A doctor at a local hospital is interested in estimating the birth weight of infants. How large a sample must she select if she desires to be 90% confident that her estimate is within 4 ounces of the true mean
Answers
Answer:
The minimum sample size needed is \(n = (\frac{1.96\sqrt{\sigma}}{4})^2\). If n is a decimal number, it is rounded up to the next integer. \(\sigma\) is the standard deviation of the population.
Step-by-step explanation:
We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:
\(\alpha = \frac{1 - 0.9}{2} = 0.05\)
Now, we have to find z in the Z-table as such z has a p-value of \(1 - \alpha\).
That is z with a pvalue of \(1 - 0.05 = 0.95\), so Z = 1.645.
Now, find the margin of error M as such
\(M = z\frac{\sigma}{\sqrt{n}}\)
In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.
How large a sample must she select if she desires to be 90% confident that her estimate is within 4 ounces of the true mean?
A sample of n is needed, and n is found when M = 4. So
\(M = z\frac{\sigma}{\sqrt{n}}\)
\(4 = 1.96\frac{\sigma}{\sqrt{n}}\)
\(4\sqrt{n} = 1.96\sqrt{\sigma}\)
\(\sqrt{n} = \frac{1.96\sqrt{\sigma}}{4}\)
\((\sqrt{n})^2 = (\frac{1.96\sqrt{\sigma}}{4})^2\)
\(n = (\frac{1.96\sqrt{\sigma}}{4})^2\)
The minimum sample size needed is \(n = (\frac{1.96\sqrt{\sigma}}{4})^2\). If n is a decimal number, it is rounded up to the next integer. \(\sigma\) is the standard deviation of the population.
Related Questions
50 Points!!!
(a) How would you characterize the relationship between the hours spent on homework and the test scores? Explain.
(b) Paul uses the function y = 8x + 40 to model the situation. What score does the model predict for 3 h of homework?
(c) What does the number 40 in Part (b) mean in the context of the situation?
Answers
Step-by-step explanation:
(a) How would you characterize the relationship between the hours spent on homework and the test scores? Explain
For this case what we see is that we have a scatter diagram, which we can model using a linear trend defining the following variables:
x: number of hours studied.
y: test scores.
The linear relationship would be of the form:
y = mx + b
(b) Paul uses the function y = 8x + 40 to model the situation. What score does the model predict for 3 h of homework?
y = 8x + 40
For three hours of study we have that the note would be approximate:
y = 8 * (3) + 40
y = 64
(c) What does the number 40 in Part (b) mean in the context of the situation?
The number 40 means that if you do not devote any study time, then you expect the test score to be 40.
Drivers who are members of the teamsters Union earn an average of $17.15 per hour (U.S. News & World Report). Assume that available data indicate wages are normally distributed with a standard deviation of $2.25. 1) What is the probability that wages are between $15.00 and $20.00 per hours?
Answers
Answer:
\(P(15<X<20)=P(\frac{15-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{20-\mu}{\sigma})=P(\frac{15-17.15}{2.25}<Z<\frac{20-17.15}{2.25})=P(-0.96<z<1.27)\)
And we can find the probability with this difference and using the normal standard table:
\(P(-0.96<z<1.27)=P(z<1.27)-P(z<-0.96)= 0.898-0.169 = 0.729\)
Step-by-step explanation:
Let X the random variable that represent the wages, and for this case we know the distribution for X is given by:
\(X \sim N(17.15,2.25)\)
Where \(\mu=17.15\) and \(\sigma=2.25\)
We want to find this probability:
\(P(15<X<20)\)
And we can use the z score formula given by:
\(z=\frac{x-\mu}{\sigma}\)
Using this formula we have:
\(P(15<X<20)=P(\frac{15-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{20-\mu}{\sigma})=P(\frac{15-17.15}{2.25}<Z<\frac{20-17.15}{2.25})=P(-0.96<z<1.27)\)
And we can find the probability with this difference and using the normal standard table:
\(P(-0.96<z<1.27)=P(z<1.27)-P(z<-0.96)= 0.898-0.169 = 0.729\)
what is 3 x 5 what does it equal
Answers
Answer:
3 x 5= 15
Step-by-step explanation:
If you count by 5's like 5, 10, 15, 20
And if you count by 3's: 3, 6, 9, 12, 15
then find the least common multiple and it is 15
Please mark me as the Branlyest ;) Thanks
Answer:
3 x 5 = 15
Step-by-step explanation:
3 + 3 + 3 + 3 + 3 = 15
I hope this helps!
Just need help with this question..
Answers
Graph appears to intersect the X axis in between 20 and 22 and algebraically the estimate of zero is 21.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Given a linear function which represents the profit of Bethany, y after x hours of dog walking.
