Answer:
a) Approximately normal.
b) The mean is 75 years and the standard deviation is 0.8485 years.
c) 0.9909 = 99.09% probability that the mean age exceeds 73 years
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Sample of 50 retirees
This means that [tex]n = 50[/tex]
Mean age and standard deviation are 75 and 6 years
This means that [tex]\mu = 75, \sigma = 6[/tex]
a. Describe the shape of the sampling distribution of the sample mean in this case
By the Central Limit Theorem, approximately normal.
b. Find the mean and standard error of the sampling distribution of the sample mean.
By the Central Limit Theorem, the mean is 75 and the standard error is [tex]s = \frac{6}{\sqrt{50}} = 0.8485[/tex]
c. What is the probability that the mean age exceeds 73 years?
This is 1 subtracted by the pvalue of Z when X = 73.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{73 - 75}{0.8485}[/tex]
[tex]Z = -2.36[/tex]
[tex]Z = -2.36[/tex] has a pvalue of 0.0091
1 - 0.0091 = 0.9909
0.9909 = 99.09% probability that the mean age exceeds 73 years
log8(216)+[log(42)_log(6)]÷log(49)
Answer:
3 log (3) + 1/2Step-by-step explanation:
log8(216) + [log(42) - log(6)] ÷ log(49) =log (216)/ log (8) + [log (7) + log (6) - log (6)] ÷ 2 log (7) =3 log (3) log (2) / 3 log (2) + log (7) / 2 log (7) = 3 log (3) + 1/2what is x in 5x - ((2x-1)÷2) = 5
Answer:
5x - ((2x-1)÷2) = 5-----(1)
(1) multiply by 2;
2 *(5x - ((2x-1)÷2) = 5)
10x - (2x-1) = 10
10x - 2x + 1 = 10
8x + 1 =10
8x = 10-1
x=9 /8
Step-by-step explanation:
Answer:
x = 9/8
Step-by-step explanation:
5x - ((2x - 1) ÷ 2) = 5
2 × (5x - ((2x - 1) ÷ 2) = 5
10x - (2x-1) = 10
10x - 2x + 1 = 10
8x + 1 = 10
8x + 1 - 1 = 10 - 1
8x = 10 - 1
8x = 9
8x ÷ 8 = 9 ÷ 8
x = 9 ÷ 8
x = 9/8 or 1 and 1/8
WILL MARK BRAINLIST
The second story gutters of a house need to be cleaned. The gutters are 18.7 ft. high on the house. If a ladder will be placed 6 ft. from the base of the house, how long will the ladder need to be to reach the gutters? Round to the nearest foot. *
A. 18 ft
B. 19 ft
C. 20 ft
D. 21 ft
Answer:
C. 20 Ft.
Step-by-step explanation:
Using The Pythagorean Theorem, a²+b²=c² , insert the known variables into the equation.
18.7²+6²=c²
This gives you 385.69 + 36 = 385.69.
Next, square the result to find the missing side length.
[tex]\sqrt{385.69[/tex]
The answer comes out to around 19.6, which can be rounded up to 20ft.
Hope this helped!
If 45/60 is equivalent to 3/x, find the value of x
find the circumference of the circle. PLEASE HELP I HAVE 5 MINUTES LEFT :(
Answer:
18.84
Step-by-step explanation:
How to find the value of x
Step-by-step explanation:
To find the value of x bring the variables to the left side and bring all what remained values to the right side and then simplify them to find the answer or the result hope I helped and a have a good luck
HELP ME PLEASE ❗❗❗❗
What is the value of Q3 of the data represented by the box plot?
Enter your answer in the box.
Answer:
Q3 = 30
Step-by-step explanation:
minimum value = 5
Q1 = 20 (this is the median of the lower half of data)
Median (sometimes called Q2) = 25
Q3 = 30 (this is the median of the upper half of data)
maximum value = 45
given that the circumference of an orange us 50.24mm find the volume of the orange
Answer: 803mm
Step-by-step explanation:
Simplify.
(5+squartrt3)2
25 + sqrtrt10
10 + 28sqrtrt3
28 + 10sqrtrt3
Answer:
Step-by-step explanation:
If the 2 is an exponent, it needs to be written as ^2.
(5+√3)² = 5² + 10√3 + 3 = 28 + 10√3
Is this A,B,C or D helppppp
Answer:
D
Step-by-step explanation:
D goes thru positive 4 and negative 3
Write 5x – 4y = 10 in slope-intercept form
A plane flying horizontally at an altitude of 1 mile and a speed of 460 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 2 miles away from the station. (Round your answer to the nearest whole number.)
Answer:
The rate increases at 398mi/h
Step-by-step explanation:
Given
[tex]\frac{dx}{dt} = 460mi/h[/tex] --- rate when [tex]y = 2[/tex] --- distance
The given parameters is represented with the attached figure
Using Pythagoras theorem [take the attached image as a point of reference]
[tex]y^2 = x^2 + 1^2[/tex]
[tex]y^2 = x^2 + 1[/tex]
Differentiate with respect to time (t):
[tex]2y \frac{dy}{dt} = 2x \frac{dx}{dt}[/tex]
Divide both sides by 2
[tex]y \frac{dy}{dt} = x \frac{dx}{dt}[/tex] --- (1)
When y = 2:
[tex]y^2 = x^2 + 1^2[/tex] --- Pythagoras Theorem
[tex]2^2 = x^2 + 1[/tex]
[tex]4 = x^2 + 1[/tex]
Collect like terms
[tex]x^2 = 4 -1[/tex]
[tex]x^2 = 3[/tex]
Solve for x
[tex]x = \sqrt 3[/tex]
So:
[tex]y \frac{dy}{dt} = x \frac{dx}{dt}[/tex]
Substitute: [tex]x = \sqrt 3[/tex], [tex]\frac{dx}{dt} = 460mi/h[/tex] and [tex]y = 2[/tex]
[tex]2 * \frac{dy}{dt} = \sqrt 3 * 460[/tex]
[tex]2 * \frac{dy}{dt} = 460\sqrt 3[/tex]
Divide by 2
[tex]\frac{dy}{dt} = 230\sqrt 3[/tex]
[tex]\frac{dy}{dt} = 230*1.7321[/tex]
[tex]\frac{dy}{dt} = 398.383[/tex]
[tex]\frac{dy}{dt} \approx 398[/tex]
students at Westbrook middle school hold green team meetings
please help with this algebra question
Answer:
i think its
[tex]P(x) = i ^{3}[/tex]
Step-by-step explanation:
which multiplication equation describes the picture of the third pies below?
Answer:4x1/3=4/3
Step-by-step explanation:
In the pictures there’s 4 one thirds and if u add them together is 4/3
What is x and y please help
Answer:
The letter "x" is often used in algebra to mean a value that is not yet known. It is called a "variable" or sometimes an "unknown". In x + 2 = 7, x is a variable, but we can work out its value if we try! A variable doesn't have to be "x", it could be "y", "w" or any letter, name or symbol.
Step-by-step explanation:
The base of the pyramid is a right triangle
The volume is ____ cubic cm.
Answer:
37 cubic cm should be the answer sorry if I am wrong
f^-1(x)= -3+^3 squareroot x+4 is the inverse function of f(x)= (x-3)^3 +4 true or false
In a certain tropical forest, litter (mainly dead vegetation such as leaves and vines) forms on the ground at the rate of 10 grams per square centimeter per year. At the same time, however, the litter is decomposing at the rate of 80% per year. Let f(t) be the amount of litter (in grams per square centimeter) present at time t. Find a differential equation satisfied by f(t).
Answer:
df(t)/dt = 10 - 0.8f(t)
Step-by-step explanation:
The net rate of change, df(t)/dt = rate in - rate out
The rate in = rate litter forms on ground = 10 g/cm²/yr
Since f(t) is the amount of litter present at time, t, in g/cm² the rate out = rate of decomposition = the percentage rate × f(t) = 80% per year × f(t) = 0.8f(t) g/cm²/yr
Since df(t)/dt = rate in - rate out
df(t)/dt = 10 - 0.8f(t)
So the desired differential equation is
df(t)/dt = 10 - 0.8f(t)
Which statement are true regarding undefinable terms in geometry
Answer: A plane has two dimensions because it is a flat surface that has length and width but no depth.
Answer:
Surface answer
Step-by-step explanation:
Because the surface has a length and width and does not have a depth
A builder is buying property where she can build new houses. The line plot shows the sizes of the lots for each house. How many acres does the builder buy? *
X. X. X
X X. X
X. X. X
X. X x
X. X x
X 2/6 3/6
X
X
X
X
X
1/6
Answer:
can you send me a pic of how it looks because it's confusing to understand
PLEASE HELP ME 30 points!!!
Multiple Choice
Eighteen students in a class play baseball.
Seventeen students in the class play basketball.
Thirty students in the class play either or both sports
Select the Venn diagram that shows the number of students who play basketball and baseball.
Answer:
A
Step-by-step explanation:
its a bec count how many student are their an see if they add IP to 30
The Venn diagram which shows the number of students who play basketball and baseball is option A.
What is Venn Diagram?Venn diagram is a diagram denoting two or more sets which is drawn using circles inside a rectangle where the part where the two circle meet denotes the intersection of two sets.
Let A denotes the students playing baseball and B denotes the student playing basketball.
N(A) = 18
N(B) = 17
N(A ∪ B) = 30
We know,
N(A ∩ B) = N(A) + N(B) - N(A ∪ B)
= 18 + 17 - 30
= 35 - 30
= 5
Number of students who play both baseball and basketball = 5
Number of students who plays only baseball = 18 - 5 = 13
Number of students who plays only basketball = 17 - 5 = 12
This is shown in A.
Hence the correct option is A.
Learn more about Venn Diagrams here :
https://brainly.com/question/1605100
#SPJ2
PLZ HELP ASAP 30 POINTS (Plz show work)
Choose a trinomial to factor.
3x2 − 15x + 18
10a2 + 5a − 30
4n2 − 10n − 24
Answer:
x=6 x=-1
a=1.5 a=-2
n=-1.5 n=4
Step-by-step explanation:
(a) (b) (c)
10a2+5a-30
x=-b+-√b2-4ac/2a
a=-5+-√(5)2-4(10)(-30)/2(10)
a=-5+-√25+1200/20
a=-5+-√1225/20
a=-5+√1225/20
a=1.5
a=-5-√1225/20
a=-2
Find the equation of the line that is perpendicular to y=1/3x+10 and passes through (3,-4)
Answer:
Step-by-step explanation:
1. perpendicular slope will be the negative of the reciprocal
2. so this will be -3 ( since the reciprocal of 1/3 is 3 and its negative is -3
3. So use the values given for x and y (3,-4)
4. substitute in the given equation using the -3 for the slope instead of 1/3
5. To find a new b we substitute for x and y
5. y = 1/3x + 10
6. -4 = -3 (3) + b
7. -4= -9+ b
8. b = 5
Equation of the line will be y = -3x + 5
how to rewrite equation 5x+7y-35=0 in slope intercept form?
The circle has a circumference of 9.42 units. What is the area of the square? Use 3.14 for π. Explain how you found the answer.
Answer:
7.065 sq. units
Step-by-step explanation:
The circumference is given, thus you can use the equation 2πr = circumference to find out the radius first, r = 1.5.
Area = πr²
∴The required area is 7.065 sq. units
PLEASE HELP ME !!!!!
Answer:
Step-by-step explanation:
1.values of x at y=0 are 1
2.5
3.
(3,-4)
4.
it is a minimum.
5.
axis of symmetry is x=3
Which of the following is true about the expression 7 + V3?
Answer:
is this a multiple-choice question?
Step-by-step explanation:
**i'll go back and change my answer, i promise**
Which graph shows a proportional relationship?
A. B. C D.
Answer:
B
Step-by-step explanation:
a proportional relationship must have a straight line when graphed and it must go through the origin (0,0)
Right off the bat we can eliminate answer choice C because the line is not straight
the answer is not a nor d
the line may be straight but it does not go through the origin therefore it is not a proportional relationship
B makes a straight line and the line goes through the origin therefore B is the answer
Question 3 Matt has yard of fishing line. He uses of the line to make fishing knots. How many yards of fishing line does Matt use to make fishing knots? Show your work Solution
Answer:
aSDFGHJLLMNNBBBBVCDDG
Step-by-step explanation:
