Note: Please make sure to properly format your answers. All dollar figures in the answers need to include the dollar sign and any amount over 1,000 should include the comma ($2,354.67). All percentage values in the answers need to include a percentage sign (%). For all items without specific rounding instructions, round your answers to two decimal places, show both decimal places (5.06).
A recent survey by the American Automobile Association showed that a family of two adults and two children on vacation in the United States will pay an average of $247 per day for food and lodging with a standard deviation of $60 per day. If the data are normally distributed, find the percentage of these families who spent:
a. Less than $167 per day. _____
b. Less than $367 per day. _____
c. More than $247 per day. _____
d. More than $350 per day. _____
e. Less than $67 per day. ______
f. Between $200 and $300 per day. _____
g. Between $360 and $400 per day. _____
h. More than the median. ____
i. Less than the mean. _____
Answers
Using the normal distribution, the percentages are given as follows:
a) 9.18%.
b) 97.72%.
c) 50%.
d) 4.27%.
e) 0.13%.
f) 59.29%.
g) 2.46%.
h) 50%.
i) 50%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.For this problem, the mean and the standard deviation are given as follows:
\(\mu = 247, \sigma = 60\)
For item a, the proportion is the p-value of Z when Z = 167, hence:
\(Z = \frac{X - \mu}{\sigma}\)
Z = (167 - 247)/60
Z = -1.33.
Z = -1.33 has a p-value of 0.0918.
Hence the percentage is of 9.18%.
For item b, the proportion is the p-value of Z when Z = 367, hence:
\(Z = \frac{X - \mu}{\sigma}\)
Z = (367 - 247)/60
Z = 2.
Z = 2 has a p-value of 0.9772.
Hence the percentage is of 97.72%.
For item c, the proportion is one subtracted by the p-value of Z when X = 247, hence:
\(Z = \frac{X - \mu}{\sigma}\)
Z = (247 - 247)/60
Z = 0
Z = 0 has a p-value of 0.5.
Hence the percentage is of 50%.
For item d, the proportion is one subtracted by the p-value of Z when X = 350, hence:
\(Z = \frac{X - \mu}{\sigma}\)
Z = (350 - 247)/60
Z = 1.72
Z = 1.72 has a p-value of 0.9573.
1 - 0.9573 = 0.0427.
Hence the percentage is of 4.27%.
For item e, the proportion is the p-value of Z when Z = 67, hence:
\(Z = \frac{X - \mu}{\sigma}\)
Z = (67 - 247)/60
Z = -3.
Z = -3 has a p-value of 0.0013.
Hence the percentage is of 0.13%.
For item f, the proportion is the p-value of Z when X = 300 subtracted by the p-value of Z when X = 200, hence:
X = 300:
\(Z = \frac{X - \mu}{\sigma}\)
Z = (300 - 247)/60
Z = 0.88.
Z = 0.88 has a p-value of 0.8106.
X = 200:
\(Z = \frac{X - \mu}{\sigma}\)
Z = (200 - 247)/60
Z = -0.78.
Z = -0.78 has a p-value of 0.2177.
0.8106 - 0.2177 = 0.5929.
Hence the percentage is 59.29%.
For item g, the proportion is the p-value of Z when X = 400 subtracted by the p-value of Z when X = 360, hence:
X = 400:
\(Z = \frac{X - \mu}{\sigma}\)
Z = (400 - 247)/60
Z = 2.55.
Z = 2.55 has a p-value of 0.9946.
X = 360:
\(Z = \frac{X - \mu}{\sigma}\)
Z = (360 - 247)/60
Z = 1.88.
Z = 1.88 has a p-value of 0.97.
0.9946 - 0.97 = 0.0246
Hence the percentage is 2.46%.
For items h and i, the distribution is symmetric, hence median = mean and the percentages are of 50%.
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Related Questions
what is the solution to this system? 2x+3y=12 -4x+5y=-2
Answers
answer: (3,2)
step by step explanation: :)
What are the factors of 2a³ + a² + 2a + 1?
O 2(a² + 1)(a + 1)
O(a + 1)(a - 1)(2a + 1)
O (a² + 1)(2a + 1)
O 2(a + 1)2 (a - 1)
Answers
Answer:
The answer is (a²+1)(2a+1)
Please help with this pls
Answers
Answer:
Step-by-step explanation:
its c
Val's checking account has a balance of $30. She deposits $100 in her
checking account and then writes a check for $30. What is the balance in
dollars after the check is cashed?
Answers
Answer:
the answer is
Step-by-step explanation:
100$ left in her acc
Answer:
$100
Step-by-step explanation:
The initial start amount is $30, she then adds $100 to her bank account:
30 + 100 = 130
Then she writes a check for $30 which, when cashed in, subtracts 30 from her balance:
130 - 30 = 100
So, after the check is cashed, her balance is $100.
Hope this helps!
make k the subject of the formula m= √k+1/4
Answers
Answer:
∴ \(k = m^{2} - \frac{1}{4}\)
Step-by-step explanation:
\(m=\sqrt{k} + \sqrt {(\frac{1}{4})}\)
\(m^{2} = k+\frac{1}{4}\)
\(k+\frac{1}{4} =m^{2}\)
∴ \(k = m^{2} - \frac{1}{4}\)
Complete the calculations so that each shows the correct sum.0.5137+1 And no the answer is not 1.5137 I tried it you need to find the sum 6th grade math. HAVE A GOOD DAY
Answers
Answer:
1.5137 is the right answer.
functions mathematics
Answers
\(.59826\)
5️⃣9️⃣8️⃣2️⃣6️⃣
PLEASE HELP I WILL GIVE BRAINLIEST
Answers
Answer:
a = 5+2 = 3
b= 7.1-3.4 = 10.5
c = 8-7 = 15
d = 9/5-3/2 = 33/10
Step-by-step explanation:
I hope this helps.
25 brainly to corret answer show all work pls
Answers
The perimeter of Max's sandbox is 21 feet.
What is perimeter of a figure?The sum of each length of external sides or boundary of a given figure is called its perimeter. To determine the perimeter of an object, add up the length of its boundaries.
Given the dimension of the Ohio park, then we have to determine the representative fraction of Max's sandbox.
Representative fraction = 10/ 25
= 2/ 5
So that;
x = 15 * 2/5
= 6 ft
y = 12.5 *2/5
= 5 ft
The perimeter of Max's sandbox = 10 + y + x
= 10 + 5 + 6
= 21 ft
The perimeter of Max's sandbox is 21 feet.
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3. The following data below represents the running times of six movies. Find
the standard deviation of the running times. Give your answer to the
nearest hundredth of a minute.
Movie
Running
Time
A
1 hr
47 min
B
1 hr
32 min
C
2 hr
14 min
D
1 hr
56 min
2 hr
32 min
F
3 hr
2 min
3.
Answers
The standard deviation of the movie times is given as follows:
27.7 minutes.
How to obtain the standard deviation of the data-set?Considering that an hour has 60 minutes, the time in minutes of each movie is given as follows:
107 minutes, 92 minutes, 134 minutes, 116 minutes, 152 minutes, 182 minutes.
The mean of a data-set is given by the sum of all observations divided by the number of observations, hence:
Mean = (107 + 92 + 134 + 116 + 152 + 182)/6
Mean = 130.5 minutes.
The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, hence:
s = sqrt([(107-130.5)² + (92-130.5)² + (134-130.5)² + (116-130.5)² + (152-130.5)² + (182-130.5)²]/7)
s = 27.7 minutes.
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PLEASE I NEED HELP
Use composition to prove that f(x) and g(x) are inverses. Check your work
Answers
F and G are inverse if both of them satisfy the condition h(x)=x. f(g(x))=g(f(x))=x, as we discovered. The argument f(x) and g(x) are inverse functions is thus established.
How do you verify that f x and G x are inverses?If f (x) and g (x) are inverse functions, it can be determined using one of two ways. For more information, see the explanation.
Explanation:
Instance 1
Inverse functions of both functions can be found using the first method.
Example.
Inverse of f (x) = x + 7 is what we're looking for.
We attempt to determine x using the equation y = x + 7.
y = x + 7
Inferring that g (x) is the inverse of f (x) from the fact that x = y 7
Finding g (x inverse )'s is now necessary.
g( x ) = x − 7
y = x − 7
x = y + 7
As a result, we discovered that f (x) is the inverse function of g (x).
f and g are equal if g is inverse of f and vice versa.
The second approach entails locating the compound functions f ( g ( x ) ) and g ( f ( x ) ). In this case, f and g are inverse if they are both h (x ) = x.
Example:
f ( g ( x ) = [ x − 7 ] + 7
G ( x ) placed as x is the expression in brackets.
f ( g ( x ) ) = x − 7 + 7 = x
g (f ( x ) = [ x + 7 ] − 7
f ( x ) inserted as x is the expression in brackets.
g ( f ( x ) ) = x + 7 − 7 = x
The equation f ( g ( x ) ) = g ( f ( x ) ) = x was what we discovered. The argument f (x) and g (x) are inverse functions is thus established.
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Piece-wise defined function
been having trouble :,)
Answers
Answer:
c.y is the correct answer
Step-by-step explanation:
because its defined in x from the left ×<=1
Need help understanding
Answers
Answer:
10pushups a minute and 3 minutes for burpee I think
2: 12/3
The question is asking if you can do 20 push-ups in 2 minutes how many can you do in 1
To make the 2 a 1 divide by 2. Rennet with fractions you have to do the same thing you did on the bottom on the top.
For example
We would have to divide 20 by 2 because we divide 2 by 2.
So 20 divide by 2 is 10
Now we have 10/1 as our answer
Now we have to do the same thing but they have us different information do it might be a little different.
36/9 = 12/?
Now we just have to work backwards.
How do you get 36 to 12?
You divide by 3
36 divided by 3 = 12
Remember whatever we do to the top we have to do to the bottom
9 divided by 3 = 3
So you get 12/3
Hope this helps and makes sense
What is the y-intercept of the equation of the line that is perpendicular to the line and passes through the point (15,-5)?
Answers
Answer:
hi
Step-by-step explanation:
First of all let’s find out the slope of the line y = x +10
As, we know the equation y= mx + c . So comparing the given equation with the general equation we get, m = 1
Now, we know that the product of two perpendicular lines is -1.
Thus, mn = -1 (considering slope of the second line as n)
Putting the value of m we get , n = -1
Now , y+5= -1( x -15) i.e y=-x + 10
if we compare again with the general equation then we find that.
The y intercept of the required equation is 10.
Thank You
Answer:
10
Step-by-step explanation:
First of all let’s find out the slope of the line y = x +10
As, we know the equation y= mx + c . So comparing the given equation with the general equation we get, m = 1
Now, we know that the product of two perpendicular lines is -1.
Thus, mn = -1 (considering slope of the second line as n)
Putting the value of m we get , n = -1
Now , y+5= -1( x -15) i.e y=-x + 10
if we compare again with the general equation then we find that.
The y intercept of the required equation is 10.
Thank You
State what additional information is required in order to know that the triangles are congruent for the for the reason given
Answers
Answer/Step-by-step explanation:
1. Only one side and an included angle is known. To prove that both triangles are congruent by the SAS Congruence Theorem, an additional information such as a corresponding second side (KJ, and HJ) must be given to be equal to each other.
KJ = HJ
2. Additional information such as a second corresponding angle (angles C and W must be known to prove both triangles are congruent by SAS.
<C = <W
3. Additional information needed is a second corresponding angles must be known to prove the AAS.
4. Additional information needed is the corresponding angles, R and L, which should be equal to prove the ASA.
<R = L
5. Additional information needed: <C = <H
6. Additional information needed: equal hypotenuse lengths of both traingles.
28. Find the volume of a pyramid with height 18 m and a square base measuring 23 m on a side.
Answers
Answer:
Answer is in attached photo.
Step-by-step explanation:
SolutionThe solution is in the attached photo, do take note that the question require us to know the formula to find the volume of a pyramid, which is:
\(\frac{L*b*h}{3}\)
where L is the length of the base, and b is the breadth (or width) of the base, and h is the height of the pyramid.
If Madison rides for 5 hours on a bicycle, what is her rate if she rides for 60 miles?
Answers
60 / 5 = 12
Which expression shows the sum of 8 and a number f
Answers
Answer:
8+f
Step-by-step explanation:
The SUM of 8 and f
Pls tell me if Im wrong
Hope this helps
A mammogram is used to screen women for breast cancer. False positives are tests that incorrectly show a positive result. 85% of positive mammograms are actually false positives. If 1,000 women receive mammograms, and 200 are told there is an abnormal finding, how many women are likely to actually have breast cancer?
Answers
Answer:
30
Step-by-step explanation:
200 x .15 (1-.85 = .15)
30
Describe the y-intercept and end behavior of the following graph:
Answers
Please pick one of the options.
Answers
9880 different possibilities are there in Sally's new combination option second 9880 is correct.
What is permutation and combination?A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.
We have:
Total unique numbers consists in a Sally locker = 3
From the digits 0 to 39
Total numbers = 40
Apply combination formula:
= C(40, 3)
= 40!/(3!37!)
= 9880
Thus, 9880 different possibilities are there in Sally's new combination option second 9880 is correct.
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a) Work out the percentage population increase from 2001 to 2011.
Give your answer to 1 decimal place.
Answers
The percentage population increase from 2001 to 2011 is 50%.
To calculate the percentage population increase from 2001 to 2011, you need the population figures for both years. Let's assume the population in 2001 was 100,000 and in 2011 it was 150,000.
The formula to calculate the percentage increase is:
Percentage Increase = ((New Value - Old Value) / Old Value) * 100
Plugging in the values:
Percentage Increase = ((150,000 - 100,000) / 100,000) * 100 = (50,000 / 100,000) * 100 = 0.5 * 100 = 50%
Therefore, the percentage population increase from 2001 to 2011 is 50%.
Please note that the actual population figures for the respective years need to be used in the calculation to obtain an accurate result. The example above is for illustrative purposes.
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please help!!!!
You invest $400 in the stock of a pharmaceutical company. If the value of the stock decreases by 3.25% each year, what will the stock be worth after 5 years?
Answers
The value of the stock would be worth $339.09 after 5 years.
How to solve an equation?An equation is an expression that can be used to show the relationship between variables and numbers.
An exponential function is given as:
y = abˣ
Where a is the initial value and b is the multiplication factor
Let y represent the value of the stock after x years.
You invest $400 in the stock of a pharmaceutical company. If the value of the stock decreases by 3.25% each year
Hence:
a = 400; b = 1 - 0.0325 = 0.9675
y = 400(0.9675)ˣ
After 5 years (x = 5):
y = 400(0.9675)⁵ = $339.09
The stock would be $339.09
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Why is this a parallelogram?
Answers
Answer:
b both pairs of opposite sides are parallel
Answer:
B or the second choice from the top
Step-by-step explanation:
The definition of a parallelogram, in my own words, is a quadrilateral with two pairs of opposite parallel sides (hence the name). Therefore, the second choice from the top is correct. Hope this helps!
PLEASE HELP! 50 POINTS! Consider the following set of sample data: (34, 32, 34, 32, 40, 37, 31, 31, 29, 27). Which of the following will give a 95% t confidence interval for the mean of the population from which the sample was drawn?
Answers
Answer:
(15.23,41.016)
Step-by-step explanation:
WE must determine the mean of the data set: Which is the sum of the set divided by the number in the set.
\(= (21 + 24 + 25 + 32 + 35 + 31 + 29 + 28)/8 = 225/8 = 28.125\)
We must also determine the standard deviation: Which is the square root of the variance and the variance is the sum of squares of the sample number minus the mean divided by the number if the set data:
\(= ((21 - 28.125)^{2} + (24 - 28.125)^{2} +(25 - 28.125)^{2} + (32 - 28.125)^{2} + (35 - 28.125)^{2} + (31 - 28.125)^{2} + (29 - 28.125)^{2} (28 - 28.125)^{2}\)
\(= 148.877/8 = 18.6\)
The 95% confidence interval is defined as: The mean ± 1.96*standard deviation divided by the sqaure root of the number of data in the set:
\(= 28.125 + (1.96 *18.6)/(\sqrt{8} )\)
\(= 41.016\)
\(= 28.125 - (1.96 * 18.6)/(\sqrt{8}) = 15.23\)
The confidence interval for this data set is (15.23,41.016)
Answer:
32.7 ± 2.262(1.19)
Step-by-step explanation:
See attached pictures
write a real-world situation that could be modeled by the equation 8+2x=6x. Then solve the problem.
Answers
Answer:
x = 2
Step-by-step explanation:
8 = 6x + -2x
8 = 4x
8 = 4x
4 4
2 = x
A geometric sequence, g(n) starts 20,60,...
Define g recursively.
Answers
Answer:
Step-by-step explanation:
T1 = 20
Tn = T(n-1)*3
Given geometric sequence is,
20, 60, .......
Recursive formula of the geometric sequence is given by,
a₁ = First term of the sequence
\(T_n=T_(n-1)\times r\)
\(T_n=\) Successive term of the sequence
\(T_{n-1}=\) Previous term of the sequence
r = common ratio
Here, \(r=\frac{\text{2nd term}}{\text{1st term}}=\frac{60}{20}\)
r = 3
Therefore, \(T_n=T{(n-1)}\times 3\)
Therefore, recursive formula of the sequence is,
\(a_1=20\)
\(T_n=3(T_{n-1})\)
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Raj and Priyanka are playing a game in which each person takes turns to snap open a book at a random page. The LAST TWO DIGITS OF THE PAGE NUMBER ON THE RIGHT SIDE is taken as the person's score.
A player's TOTAL score is calculated by adding each turn's score to the previous total. Which of the following could NOT be Priyanka's score after 4 rounds of the game?
A. 6
B. 88
D. 145
C. 250
Answers
After four rounds of the game, it is impossible that Prinyanka's score could be A. 6.
What is the lowest score Priyanka could get at round 4?The numbers of the right side are shown to be odd numbers. the lowest numbers that Priyanka can get are:
= 1, 3, 5, 7
Assuming Priyanka picks 1 and 3 which are the lowet number, the total Priyanka would get i:
= 1 + 1 + 3 + 3
= 8
it is therefore not possible to get 6 points after 4 rounds of the game.
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It takes 10 pounds of tomatoes to make 3 cups of tomato paste.
Type the answers in the boxes below.
1. At this rate, how many cups of tomato paste can be made with 25 pounds of tomatoes?
cups of tomato paste
2. At this rate, how many pounds of tomatoes are needed to make 14 cups of tomato paste?
pounds of tomatoes
Answers
7.5 cups of tomato paste can be made from 25 pounds and 14 cups can make 46.67 pounds.
What is unitary method?The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
Given, it takes 10 pounds to make 3 cups of tomato paste.
Thus, with 1 pound, number of cups can be made is equal to (3/10) cups
Thus, using 25 pounds, number of cups can be made is equal to
(3/10)*25
= 7.5 cups
3 cups of tomato paste can be made from 10 pounds
1 cup of tomato paste can be made from (10/3) pounds
14 cups of tomato paste can be made from
(10/3)*14
= 46.67 pounds
Thus, 7.5 cups of tomato paste can be made from 25 pounds and 14 cups can make 46.67 pounds.
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Please answe number 1 PLEASE
Answers
Answer:
i believe the answers D
Step-by-step explanation:
Answer:
i think its B
Step-by-step explanation: