**Hello !** I need help to do that algebra homework. I don't really know how that website works, so just tell me how much points you want if your answer is good and i'll give them to your with a lot of pleasure. Here is the homework : Thank you so much for your help ! :)
Answers
Answer:
y = √(900 -x²); see below for a graph
Step-by-step explanation:
The high point (30 ft) is the radius of the circle, so the equation is ...
x² +y² = 30²
Subtract the x-term and take the square root to find y.
y² = 30² -x²
y = √(30² -x²) = √(900 -x²)
The graph is shown in the attachment.
_____
Comment on "how that website works"
We don't know what web site you're referring to, but the one I like is Desmos. It only takes a few minutes to learn to graph the equation here.
You don't even need to solve for y to get the desired graph. You can simply specify that y ≥ 0.
Related Questions
Find the length and width of a rectangle that has the given perimeter and a maximum area. Perimeter: 116 meters
Answers
Answer:
Length = 29 m
Width = 29 m
Step-by-step explanation:
Let x and y be the length and width of the rectangle, respectively.
The area and perimeter are given by:
[tex]A=xy\\p=116=2x+2y\\y=58-x[/tex]
Rewriting the area as a function of x:
[tex]A(x) = x(58-x)\\A(x) = 58x-x^2[/tex]
The value of x for which the derivate of the area function is zero, is the length that maximizes the area:
[tex]A(x) = 58x-x^2\\\frac{dA}{dx}=0=58-2x\\ x=29\ m[/tex]
The value of y is:
[tex]y = 58-29\\y=29\ m[/tex]
Length = 29 m
Width = 29 m
if a varies inversely as the cube root of b and a=1 when b=64, find b
Answers
Answer:
b = 64/a³
Step-by-step explanation:
Using the given information, we can only find a relation between a and b. We cannot find any specific value for b.
Since a varies inversely as the cube root of b, we have ...
a = k/∛b
Multiplying by ∛b lets us find the value of k:
k = a·∛b = 1·∛64 = 4
Taking the cube of this equation gives ...
64 = a³b
b = 64/a³ . . . . . divide by a³
The value of b is ...
b = 64/a³
An instructor asks students to rate their anxiety level on a scale of 1 to 100 (1 being low anxiety and 100 being high anxiety) just before the students take their final exam. The responses are shown below. Construct a relative frequency table for the instructor using five classes. Use the minimum value from the data set as the lower class limit for the first row, and use the lowest possible whole-number class width that will allow the table to account for all of the responses. Use integers or decimals for all answers.
48,50,71,58,56,55,53,70,63,74,64,33,34,39,49,60,65,84,54,58
Provide your answer below:
Lower Class Limit Upper Class Limit Relative Frequency
Answers
Answer:
The frequency table is shown below.
Step-by-step explanation:
The data set arranged ascending order is:
S = {33 , 34 , 39 , 48 , 49 , 50 , 53 , 54 , 55 , 56 , 58 , 58, 60 , 63 , 64 , 65 , 70 , 71 , 74 , 84}
It is asked to use the minimum value from the data set as the lower class limit for the first row.
So, the lower class limit for the first class interval is 33.
To determine the class width compute the range as follows:
[tex]\text{Range}=\text{Maximum}-\text{Minimum}[/tex]
[tex]=84-33\\=51[/tex]
The number of classes requires is 5.
The class width is:
[tex]\text{Class width}=\frac{Range}{5}=\frac{51}{2}=10.2\approx 10[/tex]
So, the class width is 10.
The classes are:
33 - 42
43 - 52
53 - 62
63 - 72
73 - 82
83 - 92
Compute the frequencies of each class as follows:
Class Interval Values Frequency
33 - 42 33 , 34 , 39 3
43 - 52 48 , 49 , 50 3
53 - 62 53 , 54 , 55 , 56 , 58 , 58, 60 7
63 - 72 63 , 64 , 65 , 70 , 71 5
73 - 82 74 1
83 - 92 84 1
TOTAL 20
Compute the relative frequencies as follows:
Class Interval Frequency Relative Frequency
33 - 42 3 [tex]\frac{3}{20}\times 100\%=15\%[/tex]
43 - 52 3 [tex]\frac{3}{20}\times 100\%=15\%[/tex]
53 - 62 7 [tex]\frac{7}{20}\times 100\%=35\%[/tex]
63 - 72 5 [tex]\frac{5}{20}\times 100\%=25\%[/tex]
73 - 82 1 [tex]\frac{1}{20}\times 100\%=5\%[/tex]
83 - 92 1 [tex]\frac{1}{20}\times 100\%=5\%[/tex]
TOTAL 20 100%
The graphs below are the same shape what is the equation of the blue graph
Answers
Answer:
B. g(x) = (x-2)^2 +1
Step-by-step explanation:
When you see this type of equation your get the variables H and K in a quadratic equation. In this case the (x-2)^2 +1 is your H. The (x-2)^2 +1 is your K.
