The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 4 to 7. If there were 3794 no votes, what was the total number of votes?
The ratio of yes votes to no votes is 4 to 7, which can be simplified to 2 to 7/2 or 2:3.5. This means that for every 3.5 no votes, there are 2 yes votes. Since there were 3794 no votes, there were 3794/3.5 = <<3794/3.5=1082>>1082 sets of yes and no votes.
The total number of votes is therefore 21082 + 3794 = <<21082+3794=6858>>6858 votes.
ASAP HELP!! Determine the perimeter of the right triangle shown. Round your final answer to the nearest whole number if necessary.
A: 7 units
B: 14 units
C: 25 units
D: 26 units
Answer:
B: 14 Units
Step-by-step explanation:
We have the same homework and that's what I got.
V=150cm3 when B=25cm2 and h=18cm.
Identify hwhen V=48cm3 and B=24cm2.
The height of the similar solid is equal to 3 / 2 centimeters.
How to determine the dimension of similar solid by direct and inverse variation
In this problem we find the case of two similar solids. Dimensionally speaking, the volume is equally to the following equivalence:
[V] = [A] × [L]
Where:
[L] - Length variable, in centimeters.[A] - Area variable, in square centimeters. [V] - Volume variable, in cubic centimeters.The volume is directly proportional to the area (B), in square centimeters, and the height of the solid (h), in centimeters:
V ∝ B · h
V = k · B · h
Where k is the proportionality constant, no unit.
We can eliminate this constant by using the following relationship:
V' / (B' · h') = V / (B · h)
If we know that V' = 150 cm³, B' = 25 cm², h = 18 cm, V = 48 cm³ and B = 24 cm², then the height of the solid is:
(150 cm³) / [(25 cm²) · (18 cm)] = (48 cm³) / [(24 cm²) · h]
1 / 3 = 1 / (2 · h)
2 / 3 = 1 / h
h = 3 / 2 cm
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Please use the Standard Normal Table (link on the first page of the quiz) to find the following probabilities.
1. P(Z < -0.42) =
2. P(z > -1.25) =
3. P(z ≥ 2.13) =
4. P(z≤ 1.94) =
5. P(-0.38 < z < 1.48) =
Using the Standard Normal Table, probabilities are:
1) P(Z < 0.42) = 0.3372
2) P( Z > -1.25) = 0.89443
3) P( Z ≥ 2.13) = 0.1667
Define standard normal table.A mathematical table for the values of, which are the values of the cumulative distribution function of the normal distribution, is known as a standard normal table. It is also known as the unit normal table or the Z table. The standard normal distribution table is a collection of regions from the standard normal distribution, also referred to as a bell curve, and it shows the size of the region beneath the bell curve and to the left of a particular z-score to illustrate probabilities of occurrence in a specific population.
Given,
Using the Standard Normal Table,
Probabilities are:
1) P(Z < 0.42) = 0.3372
2) P( Z > -1.25) = 0.89443
3) P( Z ≥ 2.13) = 0.1667
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Throughout your life, you will need to adapt your budget to respond to changes in your income and expenses. Now, it is time to practice making changes to a budget.
4. Change your previous budget to reflect these new factors. (10 points)
• Your school announced that you will not have to pay for a bus pass to get to classes, because a new school program will cover this expense for all students.
• You just found out that your books will cost more than you had expected. You will now need to spend an additional $100 on books in October.
• You got an unexpected raise at work; you will now be making $650 each month.
• Make sure that you are still meeting your overall goal of saving $100 by the end of October.
To change your budget to reflect these new factors, we need to update the budget to reflect the changes in income and expenses. Here is an updated version of the budget, showing the changes:
Income:
• Salary: $650 (increased by $100 due to unexpected raise)
Expenses:
• Rent: $400 (unchanged)
• Food: $200 (unchanged)
• Entertainment: $100 (unchanged)
• Books: $100 (increased by $100 due to unexpected cost)
• Bus pass: $0 (no longer needed due to school program)
Total expenses: $700 (unchanged)
Savings:
• Savings goal: $100 (unchanged)
Total income: $650
Total expenses: $700
Total savings: -$50 (decreased by $50 due to increase in expenses)
As you can see, even with the unexpected raise in income, the overall goal of saving $100 by the end of October is not being met. To reach this goal, you will need to find ways to reduce your expenses or increase your income. Some possible options for doing this might include cutting back on entertainment expenses, finding a cheaper source of books, or looking for additional ways to earn money, such as taking on a part-time job or freelance work. By making these changes to your budget, you can ensure that you are able to meet your savings goal and manage your finances effectively.
Which expression is equivalent to (64)36−3?
Answer:6^3
Step-by-step explanation:
done
URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!
The value of x that will make the two given solids similar is: d. x = 31.
What are the Dimensions of Similar Solids?If two solids are said to be similar to each other, it means that one is a scale copy of the other, and one is enlarged by a scale factor to get the dimension of the other.
Thus, the corresponding linear dimensions of two similar solids are proportional or they have equal ratio.
Based on this definition, the equation below would be created to find the value of x that would make both solids similar to each other.
29/14.5 = x/15.5
Cross multiply:
14.5x = (15.5)(29)
14.5x = 449.5
14.5x/14.5 = 449.5/14.5
x = 31.
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The U.S Department of Transportation maintains statistics for mishandled bags per 1,000 airline passengers. In February 2013, Delta mishandled 2,05 bags per 1,000 passengers. What is the probability that in the next 1,000 passengers, Delta will have
a. no mishandled bags?
b. at least one mishandled bag?
c. at least two mishandled bags?
A: The probability of no mishandled handbags is 0.2328
B: The probabilty of at least one mishandled bags is 0.7672.
C: The probability of at least two mishandled bags is 0.197.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Calculation:Probability of mishandling is 205/1000 = 0.205
Probability of not mishandling is 795/1000 = 0.795
A: Probability of no mishandled bags is [tex](0.795)^{1000}[/tex] = 0.2328
B: Probability of at least one mishandled bags is = 1 - p(no mishandled)
= 1- 0.2328 = 0.7672
C: Probability of at least 2 mishandled bags is = 1 - p(none mishandled)-p(1 mishandled)
p(1 mishandled) = 100c1 ×[tex]p^{1}[/tex]×[tex]p^{999}[/tex] = 0.5986
∴p(atleast two mishandled) = 0.795 - 0.5986 = 0.197.
A: The probability of no mishandled handbags is 0.2328
B: The probabilty of at least one mishandled bags is 0.7672.
C: The probability of at least two mishandled bags is 0.197.
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The Cheese Spread restaurant makes a grilled cheese sandwich with 2 oz of Swiss cheese and 6 oz of cheddar cheese. Which table represents the description of the proportional relationship? Swiss Cheese (oz) 6 12 18 Cheddar Cheese (oz) 2 4 6 Swiss Cheese (oz) 2 4 6 Cheddar Cheese (oz) 6 12 18 Cheddar Cheese (oz) 2 1 0 Swiss Cheese (oz) 6 5 4 Cheddar Cheese (oz) 6 5 3 Swiss Cheese (oz) 2 1 0
The table represents the description of the proportional relationship
is Swiss Cheese (oz) 2 4 6
Cheddar Cheese (oz) 6 12 18
How to determine which table represents the description of the proportional relationship?Since the restaurant makes cheese sandwich with 2 oz of Swiss cheese and 6 oz of cheddar cheese.
Thus, the table that represents the proportional relationships will be the one that contains 2 oz of Swiss cheese with a corresponding value of 6 oz of cheddar cheese. Also, the constant of proportionality (k) must be the same (i.e. k = 6/2 = 3) for all the values.
Therefore, the table will be:
Swiss Cheese (oz) 2 4 6
Cheddar Cheese (oz) 6 12 18
Notice: k = 6/2 = 12/4 = 18/6 = 3
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the base area of the rectangular prism is 28 square meters. It the height of the prism is 14 meters what is the total volume of the prism,
Answer:
Step-by-step explanation:
28 x 14 equals 392 so the answer is 392
1. A student is helping a family member build a storage bin for their garage. They would like for the bin to have a volume of 240 ft3. If they already have the length measured at 8 feet and the width at 6 feet, what is the height needed to reach the desired volume?
2. The volume of a rectangular prism is 6,142.5 cm3. If the height is 16.25 cm and the length is 28 cm, what is the value of the width?
3.If the volume of a rectangular prism is 26,214 m3 and it has a height of 17 m, what is the value of B, the area of the base?
The height needed to reach the desired volume is 5 feet
The width is 13.5 cmThe base area is 1542 square mWhat is the height needed to reach the desired volume?From the question, we have the following parameters that can be used in our computation:
Length = 8 feet
Volume = 240 cubic feet
Width = 6 feet
The height is calculated as
Height = Volume/(Length x Width)
Substitute the known values in the above equation, so, we have the following representation
Height = 240/(8 x 6)
Evaluate
Height = 5
What is the value of the width?Here, we have
Length = 28 cm
Volume = 6142.5 cubic cm
Height = 16.25 cm
The width is calculated as
Width = Volume/(Length x Height)
Substitute the known values in the above equation, so, we have the following representation
Width = 6142.5/(28 x 16.25)
Evaluate
Width = 13.5
What is the area of the base?Here, we have
Volume = 26214 cubic m
Height = 17 cm
The base area is calculated as
Base area = Volume/Height
Substitute the known values in the above equation, so, we have the following representation
Base area = 26214/17
Evaluate
Base area = 1542
Hence, the base area is 1542 square m
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George buys 7 pairs of pants and uses a discount of $11 off. He spends $73 total. What is p, the cost of each pair of pants?
Answer:
$12 is the cost of each pair of pants
Step-by-step explanation:
First we need to know the price with no discount first: $11 + $73 = $84
The we take the real price of the pants to divide to the 7 pairs: $84 ÷ 7 = $12
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suppose baby kittens' weights are normally distributed with a mean of 12.3 and a standard deviation of 2.2. the z-score tells you how many units above the average (if z-score is positive) or below the average (if z-score is negative) any particular baby kitten's weight is. find the baby kitten weight that corresponds to the following z-scores given below. hint: use the formula x
X-μ Use the formula Z where is the mean, o is the standard deviation, and X is the baby kitten σ weight. a. Z= 1.98, X = b. Z-2.87, X =
Using the formula X=μ+Zσ, the baby kitten's weight corresponds to the z-scores Z=1.98 and Z=2.87 are 16.656 and 18.614.
In a normal distribution, data points are referred to as x, whereas in a z distribution, they are referred to as z or z scores. A z score is a standard score that indicates how many standard deviations an individual statistic is from the mean (x). The formula used to calculate this z-score is Z= (X-μ)/σ where x is the raw score, σ is the population standard deviation, and μ is the population means. From this formula, X can be calculated as X=μ+Zσ.
For the first z-score, Z = 1.98, σ = 2.2 and μ = 12.3, then
X = 12.3+1.98(2.2) = 16.656
For the second z-score, Z = 2.87, σ = 2.2 and μ = 12.3, then
X = 12.3+2.87(2.2) = 18.614
The answers are 16.656 and 18.614.
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IF POSSSIBLE INSERT A DIGIT TO make 13_0 divisible by 6
YAnswer: Yes
Step-by-step explanation: 425 / 5.000
Resultados de traducción
Resultados de traducción
You only have to verify that it is divisible by 2 and by 3. Since it ends in zero (which is an even number) it is divisible by 2. Then it only remains for it to be divisible by 3 and for this the sum of its digits must be a multiple of 3. Therefore, if x is the missing number, we have that 1+3+x+0 must be a multiple of 3. It would suffice, for example, to take x =2 (there are more possibilities as you can see). So one possibility is the number 1320
Answer:
Possible digits are 2, 5 or 8-------------------------------------
Divisibility rule by 6:
It must be an even number and sum of digits must be multiple of 3.The number 13 x 0 is even number as ends with zero and the sum of its digits is:
1 + 3 + x + 0 = 4 + xThe x is between 0 and 9.
Possible values of x to make x + 4 a multiple of 3:
x = 2, then the number is 1320 ⇒ 1320/6 = 220x = 5, then the number is 1350 ⇒ 1350/6 = 225x = 8, then the number is 1380 ⇒ 1380/6 = 230A ball rolls down a hill. It starts with velocity of 2 m/s After 2 seconds, the ball has a velocity of 12 m/s What is the acceleration of the ball?
The acceleration of the ball is 5 ms2.
What is acceleration?
Acceleration is the rate at which an object's velocity with respect to time changes. It is a vector quantity to accelerate (in that they have magnitude and direction). The direction of the net force acting on an object determines the direction of its acceleration.
The acceleration of the car in its present direction of motion is referred to as a linear acceleration (or tangential acceleration in circular motions), and the passengers on board feel a force pressing them back into their seats as a result.
The acceleration that is used to change direction is referred to as radial acceleration (or centripetal acceleration in circular travels), and the reaction that the passengers feel is a centrifugal force.
Therefore, The acceleration of the ball is 5 ms2.
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as we learned in class, an important component of non-linear least squares is the jacobian matrix, the set of partial derivatives with respect to parameters at each data point. in def calc jacobian(x,p), you will need to implement the calculation of the jacobian matrix for the function: where 'a' is the first parameter (p[0,0]), 'b' is the second (p[1,0]), an so on...
The set of partial derivatives with respect to parameters at each data point.
def calc_jacobian(x, p):
jacobian = np.zeros([len(x), len(p)])
for i in range(len(x)):
for j in range(len(p)):
jacobian[i][j] = (2 * p[j] * x[i]**j)
return jacobian
What is partial derivatives?Partial derivatives are a type of derivative in calculus that are used to measure the rate of change of a function with respect to a single independent variable, while holding the other variables constant. They are denoted with a symbol called a partial derivative operator, which is a curved d with a line over it. Partial derivatives are used to calculate derivatives in multivariable functions and to find the maximum or minimum points of a function. Partial derivatives can also be used to analyze the behavior of functions near a point, or to solve equations involving multiple variables.
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Evaluate{3(x+4)(x+1)}/{(x+2)(x-2)} for x=4
A. 10
B.-{10}/{3}
C.{10}/{3}
D. -10
Answer:
a) 10
Step-by-step explanation:
Given information,
→ [3(x + 4)(x + 1)]/[(x + 2)(x - 2)]
→ x = 4
Let's evaluate the expression,
→ [3(x + 4)(x + 1)]/[(x + 2)(x - 2)]
→ [3(4 + 4)(4 + 1)]/[(4 + 2)(4 - 2)]
→ [(3 × 8)(5)]/(6 × 2)
→ (24 × 5)/12
→ 120/12 = 10
Therefore, the answer is 10.
In an analysis of variance, differences caused by treatment effects contribute to which of the following variances? both between treatments variance and within-treatments variance between treatments variance but not within treatments variance within-treatments variance but not between treatments variance neither between treatments variance nor within-treatments variance
The analysis of variance compares the differences between treatments to determine the variance attributed to treatment effects, not the variance within treatments.
An analysis of variance (ANOVA) is a statistical technique used to compare the means of two or more groups. This technique is used to determine the variance attributed to differences between treatments. The variance between treatments is the variance between the group means of the different treatments, while the variance within treatments is the variability of the data within each treatment group. In an ANOVA, only the variance between treatments is considered to be caused by the treatment effect. This is because the within-treatment variance is assumed to be caused by random sampling error, which is independent of the treatment. Thus, in an ANOVA, only the between treatments variance is attributed to treatment effects, while the within-treatment variance is not. This allows the analyst to better understand and explain the differences between treatments.
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True or false
is every rectangle is a rhombus?
Every rectangle with four congruent sides is a square?
Every rhombus is a parallelogram?
Every quadrilateral is a rhombus?
Answer- false, true, true, and false
Step-by-step explanation:
No, rectangle is not always a rhombus because in rectangle two opposite sides are equal in length, and all the angles in rectangle is right angled but it is not necessary in rhombus.
All rectangles are squares. False! A square has ALL sides equal, but a rectangle only has opposite sides equal. All trapezoids have only one pair of parallel sides.
A parallelogram is a quadrilateral with 2 pairs of parallel sides. The opposite sides on every rhombus are parallel, so every rhombus is a parallelogram.
If you have a quadrilateral with two pairs of parallel sides, you do not necessarily have a rhombus;
A comic-strip writer churns out different numbers of comic strips each day. The writer logged the number of comic strips he wrote each day for 16 days and sorted the data in ascending order to create this data set.
1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 8
The data in the distribution is
. If the writer writes for two more days and creates 5 and 7 comic strips, respectively, the difference of the mean and the median for the new data set is
.
The difference of the mean and the median for the new data set is 0.28 and 0.50 respectively.
What are mean and median?The mean is the average value which can be calculated by dividing the sum of observations by the number of observations
Mean = Sum of observations/the number of observations
Median represents the middle value of the given data when arranged in a particular order.
We are given that 1st Data set: 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 8
mean: 3.5
median: 3
Now 2nd Data set: 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 7, 8
mean: 3.78
median: 3.5
Therefore, we need to calculate the differences If the writer writes for two more days and creates 5 and 7 comic strips,
The difference in mean:
3.78 - 3.5 = 0.28
The difference in median:
3.5 - 3 = 0.50
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The data in the distribution is positively skewed (skewed to the right). If the writer writes for two more days and creates 5 and 7 comic strips, respectively, the difference between the mean and the median for the new data set is 0.28.
(✿◕‿◕✿)
TRUE OR FALSE : artificial selection takes a relatively long time to occur while natural selection takes a relatively short time to occur.
Artificial selection takes a comparatively longer time to occur while natural selection takes a comparatively shorter time to occur.
Thus, the given statement is False.
Artificial selection takes a very short time related to natural selection. The time taken to choose the individual having the required character and then making them produce the offspring is the only time needed for the entire process.
Artificial selection can be demonstrated as the series of steps for selecting the required character and making the individuals having those character to produce the offspring having the desired character.
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Round the answer to the nearest tenth please
Answer:
28.42
Step-by-step explanation:
pretty sure its correct
diane will donate up to to charity. the money will be divided between two charities: the city youth fund and the educational growth foundation. diane would like the amount donated to the educational growth foundation to be at least three times the amount donated to the city youth fund. let denote the amount of money (in dollars) donated to the city youth fund. let denote the amount of money (in dollars) donated to the educational growth foundation. shade the region corresponding to all values of and that satisfy these requirements.
The value of x is $53.34 dollars but no higher than $115 and for y is as low as $160, but no higher than $345.
According to the question,
Diane will donate "up to $460" in charity, which means it can be less than or equal to 460, but not any higher. Then,
$460 to charity (max)
$160 + to Educational (160 being the minimum)
It is also given , Education is 3x (or higher) than City.
If we denote x to City, and y to Educational, then,
x + y = 460 . And we know that y ≥ 3x
x + 3x = 4x = 460
x = 115.
This means when she donates $115 to City, she will donate 3x (or $345) to Educational. These are the max value
She will not donate higher than $460.
A minimum requirement was placed on Educational earlier.
When y = 160,
x will be y/3,
=> x = 160/3 = $53.34. This means she donated 213.34, which is still less than $460
Therefore, x (which is City) can be the range of $53.34 dollars but no higher than $115.
y (which is Educational) will be as low as $160, but no higher than $345.
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In a chemistry class a hot liquid is placed into a refrigerator and it’s temperature in degrees Fahrenheit is modeled as a function of the number of minutes since it was place in the refrigerator. The model formed was linear function T(n)=-8n+175 give a interpretation of the parameters -8 and 175 within the context of this problem.
Answer:
In this problem, the temperature of the hot liquid (T) is being modeled as a function of the number of minutes (n) that it has been in the refrigerator. The model is a linear function, which means that the temperature will change at a constant rate as the number of minutes increases.
The parameter -8 represents the rate at which the temperature is changing. Specifically, it represents the amount by which the temperature decreases in degrees Fahrenheit for every one minute that passes. For example, if the hot liquid has been in the refrigerator for 10 minutes, its temperature will have decreased by (-8 * 10) = -80 degrees Fahrenheit.
The parameter 175 represents the initial temperature of the hot liquid when it was first placed in the refrigerator. This is the temperature at n = 0, or when no time has passed.
So in the context of this problem, the parameters -8 and 175 represent the rate at which the temperature changes and the initial temperature of the hot liquid, respectively.
A political party sends a mail survey to 1500 randomly selected registered voters in a community. The survey asks respondents to give an opinion about the job performance of the current President. Of the 1500 surveys sent out, 480 are returned, and of these, only 120 say they're satisfied with the President's job performance.
The sample is
A. the 1500 randomly selected voters receiving the questionnaire.
B. the 480 surveys returned.
C. the 120 voters surveyed that are satisfied with the President's job performance.
D. the voters in his district.
A. the 1500 randomly selected voters receiving the questionnaire.
What is survey?
A survey is a technique for acquiring data from a sample of individuals by asking pertinent questions with the goal of comprehending populations as a whole. Everyone involved in the information economy, from corporations to the media to the government and academia, relies on surveys as a vital source of information and insights.
A political party sends a mail survey to 1500 randomly selected registered voters in a community. The survey asks respondents to give an opinion about the job performance of the current President. Of the 1500 surveys sent out, 480 are returned, and of these, only 120 say they're satisfied with the President's job performance.
The sample remains the total people to whom the survey is sent
The sample is the 1500 randomly selected voters receiving the questionnaire.
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TRUE OR FALSE There were three rounds of QE: $600 billion in QE1 in early 2009, QE2 in November 2010 that was $600 billion worth of securities purchases, and QE3 that started in September 2012 and rose up to $85 billion per month worth of securities purchases that continued until October 2014
TRUE, There were three rounds of QE: $600 billion in QE1 in early 2009, QE2 in November 2010 that was $600 billion worth of securities purchases, and QE3 that started in September 2012
Exports = $300 billion
Imports = $500 billion
Trade surplus/(deficit) = $300 billion - $500 billion
= ($200 billion)
Considering all the options,
Purchases = $800 billion
Sales = $600 billion
Trade surplus/(deficit) = $600 billion - $800 billion
= ($200 billion)
Hence the right answer is c. The U.S has a trade deficit. The U.S. purchases $800 billion worth of foreign assets and foreign countries purchase $600 billion worth of U.S. assets.
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A particle moves on a circle of radius 9 cm, centered at the origin, in the xy-plane (x and y measured in centimeters). It starts at the point (0, 9) and moves counterclockwise, going once around the circle in 6 seconds. Write a parameterization for the particle's motion. x (t) = What is the particle's speed? Speed =
It moves at a 1.5 m/s speed .
What is the motion equation with parameters?Two parametric equations—x=(v0cos)t and y=(v0sin)t+h—determine the motion of a projectile. Initial velocity is denoted by the symbol v0. The angle at which the object is hurled is represented by, and the height to which it is propelled by h.Every function with a vector value offers a parameterization of a curve. A parameterization of a curve is a set of equations such as x = x (t) and y = y (t) that express the coordinates of a point on the curve in terms of a parameter.Particle velocity is the speed of an actual or hypothetical particle as it transmits a wave through a medium. A particle's speed is measured in SI in meters per second (m/s).Explanation:
Speed = d/t = 9/6 = 3/2 = 1.5m/s.
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It moves at a 1.5 m/s speed .
What is the motion equation with parameters?Two parametric equations—x=(v0cos)t and y=(v0sin)t+h—determine the motion of a projectile. Initial velocity is denoted by the symbol v0. The angle at which the object is hurled is represented by, and the height to which it is propelled by h.
Every function with a vector value offers a parameterization of a curve. A parameterization of a curve is a set of equations such as x = x (t) and y = y (t) that express the coordinates of a point on the curve in terms of a parameter.
Particle velocity is the speed of an actual or hypothetical particle as it transmits a wave through a medium. A particle's speed is measured in SI in meters per second (m/s).
Speed = d/t = 9/6 = 3/2 = 1.5m/s.
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Solve for
x. Round to the nearest tenth, if necessary.
ø= 20°
Adj = 24
Hyp = x
Cos ø = Adj/Hyp
Hyp = Adj/ Cos ø
x = 24/ cos 20
x= 24/0.9397
x= 25.5 to the nearest tenth
Write the ratio in fractional notation in lowest terms 9 nickels to 3 dollars?
Answer:
3:1
Step-by-step explanation:
divide by 3 both sides
The National Health Statistics Reports dated Oct. 22, 2008, stated that for a sample size of 277 18-year-old American males, the sample mean waist circumference was 86.3 cm. A somewhat complicated method was used to estimate various population percentiles, resulting in the following values.
5th 10th 25th 50th 75th 90th 95th
69.6 70.9 75.2 81.3 95.4 107.1 116.4
(b)Suppose that the population mean waist size is 85 cm and that the population standard deviation is 14 cm. How likely is it that a random sample of 277 individuals will result in a sample mean waist size of at least 86.3 cm? (Round your answers to four decimal places.)
(c) Referring back to (b), suppose now that the population mean waist size in 80 cm. Now what is the (approximate) probability that the sample mean will be at least 86.3 cm? (Round your answers to four decimal places.)
the probability that a random sample of 277 individuals will result in a sample mean waist size of at least 86.3 cm is 0.9982.(c)The probability that a random sample of 277 individuals will result in a sample mean waist size of at least 86.3 cm is 0.9817.
To answer (b), we first need to calculate the z-score for 86.3 cm using the population mean of 85 cm and standard deviation of 14 cm. This gives us a z-score of 0.7. We can then use the normal distribution table to calculate the probability of a sample mean of at least 86.3 cm with a z-score of 0.7, which is 0.9982. To answer (c), we need to calculate the z-score for 86.3 cm using the population mean of 80 cm and standard deviation of 14 cm. This gives us a z-score of 1.5. We can then use the normal distribution table to calculate the probability of a sample mean of at least 86.3 cm with a z-score of 1.5, which is 0.9817.
Part (b):
Z-score = (86.3 - 85) / 14
= 0.7
Probability = 0.9982
Part (c):
Z-score = (86.3 - 80) / 14
= 1.5
Probability = 0.9817
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