 52 EndFraction) (StartFraction 4 over 52 EndFraction)
(StartFraction 1 over 52 EndFraction) (StartFraction 1 over 51 EndFraction) (StartFraction 1 over 50 EndFraction)
(StartFraction 4 over 52 EndFraction) (StartFraction 4 over 51 EndFraction) (StartFraction 4 over 50 EndFraction)
(StartFraction 4 over 52 EndFraction) (StartFraction 3 over 51 EndFraction) (StartFraction 2 over 50 EndFraction)
Answer:
The answer is A
Step-by-step explanation:
Edg : )
Answer:
A
Step-by-step explanation:
Need done ASAP please
Step-by-step explanation:
a. 81 ÷ 9 = 9
b. 40 ÷ 5 = 8
c. 21 ÷ 3 = 7
d. 54 ÷ 6 = 9
e. 42 ÷ 7 = 6
f. 63 ÷ 9 = 7
g. 36 ÷ 4 = 4
h. 45 ÷ 9 = 5
i. 39 ÷ 3 = 12
j. 24 ÷ 6 = 4
apply the distributive property to factor out the gcf of 35+14
Answer:
7(5 +2)
Step-by-step explanation:
From our knowledge of times tables, we know that ...
35 = 5·7
14 = 2·7
so the greatest common factor of 35 and 14 is 7. Factoring that out, we have ...
35 +14 = 7(5 +2)
What steps should be used to find 55% of 300? Check
all that apply.
ger
Answer:
100x3=100 55x3=the answer 55x3=165 students 165 6th graders have a younger sibling.
Step-by-step explanation:
i did the assignment
55 percent of 300 is equal to 165.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100.
Given,
55% of 300
55% can be written as fraction 55/100
= (55/100) × 300
Dividing 300 by 100
= 55 × 3
Multiplying
= 165
Hence, 165 is 55 percent of 300.
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Need help with Math question
Answer:
B; {x|x<-8}
Step-by-step explanation:
*ill give you BRAINLIST * (have to get it right ) Write the equation of the line with the given slope and y-intercept.
slope = 1
y-intercept = - 3/7
Answer:
Y=x-3/4
Step-by-step explanation:
slope intercept form
(slope=x)(1x=x)
....................
Answer:
I would love to help you but all I see is dots
ten tiles numbered 1 through 10 are placed in a bag you randomly chose one tile. without replacing the tile you randomly chose a second tile. Find the probability of choosing a 4 and then an even number?
Answer:
1/10
Step-by-step explanation:
there are 10 tiles and only 1 tile numbered 4 so 1 out of 10 tiles are numbered 4
Of the 250 students at Moreland middle school, 80% ride the bus to school. Monica wants to know the number of students that ride the bus.
Answer:
200; 80% of 250 is 200
Answer:
Step-by-step explanation:
200
What is the meaning of life
Answer:
The answer of life is 42 just look it up
You have a bag of marbles that has 3 blue marbles and 4 red ones. What is the chance that you pick a blue OR a red marble?
Answer:
7/7
Step-by-step explanation:
Add up the amount of the marbles in total and read what color the marble they ask for the chances of. The color of marble should go first then the total of the marbles. (they could ask for more than one color so just add up both the colors given.)
You buy $2,500of saving bonds at 1.7%interest.how many years will it take for your investment to equal $3000?
Answer:
It will take 12 years using simple interest
Step-by-step explanation:
2,500 x 1.7% = 42.5
42.5 x 12 + 510
2500 +510 +3010
A researcher developing scanners to search for hidden weapons at airports has failed to conclude that a new scanner is significantly better than the current scanner. He made his decision based on a test using alpha equals 0.025 . Would he have made the same decision at alpha equals 0.10 question mark How about alpha equals 0.01 question mark Explain.
Answer:
Yes, he would take the same decision.
Step-by-step explanation:
Consequently, because the decision is taken on the test based on the use of alpha equals 0.025, the p-value of the test must have been greater than the given amount of importance that is 0.025 since the test is not applicable to us. So, p > 0.025.
If we know that p > 0.025, that would not mean p > 0.1 as well, because we do not know with the details given he had to make the same decision for 0.1 degree of meaning.
As for the 0.01 significance point, we 're sure p > 0.01 is greater than 0.025, so the test does not matter.