For the H you always do the opposite so in this case instead of going to the left 2 times you go to the right 2 times (affects your x)
For the K you go up or down which in this case you go up one (affects your y)
And that's how you got your (2,1) as the center of the parabola
-Hope this helps :)
4
The equation of a circle is x2 + y2 + x + Dy+ E= 0. If the radius of the circle is decreased without changing the coordinates of the center point, how are the coefficients CD,
and E affected?
O A CD, and E are unchanged.
Answers
Answer:
Step-by-step explanation:
in x²+y²+2gx+2fy+c=0
center=(-g,-f)
radius=√((-g)²+(-f)²-c)
if center is not changed ,then c will change .
Here only coefficients of E will change.
A metal alloy is 27% copper. Another metal alloy is 52% copper. How much of each should be used to make 22 g of an alloy that is 36.09% copper?
Answers
Answer:
14.0008 grams of 27% and 7.9992 grams of 52%
Step-by-step explanation:
We know that in the end we want 22 grams of 36.09% copper, meaning in the end we want 36.09% of the 22 grams to be copper. This means we can multiply 36.09% by 22 to see how much copper we want in the end.
To find out how much of each alloy to use, we can multiply the percentage of copper in the alloy be a variable x, which will be how much of that alloy we use. For the other alloy, we can multiply the percentage by (22-x) grams as we know in the end we want 22 grams and if x+y=22, than y would equal 22-x, and in this case this simplifies it to only use a single variable.
Now finally, making the equation we get 27x+52(22-x)=36.09(22). We can solve this and get 27x+1144-52x=793.98, then combine like terms and get -25x+1144=793.98. Next you have to subtract 1144 from both sides to get -25x=-350.02. Dividing both sides by -25 we get x=14.0008. This is how many grams of 27% copper was used. Now we can subtract this from 22 to get how much 52% copper was used, and we get 22-14.0008=7.9992 grams of 52% copper.
7.1 A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then she wins one-half of the value that appears on the die. Determine her expected winnings.
Answers
Answer:
1.875
Step-by-step explanation:
To find the expected winnings, we need to find the probability of all cases possible, multiply each case by the value of the case, and sum all these products.
In the die, we have 6 possible values, each one with a probability of 1/6, and the value of each output is half the value in the die, so we have:
[tex]E_1 = \frac{1}{6}\frac{1}{2} + \frac{1}{6}\frac{2}{2} +\frac{1}{6}\frac{3}{2} +\frac{1}{6}\frac{4}{2} +\frac{1}{6}\frac{5}{2} +\frac{1}{6}\frac{6}{2}[/tex]
[tex]E_1 = \frac{1}{12}(1+2+3+4+5+6)[/tex]
[tex]E_1 = \frac{21}{12} = \frac{7}{4}[/tex]
Now, analyzing the coin, we have heads or tails, each one with 1/2 probability. The value of the heads is 2 wins, and the value of the tails is the expected value of the die we calculated above, so we have:
[tex]E_2 = \frac{1}{2}2 + \frac{1}{2}E_1[/tex]
[tex]E_2 = 1 + \frac{1}{2}\frac{7}{4}[/tex]
[tex]E_2 = 1 + \frac{7}{8}[/tex]
[tex]E_2 = \frac{15}{8} = 1.875[/tex]
Jeremy makes $57,852 per year at his accounting firm. How much is Jeremy’s monthly salary? (There are 12 months in a year.) How much is Jeremy’s weekly salary? (There are 52 weeks in a year.)
Answers
Answer:
Monthly: $4,821
Weekly: $1112.54
Step-by-step explanation:
Monthly
A monthly salary can be found by dividing the yearly salary by the number of months.
salary / months
His salary is $57,852 and there are 12 months in a year.
$57,852/ 12 months
Divide
$4,821 / month
Jeremy makes $4,821 per month.
Weekly
To find the weekly salary, divide the yearly salary by the number of weeks.
salary / weeks
He makes $57,852 each year and there are 52 weeks in one year.
$57,852 / 52 weeks
Divide
$1112.53846 / week
Round to the nearest cent. The 8 in the thousandth place tells use to round the 3 up to a 4 in the hundredth place.
$1112.54 / week
Jeremy makes $1112.54 per week
The additive inverse of x/y is
Answers
Answer
The additive inverse is
-x/-y
That is equal to x/y
hope this may help you
Heather is writing a quadratic function that represents a parabola that touches but does not cross the x-axis at x = –6. Which function could Heather be writing? f(x) = x2 + 36x + 12 f(x) = x2 – 36x – 12 f(x) = –x2 + 12x + 36 f(x) = –x2 – 12x – 36
Answers
Answer:
f(x) = –x^2 – 12x – 36
Step-by-step explanation:
The parent function, x^2, touches the x-axis at x=0. Translating it 6 units left replaces x with x-(-6) = x+6, so the function is ...
f(x) = (x+6)^2 = x^2 +12x +36
Reflecting the graph across the x-axis doesn't change the x-intercept, so Heather could be writing ...
f(x) = -x^2 -12x -36
It's D.
I have to have at least 20 characters.
Find the area of the irregular figure. Round to the nearest hundredth.
Answers
Answer:
23.14
Step-by-step explanation:
Solve for the area of the figure by dividing it up into parts. You can divide into a half-circle and a triangle
Half-Circle
The diameter is 6. This means that the radius is 3. Use the formula for area of a circle. Divide the answer by two since you only have a half-circle.
A = πr²
A = π(3)²
A = 9π
A = 28.274
28.274/2 = 14.137
Triangle
The base is 3 and the height 6. Use the formula for area of a triangle.
A = 1/2bh
A = 1/2(6)(3)
A = 3(3)
A = 9
Add the two areas together.
14.137 + 9 = 23.137 ≈ 23.14
The area is 23.14.
Answer:
23 sq. unitsStep-by-step explanation:
The figure consists of a semi circle and a triangle
Area of the figure = Area of semi circle + Area of triangle
Area of semi circle is 1/2πr²
where r is the radius
radius = diameter/2
radius = 6/2 = 3
Area of semi circle is
1/2π(3)²
1/2×9π
14.14 sq. units
Area of a triangle is 1/2×b×h
h is the height
b is the base
h is 6
b is 3
Area of triangle is
1/2×3×6
9 sq. units
Area of figure is
14.14 + 9
= 23.14
Which is 23 sq. units to the nearest hundredth
Hope this helps you.
7. The mean age at first marriage for respondents in a survey is 23.33,
with a standard deviation of 6.13. For an age at first marriage of 33.44,
the proportion of area beyond the Z score associated with this age is
.05. What is the percentile rank for this score?
Answers
Answer:
[tex] \mu = 23.33, \sigma =6.13[/tex]
And for this case we are analyzing the value os 33.44 and we can use the z score formula given by:
[tex] z=\frac{X -\mu}{\sigma}[/tex]
And replacing we got:
[tex] z=\frac{33.44 -23.33}{6.13}= 1.649[/tex]
We know that the proportion of area beyond the Z score associated with this age is .05 so then the percentile would be: 95
Step-by-step explanation:
For this case we have the following parameters:
[tex] \mu = 23.33, \sigma =6.13[/tex]
And for this case we are analyzing the value os 33.44 and we can use the z score formula given by:
[tex] z=\frac{X -\mu}{\sigma}[/tex]
And replacing we got:
[tex] z=\frac{33.44 -23.33}{6.13}= 1.649[/tex]
We know that the proportion of area beyond the Z score associated with this age is .05 so then the percentile would be: 95
The slope of the line passing through the points (7, 5) and (21, 15) is
Answers
Answer:
5/7
Step-by-step explanation:
We are given two points so we can find the slope by using
m = (y2-y1)/(x2-x1)
= (15-5)/(21-7)
=10/14
5/7
the ellipse is centered at the origin, has axes of lengths 8 and 4, its major axis is horizontal. how do you write an equation for this ellipse?
Answers
Answer:
The equation for this ellipse is [tex]\frac{x^{2}}{64} + \frac{y^{2}}{16} = 1[/tex].
Step-by-step explanation:
The standard equation of the ellipse is described by the following expression:
[tex]\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}} = 1[/tex]
Where [tex]a[/tex] and [tex]b[/tex] are the horizontal and vertical semi-axes, respectively. Given that major semi-axis is horizontal, [tex]a > b[/tex]. Then, the equation for this ellipse is written in this way: (a = 8, b = 4)
[tex]\frac{x^{2}}{64} + \frac{y^{2}}{16} = 1[/tex]
The equation for this ellipse is [tex]\frac{x^{2}}{64} + \frac{y^{2}}{16} = 1[/tex].
In a survey, 205 people indicated they prefer cats, 160 indicated they prefer dots, and 40 indicated they don’t enjoy either pet. Find the probability that if a person is chosen at random, they prefer cats
Answers
Answer: probability = 0.506
Step-by-step explanation:
The data we have is:
Total people: 205 + 160 + 40 = 405
prefer cats: 205
prefer dogs: 160
neither: 40
The probability that a person chosen at random prefers cats is equal to the number of people that prefer cats divided the total number of people:
p = 205/405 = 0.506
in percent form, this is 50.6%
The width of a casing for a door is normally distributed with a mean of 24 inches and a standard deviation of 1/8 inch. The width of a door is normally distributed with a mean of 23 7/8 inches and a standard deviation of 1/16 inch. Assume independence. a. Determine the mean and standard deviation of the difference between the width of the casing and the width of the door. b. What is the probability that the width of the casing minus the width of the door exceeds 1/4 inch? c. What is the probability that the door does not fit in the casing?
Answers
Answer:
a) Mean = 0.125 inch
Standard deviation = 0.13975 inch
b) Probability that the width of the casing minus the width of the door exceeds 1/4 inch = P(X > 0.25) = 0.18673
c) Probability that the door does not fit in the casing = P(X < 0) = 0.18673
Step-by-step explanation:
Let the distribution of the width of the casing be X₁ (μ₁, σ₁²)
Let the distribution of the width of the door be X₂ (μ₂, σ₂²)
The distribution of the difference between the width of the casing and the width of the door = X = X₁ - X₂
when two independent normal distributions are combined in any manner, the resulting distribution is also a normal distribution with
Mean = Σλᵢμᵢ
λᵢ = coefficient of each disteibution in the manner that they are combined
μᵢ = Mean of each distribution
Combined variance = σ² = Σλᵢ²σᵢ²
λ₁ = 1, λ₂ = -1
μ₁ = 24 inches
μ₂ = 23 7/8 inches = 23.875 inches
σ₁² = (1/8)² = (1/64) = 0.015625
σ₂ ² = (1/16)² = (1/256) = 0.00390625
Combined mean = μ = 24 - 23.875 = 0.125 inch
Combined variance = σ² = (1² × 0.015625) + [(-1)² × 0.00390625] = 0.01953125
Standard deviation = √(Variance) = √(0.01953125) = 0.1397542486 = 0.13975 inch
b) Probability that the width of the casing minus the width of the door exceeds 1/4 inch = P(X > 0.25)
This is a normal distribution problem
Mean = μ = 0.125 inch
Standard deviation = σ = 0.13975 inch
We first normalize/standardize 0.25 inch
The standardized score of any value is that value minus the mean divided by the standard deviation.
z = (x - μ)/σ = (0.25 - 0.125)/0.13975 = 0.89
P(X > 0.25) = P(z > 0.89)
Checking the tables
P(x > 0.25) = P(z > 0.89) = 1 - P(z ≤ 0.89) = 1 - 0.81327 = 0.18673
c) Probability that the door does not fit in the casing
If X₂ > X₁, X < 0
P(X < 0)
We first normalize/standardize 0 inch
z = (x - μ)/σ = (0 - 0.125)/0.13975 = -0.89
P(X < 0) = P(z < -0.89)
Checking the tables
P(X < 0) = P(z < -0.89) = 0.18673
Hope this Helps!!!
For a certain salesman, the probability of selling a car today is 0.30. Find the odds in favor of him selling a car today.
Answers
Answer:
The odds in favor of him selling a car today are 3 to 10
Step-by-step explanation:
Probability and odds:
Suppose we have a probability p.
The odds are of: 10p to 10
In this question:
Probability of selling a car is 0.3.
10*0.3 = 3
So the odds in favor of him selling a car today are 3 to 10
[!] Urgent [!] Find the domain of the graphed function.
Answers
The problem is: On a Map, 3 inches represents 40 miles, How many inches represents 480 miles?
Answers
480/40=12
12x3=36
Simplify the expression (5j+5) – (5j+5)
Answers
Answer:
0
Step-by-step explanation:
multiply the negative thru the right part of the equation so, 5j+5-5j-5. The 5j and the 5 than cancel out with each other. Hope this helps!
Answer:
0
Explanation:
step 1 - remove the parenthesis from the expression
(5j + 5) - (5j + 5)
5j + 5 - 5j - 5
step 2 - combine like terms
5j + 5 - 5j - 5
5j - 5j + 5 - 5
0 + 0
0
therefore, the simplified form of the given expression is 0.
what is the axis of symmetry of f(x)=-3(x+2)^2+4
Answers
Answer:
line passes through the vertex
Step-by-step explanation:
f(x)=-3(x+2)^2+4
x=-2 it is the x of the vertex
Evaluate the expression (image provided). A.) 1.5 B.) 6 C.) 6^15 D.) 1.5^6
Answers
Answer:
1.5
Step-by-step explanation:
6 to the log base of 6 will be one (they essentially cancel each other out, log is the opposite of exponents) and we are left with 1.5.
a) Al usar un microscopio el microscopio se amplía una célula 400 veces. Escribe el factor de ampliación como cociente o como escala.
b) La imagen de una célula usando dicho microscopio mide 1,5 mm ¿ Cuánto mide la célula en la realidad?
Answers
Answer:
x = 0,00375 mm
Step-by-step explanation:
a) El factor de ampliación es 400/1 es decir el tamaño real se verá ampliado 400 veces mediante el uso del microscopio
b) De acuerdo a lo establecido en la respuesta a la pregunta referida en a (anterior) podemos establecer una regla de tres, según:
Si al microscopio el tamaño de la célula es 1,5 mm, cual será el tamaño verdadero ( que es reducido 400 en relación al que veo en el microscopio)
Es decir 1,5 mm ⇒ 400
x (mm) ⇒ 1 (tamaño real de la célula)
Entonces
x = 1,5 /400
x = 0,00375 mm
The following data represent the miles per gallon for a particular make and model car for six randomly selected vehicles. Compute the mean, median, and mode miles per gallon 24.2. 22.2. 37.8, 22.7. 35 4. 31.61. Compute the mean miles per gallon. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The mean mileage per gallon is _______B. The mean does not exist 2. Compute the median miles per gallon. Select the correct choice below and, if necessary, fill in the answer box to complete your choice A. The median mileage per gallon is __________B. The median does not exist. 3. Compute the mode miles per gallon. Select the correct choice below and, if necessary,fill in the answer box to complete your choice. A. The mode is _________B. The mode does not exist.
Answers
Answer:
A. The mean mileage per gallon is _____ 28.99__
A. The median mileage per gallon is _____27.905_____
B. The mode does not exist.
Step-by-step explanation:
Mean= Sum of values/ No of Values
Mean = 24.2 + 22.2+ 37.8+ 22.7 + 35.4 +31.61/ 6
Mean = 173.91/6= 28.985 ≅ 28.99
The median is the middle value of an ordered data which divides the data into two equal halves. For an even data the median is the average of n/2 and n+1/2 value where n is the number of values.
Rearranging the above data
22.2 , 22.7 , 24.2 , 31.61 , 35.4, 37.8
Third and fourth values are =24.2 + 31.61 = 55.81
Average of third and fourth values is = 55.81/2= 27.905
Mode is the values which is occurs repeatedly.
In this data there is no mode.
Silver Lake has a population of 114,000. The population is decreasing at a rate of 1.5% each year. Which of the following choices is the correct function? a p(s) = 114000• 0.985x b p(s) = 114000x c p(s) = 114000x + 0.985 d None of these choices are correct.
Answers
Answer: D
Step-by-step explanation:
According to the question, Silver Lake has a population of 114,000. The population is decreasing at a rate of 1.5% each year
The initial population Po = 114000
Rate = 1.5% = 0.015
The declining population formula will be:
P = Po( 1 - R%)x^2
The decay formula
Since the population is decreasing, take away 0.015 from 1
1 - 0.015 = 0.985
Substitutes all the parameters into the formula
P(s) = 114000(0.985)x^2
P(s) = 114000× 0985x^2
The correct answer is written above.
Since option A does not have square of x, we can therefore conclude that the answer is D - non of the choices is correct.
Fill in the table using this function rule.
Answers
Answer:
1, 2.2, 5.5, 10.2.
Step-by-step explanation: these are simplified to the nearest tenth
Given a right triangle with a hypotenuse length of radical 26 and base length of 3. Find the length of the other leg (which is also the height).
Answers
Answer:
√17
Step-by-step explanation:
The Pythagorean theorem can be used for the purpose.
hypotenuse² = base² +height²
(√26)² = 3² +height²
26 -9 = height²
height = √17
The length of the other leg is √17.
Determine the logarithmic regression of the data below using either a calculator or spreadsheet program. Then, estimate the x−value when the y−value is 5.2. Round your answer to one decimal place. (4.7,10.7),(7.8,20.6),(10.5,30.2),(15.6,41),(20.8,56.1),(22,65.1). Please help right away! Thank you so much!
Answers
Answer:
y ≈ 33.7·ln(x) -45.94.6Step-by-step explanation:
A graphing calculator can perform logarithmic regression, as can a spreadsheet. The least-squares best fit log curve is about ...
y ≈ 33.7·ln(x) -45.9
The value of x estimated to make y = 5.2 is about 4.6.
The mean MCAT score 29.5. Suppose that the Kaplan tutoring company obtains a sample of 40 students with a mean MCAT score of 32.2 with a standard deviation of 4.2. Test the claim that the students that took the Kaplan tutoring have a mean score greater than 29.5 at a 0.05 level of significance.
Answers
Answer:
We conclude that the students that took the Kaplan tutoring have a mean score greater than 29.5.
Step-by-step explanation:
We are given that the Kaplan tutoring company obtains a sample of 40 students with a mean MCAT score of 32.2 with a standard deviation of 4.2.
Let [tex]\mu[/tex] = population mean score
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] 29.5 {means that the students that took the Kaplan tutoring have a mean score less than or equal to 29.5}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 29.5 {means that the students that took the Kaplan tutoring have a mean score greater than 29.5}
The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean MCAT score = 32.2
s = sample standard deviation = 4.2
n = sample of students = 40
So, the test statistics = [tex]\frac{32.2-29.5}{\frac{4.2}{\sqrt{40} } }[/tex] ~ [tex]t_3_9[/tex]
= 4.066
The value of t-test statistics is 4.066.
Now, at 0.05 level of significance, the t table gives a critical value of 1.685 at 39 degrees of freedom for the right-tailed test.
Since the value of our test statistics is more than the critical value of t as 4.066 > 1.685, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we conclude that the students that took the Kaplan tutoring have a mean score greater than 29.5.
The Marine Corps is ordering hats for all the new recruits for the entire next year. Since they do not know the exact hat sizes they will use statistics to calculate the necessary numbers. This is the data from a sample of the previous recruits: 7.2, 6.8, 6, 6.9, 7.8, 6.2, 6.4, 7.2, 7.4, 6.8, 6.7, 6, 6.4, 7, 7, 7.6, 7.6, 6, 6.8, 6.4 a. Display the data in a line plot and stem-and-leaf plot. (These plots don’t need to be pretty; just make sure I can make sense of your plots.) Describe what the plots tell you about the data. b. Find the mean, median, mode, and range. c. Is it appropriate to use a normal distribution to model this data? d. Suppose that the Marine Corps does know that the heights of new recruits are approximately normally distributed with a mean of 70.5 inches and a standard deviation of 1.5 inches. Use the mean and standard deviation to fit the new recruit heights to a normal distribution and estimate the following percentages. d1. What percent of new recruits would be taller than 72 inches? d2. What percent of new recruits would be shorter than 67.5 inches? d3. What percent of new recruits would be between 69 and 72 inches? d4. Between what two heights would capture 95% of new recruits?? By using statistics are the numbers changed to whole numbers?
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This is a stem and leaf plot.
mean is 138.2/20=6.91
median of 20 is half way between 10th and 11th or an ordered plot. The 10th and the 11th are both 6.8, so that is the median.
6.4 and 6.8 are modes, but they are so minimal I would say there isn't a clear mode.
The range is 1.8, the largest-the smallest
This is not a normal distribution.
z=(x-mean) sd
a.(72-70.5)/1.5=1 so z>1 is the probability or 0.1587.
b.shorter than 67.5 inches is (67.5-70.5)/1.5 or z < = -2, and probability is 0.0228.
c.Between 69 and 72 inches is +/- 1 sd or 0.6826.
95% is 1.96 sd s on either side or +/- 1.96*1.5=+/- 2.94 interval on either side of 70.5
(67.56, 73.44)units in inches
Step-by-step explanation: