Answer:
1. 1056.67
2. 29th percentile.
3. 79
4. 77
Step-by-step explanation:
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.
Mean score of 1150, standard deviation of 90
This means that [tex]\mu = 1150, \sigma = 90[/tex]
1. What is the score for someone in the 15th percentile?
This is X when Z has a p-value of 0.15, so X when Z = -1.037.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.037 = \frac{X - 1150}{90}[/tex]
[tex]X - 1150 = -1.037*90[/tex]
[tex]X = 1056.67[/tex]
2. What is the percentile rank of someone with a score of 1100?
This is the p-value of Z when X = 1100. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1100 - 1150}{90}[/tex]
[tex]Z = -0.555[/tex]
[tex]Z = -0.555[/tex] has a p-value of 0.29, so 29th percentile.
3. How many students have scores of 1060 or greater?
The proportion is 1 subtracted by the p-value of Z when X = 1060. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1060 - 1150}{90}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a p-value of 0.1587.
Out of 500:
0.1587*500 = 79
79 is the answer.
4. How many students scored between 1200 and 1250?
The proportion is the p-value of Z when X = 1250 subtracted by the p-value of Z when X = 1200. So
X = 1250
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1250 - 1150}{90}[/tex]
[tex]Z = 1.1[/tex]
[tex]Z = 1.1[/tex] has a p-value of 0.8643.
X = 1200
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1200 - 1150}{90}[/tex]
[tex]Z = 0.555[/tex]
[tex]Z = 0.555[/tex] has a p-value of 0.7106
0.8643 - 0.7106 = 0.1537
Out of 500:
0.1537*500 = 77
77 is the answer.
Which expression is equivalent to 3√x10
Answer:
Hes correct ^
Step-by-step explanation:
A sample of 375 college students were asked whether they prefer chocolate or vanilla ice cream. 210 of those surveyed said that they prefer vanilla ice cream. Calculate the sample proportion of students who prefer vanilla ice cream.
Answer:
The sample proportion of students who prefer vanilla ice cream is 0.56.
Step-by-step explanation:
Sample proportion of students who prefer vanilla ice cream:
Sample of 375 students.
Of those, 210 said they prefer vanilla ice cream.
The proportion is:
[tex]p = \frac{210}{375} = 0.56[/tex]
The sample proportion of students who prefer vanilla ice cream is 0.56.
ifteen accounting majors had an average grade of 90 on a finance exam. Seven marketing majors averaged 85, while ten finance majors averaged 93 on the same exam. What is the weighted mean for the 32 students taking the exam? A. 89.84 B. 89.33 C. 89.48 D. Impossible to determine without more information
Answer:
A. 89.84
Step-by-step explanation:
Weighed mean:
Sum of the multiplications of each value by its weight, divided by the sum of the weights.
Weights:
15 had an average of 90.
7 averaged 85.
10 averaged 93.
What is the weighted mean for the 32 students taking the exam?
[tex]M = \frac{15*90 + 7*85 + 10*93}{15 + 7 + 10} = 89.84[/tex]
Thus the correct answer is given by option A.
I NEED HELP PLEASE!!
Answer:
70
Step-by-step explanation:
70 because as the number of trials increase, the actual ratio of outcomes will converge on the expected ratio.
evaluate 3^2*5^5*3^3*5^3/3^4*3^4
[tex] \frac{{3}^{2} \times {5}^{5} \times {3}^{3} \times {5}^{3} }{ {3}^{4} \times {3}^{4} } \\ = \frac{ {3}^{5} \times {5}^{8} }{ {3}^{8} } \\ = \frac{ {5}^{8} }{ {3}^{3} } \\ = \frac{390625}{27} \\ = 14467.592592......[/tex]
This is the solution.
Which equation shows that the Pythagorean identity is true for 0 = 27? Select
the equation that is in the form sin?(27) + cos2(27) = 1.
A. 02 + (-1)2 = 1
B. 02 + 12 = 1
C. (-1)² + 02 = 1
D. 12 + 02 = 1
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Answer:
B. 0^2 +1^2 = 1
Step-by-step explanation:
For θ = 2π, the trig identity is ...
sin(2π)² +cos(2π)² = 1
0² +1² = 1
What will you get when you multiply the two variables?
Answer:
When variables are the same, multiplying them together compresses them into a single factor (variable). ... When multiplying variables, you multiply the coefficients and variables as usual. If the bases are the same, you can multiply the bases by merely adding their exponents.
Step-by-step explanation:
The equation of a parabola in standard form is
y = mx + b
y = mx2 + b
y = ax2 + bx + c
y = a(x - h)2 +k
Answer: y = ax2 + bx + c
looks like a slightly trick question...
y = ax2 + bx + c is the standard form...
y = a(x - h)2 +k is the graphing form
Step-by-step explanation:
Simplify 4(a + 1) + 5(a + 2).
Answer: [tex]9a+14[/tex]
Step-by-step explanation:
Simplify: [tex]4(a+1)+5(a+2)[/tex]
Step 1. Distribute 4 into a and 1. By distributing you would get 4a and 4.
[tex]4*a=4a. \\4*1=4[/tex]
Step 2. Plug 4a+4 back into the remaining equation, which can be viewed below:
[tex]4a+4+5(a+2)[/tex]
Step 3. Distribute, [tex]5(a+2)[/tex] again. Same principle as what you did previously. You should get 5a and 10.
[tex]5*a=5a.\\5*2=10.[/tex]
Step 4. Plug 5a+10 back into the leftover equation, which is as follows.
[tex]4a+4+5a+10[/tex]
Step 5. Combine like terms. Which is broken down below,
[tex]4a+5a=9a.\\4+10=14.[/tex]
Once you're done combining like terms, you'll get the simplified answer which is: [tex]9a+14[/tex]
Answer:
9a +14
Step-by-step explanation:
4(a + 1) + 5(a + 2)
Distribute
4a+4 +5a+10
Combine like terms
4a+5a +4+10
9a +14
The mean gross annual incomes of certified welders are normally distributed with the mean of $20,000 and a standard deviation of $2,000. The ship building association wishes to find out whether their welders earn more or less than $20,000 annually. The alternate hypothesis is that the mean is not $20,000.
Required:
What is the alternate hypothesis?
Answer:
H1 : μ ≠ 20000
Step-by-step explanation:
Given that :
Population mean salary, μ = 20,000
To test if mean salary is more or less Than population mean salary, μ, this means we are testing if the mean salary is different from 20,000
Hence, the hypothesis :
Null, H0 : The mean salary is 20000
Alternative, H1 : The mean salary is not 20000
Using notation :
H0 : μ = 20000
H1 : μ ≠ 20000
Hence, alternative hypothesis is : H1 : μ ≠ 20000
1.8>4.7+w
Does anyone know what this may be ? Thank you very much .
Answer:
-2.9 > w
Step-by-step explanation:
1.8>4.7+w
Subtract 4.7 from each side
1.8-4.7>4.7-4.7+w
-2.9 > w
Answer:
w = -2.9
Step-by-step explanation:
We are given a weighted coin (with one side heads, one side tails), and we want to estimate the unknown probability pp that it will land heads. We flip the coin 1000 times and it happens to land heads 406 times. Give answers in decimal form, rounded to four decimal places (or more). We estimate the chance this coin will land on heads to
Answer:
0.4060
Step-by-step explanation:
To calculate the sample proportion, phat, we take the ratio of the number of preferred outcome to the total number of trials ;
Phat = number of times coin lands on head (preferred outcome), x / total number of trials (total coin flips), n
x = 406
n = 1000
Phat = x / n = 406/ 1000 = 0.4060
The estimate of the chance that this coin will land on heads is 0.406
Probability is the likelihood or chance that an event will occur.Probability = Expected outcome/Total outcomeIf a coin is flipped 1000 times, the total outcomes will 1000
If it landed on the head 406 times, the expected outcome will be 406.
Pr(the coin lands on the head) = 406/1000
Pr(the coin lands on the head) = 0.406
Hence the estimate of the chance that this coin will land on heads is 0.406
Learn more on probability here: https://brainly.com/question/14192140
What is the area of this triangle?
Enter your answer in the box.
units2
Answer:
8 units^2
Step-by-step explanation:
The area of a tringle is 1/2 bh. The base, LK, measures 4 while the height is also 4(you can get these values by counting the squares). This means the area is:
1/2 * (4)(4) = 1/2 * 16 = 8 units^2
Which polynomial function is best represented by the graph?
ƒ(x) = –x(x – 1)4
ƒ(x) = x2(x + 1)3
ƒ(x) = x2(x – 1)3
ƒ(x) = x(x – 1)4
Answer: ƒ(x) = x2(x – 1)3
A young couple purchases their first new home in 2011 for $95,000. They sell it to move into a bigger home in 2018 for $105,000.
Find the quotient of -196/4
Answer:
this is the answer
Step-by-step explanation:
thank you
Answer:
-196/4 = -49
Step-by-step explanation:
Mental math. If you can't do that then use a calculator. It's faster to type it in on g oogle
There are 45 applicants for two Software
Maker positions.
I
Find "n" if the Standard Error of Mis 4 and the population standard deviation is 16.
Given:
Standard error = 4
Population standard deviation = 16
To find:
The value of n.
Solution:
The formula of standard error is:
[tex]SE=\dfrac{\sigma}{\sqrt{n}}[/tex]
Where, SE is standard error , [tex]\sigma[/tex] is population standard deviation and n is the total number of elements.
Substituting [tex]SE=4,\sigma=16[/tex] in the above formula, we get
[tex]4=\dfrac{16}{\sqrt{n}}[/tex]
[tex]\sqrt{n}=\dfrac{16}{4}[/tex]
[tex]\sqrt{n}=4[/tex]
Taking square on both sides, we get
[tex]n=4^2[/tex]
[tex]n=16[/tex]
Therefore, the value of n is 16.
I need help ASAP please and thank you
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Answer:
C. 4 +√(x+5)
Step-by-step explanation:
The sign between the terms changes to form the conjugate. The radical contents are unchanged.
The conjugate of 4 -√(x+5) is 4 +√(x+5).
_____
Additional comment
The utility of a conjugate is that the product of a number and its conjugate is the difference of two squares. The squares are intended to remove an undesirable feature of the number, its imaginary part or its irrational part, for example. Here, the product of the number and its conjugate would be ...
(a -b)(a +b) = a² -b²
4² -(√(x+5))² = 16 -(x +5) = 11 -x . . . . no longer contains a root
If you multiply the sum of 546 and 1711 by zero, what will be your result?
Answer:
0
Step-by-step explanation:
any numbers multiply by zero always equals to zero
find the value of trigonometric ratio
Answer:
8/17
Step-by-step explanation:
cosC = adjacent/hypotenuse = BC/AC = 8/17
A data set includes data from student evaluations of courses. The summary statistics are n=89, x=3.44, s=0.67. Use a 0.05 significance level to test the claim that the population of student course evaluations has a mean equal to 3.50. Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.
What are the null and alternative hypotheses?
A.
H0: μ=3.50
H1: μ>3.50
B.
H0: μ=3.50
H1: μ<3.50
C.
H0: μ≠3.50
H1: μ=3.50
D.
H0: μ=3.50
H1: μ≠
(I also need the test statistic and p-value) thank you so much in advance :)
We're told that "the claim that the population of student course evaluations has a mean equal to 3.50". So this means μ=3.50 makes up the null H0
The alternative would be H1: μ ≠ 3.50 since it's the opposite of the claim made in the null.
We go with answer choice D to form the null and alternative hypotheses.
The sign ≠ in the alternative hypothesis tell us that we have a two tail test.
---------------------------------------
Let's compute the test statistic
z = (xbar - mu)/(s/sqrt(n))
z = (3.44 - 3.50)/(0.67/sqrt(89))
z = -0.84483413122896
z = -0.84
The test statistic is roughly -0.84
---------------------------------------
Despite not knowing what sigma is (aka the population standard deviation), we can see that n > 30 is the case. So we can use the Z distribution. This is the standard normal distribution. When n > 30, the T distribution is fairly approximately the same as the Z distribution.
Use a calculator or a Z table to determine that
P(Z < -0.84) = 0.2005
which is approximate
Because we're doing a two-tail test, this means we double that result to get 2*0.2005 = 0.401
The p-value is roughly 0.401
-----------------------------------------
Since the p-value is larger than alpha = 0.05, we don't have enough evidence to reject the null. So you can say that we fail to reject the null, or we accept the null.
The conclusion based on that means that μ=3.50 must be true (unless other evidence comes along to disprove this). In other words, the mean evaluation score from students appears to be 3.50
If two bags of popcorn and three drinks cost $14,
and four bags of popcorn and one drink costs
$18, how much does a drink cost?
Answer:
2dollars
Step-by-step explanation:
one bag of popcorn is 4 dollars so 4 bags of popcorn is 16 plus 1 drink which is 2 dollars equal 18.
The cost of each popcorn is $4 and the cost of each drink will be $2.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
If two bags of popcorn and three drinks cost $14, and four bags of popcorn and one drink costs $18.
Let the cost of each popcorn be 'x' and the cost of each drink be 'y'. Then the equations are given as,
2x + 3y = 14 ...1
4x + y = 18 ...2
From equations 1 and 2, then we have
2x + 3(18 - 4x) = 14
2x + 54 - 12x = 14
10x = 40
x = $4
Then the value of the variable 'y' is calculated as,
y = 18 - 4(4)
y = 18 - 16
y = $2
The cost of each popcorn is $4 and the cost of each drink will be $2.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
#SPJ2
Does the graph represent a function and if so, why?
A.Yes, no two ordered pairs on this graph have the same second element.
B.Yes, there is more than one ordered pair on this graph.
C.Yes, no two ordered pairs on this graph have the same first element.
D.No, there is a limited number of ordered pairs on this graph.
Answer:
A. yes
Step-by-step explanation:
Student is 19 years old in the world has a population of 6.7 billion assuming that the population continues to grow in annual rate of 1.1%, predict what the worlds population will be when the student is 52
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Answer:
9.6 billion
Step-by-step explanation:
The population multiplier is 1+1.1% = 1.011 each year. After 52-19 = 33 years, the multiplier will be 1.011^33 ≈ 1.4348.
When the student is 52, the population of the world will be about ...
6.7 billion × 1.4348 ≈ 9.6 billion
what vulnerable does the 4 represents in the number 487.009
Answer:
400 :D
Step-by-step explanation:
What is the value of x?
2
3
6
7
Answer:
i think 3
Step-by-step explanation:
Answer: [A] 2
Step-by-step explanation:
100% on edge 2023
Mr.Peter earned $25 per week how much does he earned in a year
Answer: Approximately $1,300
Step-by-step explanation:
There is around 52 weeks in a normal year.
$25 · 52 = $1300
Answer:
1300
Step-by-step explanation:
There are 52 weeks in a year
52 * 25 = 1300
which fraction has a greater value than 0.4
Answer:
0.4 as a fraction is 2/5, so as long as the fraction is greater than 2/5 then you are good
5/9 || 0.55
Step-by-step explanation:
tìm cực trị của hàm số z(x,y)=x^{3}+y^{3}+3xy-30
Answer:
Hence, MEAN OF FIRST FIVE COMPOSITE NOS IS 7.5