(a) From the graph, we have to estimate the zero.
The graph seems to intersect the X axis in between 20 and 22, approximately 21.
(b) To solve this algebraically, we have the profit function,
y = 23x - 480
When y = 0,
23x - 480 = 0
23x = 480
x = 20.87 ≈ 21
Hence the graphical method gives the same estimate as the algebraic method.
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X (B+7)=9 solve for x &Justification
Answers
Answer:
\(x= \frac{9}{B+7}\)
Step-by-step explanation:
Let us isolate x on the left:
\(x= \frac{9}{B+7}\)
I simply divided B+7 on both sides.
I hope this helps! :)
The value for the variable x is 9/ ( B+ 7).
What is Eqaution?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
x(B+7)=9
Now, solving for the variable 'x'
x= 9/ ( B+ 7)
Hence, the value for the variable x is 9/ ( B+ 7).
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What is the solution of the inequality −3x−3>12 ?
Answers
Answer:
\(x < -5\)
Step-by-step explanation:
-3x-3>12
Divide by -3, since you are dividing by a negative, flip the equality sign:
x+1<-4
Subtract 1 from both sides:
x<-5
Hello,
I hope you and your family are doing well!
To solve the inequality −3x−3>12, you can start by moving everything to one side of the inequality by adding 3 to both sides. This gives you −3x>15.
Next, you can divide both sides of the inequality by -3 to get x<-5.
Finally, you can simplify the inequality to its final form by flipping the direction of the inequality symbol, since you divided it by a negative number. This gives you the final solution: x>-5.
So, the solution to the inequality −3x−3>12 is x>-5. This means that any value of x that is greater than -5 will satisfy the inequality.
The answer is: x > -5
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Happy Holidays!
The value of a is the value of 3x2 - 4x - 3 when x = -2. Find the value of 3a - 3.
Answers
Step-by-step explanation:
put the value of x in equation and you get the answer
then put value of a on 3a-3
Please hurry class ends in 20 minutes
Answers
Answer:
33 inches
Step-by-step explanation:
Use triangle calculator online
Solve for x 15+5x=20x
Answers
Answer:
Step-by-step explanation:
15+5x=20x
-5x -5x => Subtract 5x from each side
You get
15 = 15x
Divide both sides by 15
1=x
Find the mean median range and interquartile range of the following data set 11,13,17,20,22,25,27,31,31,33
Answers
Answer:
Mean: 23
Median: 23.5
Range: 22
Step-by-step explanation:
How to find the mean: Add all the numbers then divide by the amount of numbers.
How to find the median: Find the middle of all the numbers, there are two middle numbers here so you have to add those two middle numbers and then divide by two to get your answer.
How to find range: Take your highest number and subtract by your lowest
Find the vertex of the quadratic function.
ƒ(x) = 2(x−1)² +3
a. (1,3)
b. (2, -1)
c. (-1,3)
d. (2,3)
Answers
hi,
the function is given with it's canonic form.
canonic form is : f(x) = a ( x-α)² + β
α and β are the value of the coordonnates of the vertex.
so here we have : ƒ(x) = 2(x−1)² +3
with α = 1 and β = 3
so vertex is V (1;3)
So yes, answer is A.
need help on this question asap!
Answers
Answer:
≈ +1
Step-by-step explanation:
Firstly, the r value, or the correlation coefficient, would be positive because the correlation is positive. The set of points are moving from bottom to top.
It would be close if not exactly to 1 because the closer the set of points are all clustered closely around or on one singe line, the closer it is to 1. In this case, all points seem to be on one single line, suggesting that it has a perfect correlation of 1.
Please help asap!!! :(
Answers
Answer:
Our maximum is 19 when x=3 and y=7 and our minimum is -21 when x=3 and y = -3
Step-by-step explanation:
First, we can graph these inequalities out. As you can see in the picture, the three vertices where the inequalities all connect form a triangle. We can check each of these vertices to find our minimum and maximum.
First, we have (3,7). 4y-3x = 4(7)-3(3)=28-9=19
Next, for (3, -3), we have 4y-3x = 4(-3)-3(3) = -12-9=-21
Finally, for (0.5, 2), we have 4y-3x=4(2)-3(0.5)=8-1.5 = 6.5
Our maximum is 19 when x=3 and y=7 and our minimum is -21 when x=3 and y = -3
3^x = 9x. What is the value of x?
Answers
x = 3
\(3^{3} =\) 3 x 3 x 3 = 27
9x = 9 x 3 = 27
Workers in an office of 90 staff were asked their favourite type of take-away.
The results are summarised in the table.
Take-away Frequency Angle
Pizza 6 a
Curry 8 b
Fish & chips 21 c
Kebab 5 d
Other 50 e
What fraction of a person is one degree?
Give your answer in its simplest form.
Answers
The fraction of person that represents a degree is 1/4
What is Π chart ?A Π chart is a type of representation used in showing data representing the parts sometimes in degrees.
Π charts are made in circle and use the features of circle
Considering the problem at hand, the total number of workers in the office is 90
The total angle of a circle is 360
if 90 person is equivalent to 360 then one person would be
1 person = 360 / 90
1 person = 4 degrees
therefore 1 degree will be 1/4 person
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Question 1 of 10
What is the approximate distance between the points (-3,-4) and (-8, 1) on a
coordinate grid?
O A. 11.40 units
OB. 12.08 units
O C. 7.07 units
D. 3.16 units
Answers
Answer:
Step-by-step explanation:
Answer:
the approximate distance between the points is
√25+25 = 5√2
=7.07
Step-by-step explanation:
What is the meaning of "\( \varphi (x,y)\) be \( y\wedge \phi (x)\) "?
![What is the meaning of "[tex] \varphi (x,y)[/tex] be [tex] y\wedge \phi (x)[/tex] "?](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/IEnaK9Mnw3ftGn7VoWymvKjzqCukNTp6.png)
Answers
The given passage provides a proof that the Separation Axioms follow from the Replacement Schema.
The proof involves introducing a set F and showing that {a: e X : O(x)} is equal to F (X) for every X. Therefore, the conclusion is that the Separation Axioms can be derived from the Replacement Schema.In the given passage, the author presents a proof that demonstrates a relationship between the Separation Axioms and the Replacement Schema.
The proof involves the introduction of a set F and establishes that the set {a: e X : O(x)} is equivalent to F (X) for any given set X. This implies that the conditions of the Separation Axioms can be satisfied by applying the Replacement Schema. Essentially, the author is showing that the Replacement Schema can be used to derive or prove the Separation Axioms. By providing this proof, the passage establishes a connection between these two concepts in set theory.
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Mrs. bell has a 256 ounce bag of potting soil what is the greatest number of 6 ounce pots she can completely fill with soil
Answers
256 divided by 6 = 42
Hope this helps!!
A farmer saw some chickens and pigs in a field. He counted 53 heads and 138 legs. Determine exactly how many chickens and pigs he saw.
Answers
The number of chickens and pigs the farmer saw on the field are 37 and 16 respectively.
How many chickens and pigs he saw?Let
Number of chickens = x
Number of pigs = y
x + y = 53
2x + 4y = 138
From (1)
x = 53 - y
Substitute x = 53 - y into (2)
2x + 4y = 138
2(53 - y) + 4y = 138
106 - 2y + 4y = 138
- 2y + 4y = 138 - 106
2y = 32
divide both sides by 2
y = 32/2
y = 16
Substitute y = 16 into
x + y = 53
x + 16 = 53
x = 53 - 16
x = 37
Therefore, there are 37 chickens and 16 pigs respectively.
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A teacher gave a reading test to a class of 5th grade students and computed the mean, median, and mode for the test scores. Which of the following statements cannot be an accurate description of the scores?
a. The majority of the students had scores above the mean
b. The majority of the students had scores above the median
c. The majority of the students had scores above the mode
d. All of the other options are false statements
PLEASE EXPLAIN
Answers
In a case whereby teacher gave a reading test to a class of 5th grade students and computed the mean, median, and mode for the test scores. the statements that cannot be an accurate description of the scores is b. The majority of the students had scores above the median.
What is the justification for this?A data set's mean is its average. The most frequent value in a data set is called the mode. The centre of the group of numbers is known as the median, which implies that the since there could majority of the students had scores above the mode, but ion the case of median, since it is value in the middle of a data set then majority of the the students can not scores above the median.
The midway number in a set of data is known as the median. The data should first be arranged and ranked from smallest to greatest. Divide the total number of observations by two to get the midway value. The value in that location is the median if there are an odd number of observations; otherwise, round the number up.
Therefore, option B is correct.
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Which equation represents the inverse of y=(x+5)^2, for x>0?
Answers
Answer:
b
Step-by-step explanation:
The lines below are parallel. If the slope of the green line is -3, what is the slope of the red line?
Answers
Answer:
The lines would be equal, meaning the slope of the red line is also -3.
Step-by-step explanation:
SIMPLE:
Parallel lines have the same slope.
