A nutritionist wants to determine how much time nationally people spend eating and drinking. Suppose for a random sample of 1082 people age 15 or older, the mean amount of time spent eating or drinking per day is 1.53 hours with a standard deviation of 0.71 hour.
a. Determine and interpret a 95% confidence interval for the mean amount of time Americans age 15 or older spend eating and drinking each day
b. The nutritionist is 95% confident that the amount of time spent eating or drinking per day for any individual is between_________and_________hours.
c. There is a 95% probability that the mean amount of time spent eating or drinking per day is between and hours.
d. The nutritionist is 95% confident that the mean amount of time spent eating or drinking per day is between_______and_____________
Answers
Answer:
a) The 95% confidence interval for the mean amount of time Americans age 15 or older spend eating and drinking each day is (1.49, 1.57).
d) The nutritionist is 95% confident that the mean amount of time spent eating or drinking per day for any individual is between 1.49 and 1.57 hours.
(c and b can not be concluded from the confidence interval)
Step-by-step explanation:
We have to calculate a 95% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
The sample mean is M=1.53.
The sample size is N=1082.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
\(s_M=\dfrac{s}{\sqrt{N}}=\dfrac{0.71}{\sqrt{1082}}=\dfrac{0.71}{32.89}=0.022\)
The degrees of freedom for this sample size are:
\(df=n-1=1082-1=1081\)
The t-value for a 95% confidence interval and 1081 degrees of freedom is t=1.962.
The margin of error (MOE) can be calculated as:
\(MOE=t\cdot s_M=1.962 \cdot 0.022=0.042\)
Then, the lower and upper bounds of the confidence interval are:
\(LL=M-t \cdot s_M = 1.53-0.042=1.49\\\\UL=M+t \cdot s_M = 1.53+0.042=1.57\)\(LL=M-t \cdot s_M = 1.53-0.042=1.49\\\\UL=M+t \cdot s_M = 1.53+0.042=1.57\)
The 95% confidence interval for the mean is (1.49, 1.57).
Related Questions
PLEASE FAST
Solve the equation for t.
4(t – 2.9) ≥ 3.6
t ≥ 17.3
t ≥ 11.5
t ≥ 3.8
t ≥ 1.6
Answers
Answer:3.8
Step-by-step explanation:
!!!MULTIPLE CHOICE QUESTIONHow do you apply the scale factor of 1/3 to each of the points of the image?
Answers
When you apply a scale factor to the pointsof an image, you only multiply by the scale factor each coordinate of each point.
Hence, for a scale factor of 1/3 you:
multiply by 1/3
a new condominium improvement project requires 11 3/4 gallons of paint for each unit. how many units can be painted with 376 gallons of paint
Answers
376 gallons of paint will paint 32 units of the project.
Conversion of Mixed Fraction to Improper FractionWe need to first of all convert the mixed fraction into improper fraction.
\(11\frac{3}{4}=\frac{47}{4}\)Now that we've calculated that, let us find how many units can be painted with 376 gallon
If 1 unit will consume 47/4 gallons of paint
x unit will consume x gallons of paint
\(\begin{gathered} 1=\frac{47}{4} \\ x\text{ unit}=376 \\ x=\frac{376\times1}{\frac{47}{4}} \\ x=32 \end{gathered}\)NB: what we did was cross multiply both sides and solve for x.
From the calculations above, we can see that 376 gallons will paint 32 units.
The value of homes sold in Hampton VA are normally distributed with a mean of $200,000
and a standard deviation of $10,000. If 1216 houses were sold in 2012, how many houses would
have a value greater than one standard deviation above the mean?
Answers
Answer:
\(X \sim N(200000,100000)\)
Where \(\mu=200000\) and \(\sigma=10000\)
From the empirical rule we know that within one deviation from the mean we have 68% of the values so then 1 deviation above the mean we will have (100-68)/2 = 16% and then the number of houses that are greater than one deviation above the mean are:
\( Number = 1216*0.16 = 194.56\)
And the answer woud be between 194 and 195 houses
Step-by-step explanation:
Let X the random variable that represent the value of homes in Hampton VA of a population, and for this case we know the distribution for X is given by:
\(X \sim N(200000,100000)\)
Where \(\mu=200000\) and \(\sigma=10000\)
From the empirical rule we know that within one deviation from the mean we have 68% of the values so then 1 deviation above the mean we will have (100-68)/2 = 16% and then the number of houses that are greater than one deviation above the mean are:
\( Number = 1216*0.16 = 194.56\)
And the answer woud be between 194 and 195 houses
8. Which set of numbers is arranged in increasing order?
A 23 873. 24 765,25 000.5 678)
B. (16 287. 16 728.16 827, 16 872
C. 98 782.98 728.98 287.98 278)
D. 78 082.78 802.78 208.78 028)
Answers
Answer:
its B :)
Step-by-step explanation:
i took the test
Please all parts of this question:
Answers
The result of the definite integral by substitution is 214440.6.
How to apply substitution on definite integrals
In this problem we find the case of a definite integral, that is, an integral with definite limits, that must be simplified by algebraic substitution to be solved quicker. First, write the substitution formula and its derivative:
u = 6 · x - 7
du = 6 dx
f(u) = u⁴
Second, define the new limits of the definite integral:
a = 6 · 2 - 7
a = 5
b = 6 · 5 - 7
b = 23
Third, simplify the integral by means of the substitution formula:
\(\frac {1}{6}\int\limits^{23}_{5} {u^{4}} \, du\)
Fourth, integrate the expression:
\(I = \frac{1}{30} \cdot u^{5}\left|_{5}^{23}\)
I = (1 / 30) · (23⁵ - 5⁵)
I = 214440.6
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Find the inverse of A = 9, -2 -10, 7 , if it exists.
Answers
The inverse of matrix A, if it exists, is:
A^(-1) = [7/43, 2/43; 10/43, 9/43]
To find the inverse of a matrix A, we need to determine if the matrix is invertible by calculating its determinant. If the determinant is non-zero, then the matrix has an inverse.
Given the matrix A = [9, -2; -10, 7], we can calculate its determinant as follows:
det(A) = (9 * 7) - (-2 * -10)
= 63 - 20
= 43
Since the determinant is non-zero (43 ≠ 0), we can proceed to find the inverse of matrix A.
The formula to calculate the inverse of a 2x2 matrix is:
A^(-1) = (1/det(A)) * [d, -b; -c, a]
Plugging in the values from matrix A and the determinant, we have:
A^(-1) = (1/43) * [7, 2; 10, 9]
Simplifying further, we get:
A^(-1) = [7/43, 2/43; 10/43, 9/43].
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chau made $270 for 18 hours of work. At the same rate, how many hours would he have to work to make $105
Answers
Answer:
7 hours
Step-by-step explanation:
here,
270/18=105/x
x=(105*18)/270
x=7
Chau made $270 for 18 hours of work. At the same rate, Therefore Chau would have to work 7 hours at the same rate to make $105.
To find out how many hours Chau would have to work to make $105 at the same rate, we can set up a proportion using the given information:
Let x be the number of hours Chau needs to work to make $105.
We know that Chau made $270 for 18 hours of work, so the rate of earnings per hour is:
Rate = Total earnings / Number of hours
Rate = $270 / 18 hours
Rate = $15 per hour
Now, we can set up the proportion:
$15 per hour = $105 / x hours
To find x, we can cross-multiply:
$15 × x = $105
Now, solve for x:
x = $105 / $15
x = 7 hours
So, Chau would have to work 7 hours at the same rate to make $105.
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find the property
plssss help
Answers
Subtract 7 from both sides. Subtract 7 from 23 to get 16. Divide both sides by 4. Divide 16 by 4 to get 4.
What Is Angle Congruence’s Symmetric Property?According to the symmetric property, if one geometric form is congruent to another, the second shape is likewise congruent to the first. The symmetric property of congruence states that for all angles A and B, if AB A B then BA B A.Transitive Property of Congruence. “If two shapes are congruent to the third shape, then all the shapes are congruent to each other,” asserts the transitive property of congruence.
We can solve an equation by applying the four equality properties: addition, subtraction, multiplication, and division. To get the value of an unknown variable, we simply add, subtract, multiply, or divide both sides of an equation.
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The U.S Census Bureau provides data on the number of young adults, age 18-24, who are living in their parents’home. Let
M= the event a male young adult is living in his parent’ home
F = the event a female young adult is living in her parent’ home
If we randomly select a male young adult and a female adult, the Census Bureau data enable us to conclude P(M)=0,56 and P(F)=0,42 (The World Almanac, 2006).The probability that both are living in their parent’home is 0,24
a, What is the probability at least one of the two young adults selected is livingin his or her parent’ home?
b, What is the probability both young adults selected are living on their own (neither is living in their parent’ home?
Answers
a) The probability that at least one of the two young adults selected is living in his or her parent’s home is; 0.74.
b) The probability both young adults selected are living on their own is; 0.26
How to solve Conditional Probability?We are given the events as;
M = the event a male young adult is living in his parent’ home
F = the event a female young adult is living in her parent’ home
We are also given that;
Probability that a male young adult is living in his parent’ home; P(M) = 0.56
Probability that a female young adult is living in her parent’ home; P(F) = 0.42
a) The probability that at least one of the two young adults selected is living in his or her parent’ home is;
P(at least one of the two young adults selected is living in his or her parents home) = P(M or F) = P(M) + P(F) - P(M and F)
= 0.56 + 0.42 - 0.24 = 0.74.
B) The probability both young adults selected are living on their own which means neither is living with their parents is;
P(neither living with parents) = 1 - P(M or F)
= 1 - 0.74 = 0.26.
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I need help on this pls
Answers
Here are the prices for cans of juice that are the same brand and the same size at different stores. Which store offers the best deal? Store X: 4 cans for $2.48 Store Y: 5 cans for $3.00 *
Answers
Answer:
Y=300
X= 4
M= 49x9=4
3x4=3
Step-by-step explanation:
If the discriminant is 22, then the roots of the quadratic equation are ________________.irrationalrationalreal and equalcomplex
Answers
Given:
The discriminant is 22.
Required:
To choose the correct option for the roots.
Explanation:
The desciminant is 22 means
\(b^2-4ac=22\)We know that if
\(b^2-4ac>0\)the equation has two distinct real number roots.
Therefore the roots are irrational or rational.
Final Answer:
The roots are irrational or rational.
a typist types 1700 words in 1 hour and 30 minute. calculate the rate at which the typist works in words per minute
Answers
Solution:
Note that:
Typist = 1700 words = 1 hour 30 minutesSimplify the equation to find the word per minute.
=> 1700 words = 1 hour 30 minutes=> 1700 words = 90 minutes=> 170/9 words = 1 minuteThe word per minute is 170/9 words per minute.
Typist = \(1700\)
words = 1 hour \(30\) minutes
Lets, find the word per minute :
\(1700\) words = \(1hour 30\) minutes
\(1700\) words = \(90\) minutes
\(\frac{170}{9}\) words = \(1\) minute
The word per minute is \(\frac{170}{9}\) words per minute.
i don’t know how to do this please helppp
Answers
Answer:
Given the 2 values, height and the base, of these 2 triangles, we can assume that they are similar (meaning they share the same angles) as we have no other information to determine the height of the tree.
Therefore, if these triangles are similar, their corresponding sides are proportional. In other words, PZ/RT = QZ/ST or RT/PZ=ST/QZ
Hence, if we find the ratio of this, we can use it to find the side h
QZ/ST=PZ/RT
48/12=PZ/4
PZ/4=48/12
(PZ/4)3=48/12
PZ(3)/12=48/12
48/3=16
16=PZ.
3Step-by-step explanation:
PLEASE HELP FIND FOR X QUICK PLEASE!!!!
Answers
Greetings from Brasil...
Assuming that the line segments CE and FH are parallel, then:Angle W
Here we have Opposite Angles by Vertex, so
W = 14
According to the attached figure, the angle W is also corresponding, so in the triangle CEG one of the angles will be 14°
Angle Z
The sum of the interior angles of a triangle is 180°, so for triangle CEG:
Z + W + 78 = 180
Z + 14 + 78 = 180
Z = 88
Angle X
Z and 4X are complementary angles, then
Z + 4X = 180
88 + 4X = 180
X = 23
___________________________________
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Gravano Engineering Co has the following items appearing in its statement of financial position at the year end:
LOADING...(Click here to view financial data.)
What is the total for:
1. Non-current assets?
2. Current assets?
Answers
Therefore , the solution of the given problem of unitary method comes out to be entire current assets are $56,000.
What does an united method entail ?To finish a job using a unitary method, take the measurements of this minuscule subsection and divide the result by two. Simply put, the unit method removes a desired item from both specific set and pixel subsets. 40 pens, for instance, will indeed cost Rs/kg ($1.01). It's conceivable that one nation variables will have complete control over the strategy used to achieve this. Almost all living things have a unique trait. There are open comments and additions (mathematics, algebra).
Here,
Non-current assets:
The total property, plant, as well as equipment (PPE) is $65,000 plus 27,000 plus 20,000, which comes to $112,000
25 000 intangible assets
The entire non-current assets are therefore $112,000 plus $25,000, or $137,000
Total assets: 32,000 in inventories
Receivables from trade and other sources = 12,500 + 9,000 = $21,500
2,500 in both the bank and the cash.
The entire current assets are therefore $56,000 ($32,000 + $21,500 + 2,500).
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The nutritional chart on the side of a box of a cereal states that there are 87 calories in a 3/4 cup serving. How many calories are in 8 cups of the cereal?
Answers
Answer:
Total calories in 8 cup = 928 calories
Step-by-step explanation:
Given:
Calories in 3/4 cup of cereal = 87 calories
Find:
Total calories in 8 cup
Computation:
Total calories in 8 cup = 8 x 87 x [4/3]
Total calories in 8 cup = 928 calories
Simplify the expression using order of operation (11 - 8)^3 - 2 x 6
Answers
Answer:
500
Step-by-step explanation:
(11-3)^3-2x6
first evaluate 11-3-->8
then cube it-->8^3=512
then multiply 2x6-->12
then subtract the two-->512-12=500
\(\huge\textsf{Hey there!}\)
\(\huge\textsf{Just do PEMDAS}\)
\(\huge\textsf{Parentheses}\)
\(\huge\textsf{Exponents}\)
\(\huge\textsf{Multiplication}\)
\(\huge\textsf{Division}\)
\(\huge\textsf{Addition}\)
\(\huge\textsf{Subtraction}\)
\(\mathsf{(11 - 8)^3 - 2\times 6}\)
\(\mathsf{11 - 8 = \boxed{\bf 3}}\)
\(\mathsf{3^3 - 2 \times 6}\)
\(\mathsf{3^3 = 3\times 3\times 3 = 9\times 3 = \boxed{\bf 27}}\)
\(\mathsf{27 - 2 \times6 }\)
\(\mathsf{2\times 6 = \boxed{\bf 12}}\)
\(\mathsf{27 - 12}\)
\(\boxed{\mathsf{\bf= 15}}\)
\(\boxed{\boxed{\huge\textsf{Answer: \bf 15}}}\huge\checkmark\)
\(\large\textsf{Good luck on your assignment and enjoy your day!}\)
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pls solve the photo?
Answers
Answer:
8. B
9. D
Step-by-step explanation:
I think this is right if I'm not mistaken ..
help me pls this is hard
Answers
Answer:
the 40th number in the pattern is 9
I need help ASAP
Mateo earns a yearly salary of 40,000. Rico earns a yearly salary of 51,000. Mateo will receive a salary increase of 3,500 per year, and Rico will receive a salary increase of 2,800 per year
Which equation can be used to find n, the number of years it will take Mateo to earn the same salary as Rico?
A: 40,000+3,500n=51,000+ 2,800
B: 40,000+3,500n=51,000n+ 2,800n
C: 40,000n+3,500=51,000n+ 2,800
D: 40,000+3,500n=51,000n+ 2,800
Answers
Using log evaluate 3^x=10
Answers
Answer:
x ≈ 2.09590327429
Step-by-step explanation:
You want the solution to 3^x = 10 using logarithms.
LogsTaking logarithms of both sides of the given equation, we have ...
x·log(3) = log(10)
Dividing by the coefficient of x gives ...
x = log(10)/log(3)
x ≈ 2.09590327429
__
Additional comment
If the logarithm to the base 10 is used, then this becomes ...
x = 1/log₁₀(3)
The meaning of "log( )" varies with the context. In high-school algebra, it usually means "log₁₀( )". In other contexts, it may mean "ln( )", the natural logarithm.
For the purpose here, it doesn't matter what base the logarithms have, as long as log(10) and log(3) are to the same base.
<95141404393>
The approximate value of x that satisfies the equation 3^x = 10 is approximately 1.46497.
To evaluate the equation 3^x = 10 using logarithms, we can take the logarithm of both sides of the equation. The most commonly used logarithm is the base 10 logarithm, also known as the common logarithm (log).
Taking the log of both sides, we get:
log(3^x) = log(10)
Now, we can apply the logarithmic property that states log(a^b) = b * log(a). Applying this property to the left side of the equation:
x * log(3) = log(10)
Next, we can divide both sides of the equation by log(3) to isolate the variable x:
x = log(10) / log(3)
Using a calculator, we can evaluate the right side of the equation:
x ≈ 1.46497
Therefore, the approximate value of x that satisfies the equation 3^x = 10 is approximately 1.46497.
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HELPPP!!
Statement:
Some whole numbers are
irrational numbers.
True or False?
Some rational numbers are not whole numbers.
True or False?
Some irrational numbers are not integers.
True or False?
All rational numbers are integers.
Answers
Answer:
Step-by-step explanation:
Comment
A rational number is one that can be expressed as x/y. The first statement is false. All whole numbers are rational. They can always be expressed as x/1
Some rational numbers are not whole numbers. That's true. 4/7 is rational but not whole.
Some irrational numbers are not integers. I'm tempted to say this is true.
pi is irrational and it certainly is not an integer.
Answer
false
true
true.
Is a triangle with sides of 5 meters, 12 meters, and 13 meters a right triangle? Explain/Show your work.
Answers
Answer:
Step-by-step explanation:
Solve the inequation x - 12 ≤ 3 - 2x and graph its solution.
Let's do these one-by-one.
The solution to x - 12 ≤ 3 - 2x is:
Answers
Answer:
Step-by-step explanation:
x - 12 ≤ 3 - 2x
3x ≤ 15
x ≤ 5
To graph this, just draw a VERTICAL line passing through x = 5, then shade the area to the LEFT
85 cm with area base of 245cm
Answers
The Volume of rectangular prism (V) = 20,825 \(cm^{3}\)
What is rectangular prism?A rectangular prism is a three-dimensional geometric shape that is formed by six rectangular faces joined together at right angles.
I think the question is, find out the volume of the rectangular prism in cubic centimeters? Given that the height is 85cm and area of base is 245cm².
We know that the formula for calculating the volume of a rectangular prism is as follows,
Volume of rectangular prism (V) = Area of base × height of the prism
Volume of rectangular prism (V) = 245cm² × 85cm
Volume of rectangular prism (V) = 20,825 \(cm^{3}\)
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Write a multiplication expression without exponents that is equivalent to 3^4
How many factors of 3 did you write?
Answers
Answer:
Answer: 3⁴ = 3×3×3×3
3⁴ means multiply four threes together.
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
You just needed to Multiply maning the three, 4 times
original price is 45 and the new price is 56 what is the percent change
Answers
Answer:
podés hacerlo de varias formas cra
In a triangle with angles measuring a, b and c degrees, the mean of b and c is a. What is the
value of a?
Answers
Answer:
60
Step-by-step explanation:
\(a+b+c=180\\\frac{b+c}{2}=a \rightarrow b+c=2a\\\\a+2a=180\\3a=180\\a=60\)
Therefore, the value of a is 60 degrees