I have attached a picture of the question but have typed out the option, i know a little bit about the function and what it would look like but im confuzed on what the plane y=?z=sin(xy)Give reasons for your choices. This function is [zero / linear / parabolic / period] in both x and y, and the function is [the same / not the same]when x is interchanged with y, so its graph is [ symmetric / not symmetric] about the plane y =[ ] . In addition, the function is [zero / linear / parabolic / periodic ] along the x- and y-axes. These conditions are satisfied only by [A / B / C / D / E / F ] and [ I / II / III / IV / V / VI ].
Answers
The function is periodic in both x and y, and the function is the same when x is interchanged with y, so its graph is symmetric about the plane y = 0. In addition, the function is periodic along the x- and y-axes. These conditions are satisfied only by C and IV.
A: The function plane does not have a zero or linear behavior, so this option is not correct.
B: The function does not have a linear behavior, so this option is not correct.
C: The function is periodic in both x and y, so this option is correct.
D: The function does not have a parabolic behavior, so this option is not correct.
E: The function does not have a periodic behavior, so this option is not correct.
F: The function does not have a linear behavior, so this option is not correct.
I: The function is the same when x is interchanged with y, so this option is correct.
II: The function is not symmetric about the plane y = 1, so this option is not correct.
III: The function is not symmetric about the plane y = 2, so this option is not correct.
IV: The function is symmetric about the plane y = 0, so this option is correct.
V: The function is periodic along the x- and y-axes, so this option is correct.
VI: The function is not linear along the x- and y-axes, so this option is not correct.
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write down the first 5 multiples of 3
Answers
Answer:
3, 6, 9, 12, 15
Step-by-step explanation:
Helping in Jesus' name.
Brainliest for correct answer
Answers
And triangles B has the area of 20cm
From a plate of 18 apple slices, Nancy ate 3. Then Meg came along and ate 4 slices. Jim then ate 3 slices. Bruce took 6 slices for himself and a friend. in simplest form, what what fraction of the apple slices are still on the plate?
Answers
thanks for the points heres the answer 2
18
Picture included!
Find the unknowns in the graph below:
Answers
All the values of x, y and z are,
z = 12.99
y = 7.01
x = 28.3 degree
We have to given that;
In a triangle,
Two angles are, 61.7 degree and 90 degree
And, One side is, 14.76.
Now, We can formulate;
sin 61.7° = Perpendicular / Hypotenuse
sin 61.7° = z / 14.76
0.88 = z / 14.76
z = 0.88 x 14.76
z = 12.99
And, By Pythagoras theorem we get;
14.76² = z² + y²
14.76² = 12.99² + y²
217.85 = 168.74 + y²
y² = 217.85 - 168.74
y² = 49.1
y = 7.01
And, By sum of all the angles in triangle, we get;
x + 61.7 + 90 = 180
x + 151.7 = 180
x = 180 - 151.7
x = 28.3 degree
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((-6) + 7 - 3) x 2 divided by 4. Order of operations? I think the answer is -1.
Answers
Answer:
-1
Step-by-step explanation:
The order of operation (PEMDAS) states that:
P - ParenthesisE - ExponentsM - MultiplicationD - DivisionA - AdditionS - SubtractionGiven expression:
[{(-6) + 7 - 3} x 2] ÷ 4We can see that "-6" is the integer that is inside the parenthesis "( )". Therefore, we can open the parenthesis "( )".
⇒ [{-6 + 7 - 3} x 2] ÷ 4Simplify the expression inside the curvy brackets "{ }" using PEMDAS.
⇒ [{1 - 3} x 2] ÷ 4 [PEMDAS]⇒ [{-2} x 2] ÷ 4 [PEMDAS]Now we can open the curvy brackets "{ }".
⇒ [-2 x 2] ÷ 4Simplify the expression inside the long brackets "[ ]" using PEMDAS.
⇒ [-4] ÷ 4Finally, open the long brackets "[ ]" and simplify the expression obtained.
⇒ -4 ÷ 4 ⇒ -1In 1990, there were 4,500 deaths due to lung diseases in miners aged 20 to 64 years. The expected number of deaths in this occupational group, based on age-specific deaths rates from lung diseases in all males aged 20 to 64 years, was 1,800 during 1990. What is the standardized mortality ratio (SMR) for lung disease in miners
Answers
Answer:
2.5
Step-by-step explanation:
We have that the standardized mortality ratio (SMR) is the relationship between the number of deaths observed in a year, that is, those that occurred and the number of expected deaths, that is, those that were predicted.
SMR = observed / expected
therefore if we replace we have:
SMR = 4500/1800
SMR = 2.5
Which means that the standardized mortality ratio (SMR) is 2.5
HELLPPPP Im DYING NOT really tho
Answers
Answer:
More pencils than pens
Step-by-step explanation: