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
A seller has a house that is 1800 square feet. The neighborhood comps show
the line of best fit to be y = 0.074x +50 48. What is a fair price for this house?
A. $150,000
B. $183.68
C. $150.00
D. $184,000
SUBMIT
A fair price for this house is $183.68. Therefore, option B is the correct answer.
What is the equation of a line?The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.
Given that, a seller has a house that is 1800 square feet.
The neighborhood comps show the line of best fit to be y = 0.074x+50.48.
Substitute x=1800 in the given equation, we get
y=0.074×1800+50.48
y=$183.68
Therefore, option B is the correct answer.
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WILL GIVE BRAINLIEST
1522 customers at a major retailer were surveyed whether or not they made a purchase and were satisfied with the service they received. The table below organized the responses
a) a total of 677 were not satisfied. Of these 494 made a purchase 494/677
b) a total of 624 made a purchase. Of these 494 were not satisfied 494/624
Find the arithmetic mean of the sales per day in a fair price shop in a week.
Rs 10000, Rs 10250, Rs 10790, Rs 9865, Rs 15350, Rs 10110.
Answer:
11060.83
Step-by-step explanation:
Sum = 10000 + 10250 + 10790 + 9865 + 15350 + 10110
= 66365
No. of days (N) = 6
Arithmetic mean = Sum/ N
= 66365/6
= 11060.83
Step-by-step explanation:
sum =Rs 10000+ Rs 10250+ Rs 10790+Rs 9865+ Rs 15350+Rs 10110.=rs66365
n=6
mean=sum/n=rs66365/6=11060.833
Finding the area of each
Answer:
C.
HOPE THIS HELPS
-Todo <3
Step-by-step explanation:
2*2=4
Write an equation and solve for the missing anglemeasure.
Equation: _______________________
Angle g = ___________
Answer:
Equation: [tex]143 + g = 180[/tex]
[tex]g =37[/tex]
Step-by-step explanation:
Given
The attached figure
Required
The equation to find g and the solution
From the attached: Angles ACD, DCE and ECB lie on a straight line.
Where
[tex]ACD = 90[/tex] [tex]DCE = 53[/tex] [tex]ECB = g[/tex]
This means that:
[tex]ACD + DCE + ECB = 180[/tex]
[tex]90 + 53 + g = 180[/tex]
[tex]143 + g = 180[/tex]
Subtract 143 from both sides
[tex]-143 + 143 + g = 180 - 143[/tex]
[tex]g = 37[/tex]
POSSIBLE POINTS: 15
A can of soda contains 0.355 liters of soda. How many milliliters of soda are in one can?
Find a coterminal angle between 0 and 360 degrees.
525°
A) 35°
C) 145°
B) 165°
D) 285°
Katie wants to collect over a hundred seashells she already has 34 seashells in her collection each day she finds 12 more seashells on the beach Katie can use fractions of days to find seashells write an equality to determine the number of days D it will take Katie to collect over a 100 seashells. no explanation needed
Answer:
6
Step-by-step explanation:
8ty grade math, please help.
-Find the volume-
Answer:
47.12389 Rounded is 47.12
Step-by-step explanation:
V=πr2h=π·12·15≈47.12389
Find the mean of the sets of data:
2.
12, 67, 34, 10, 78, 78, 49
3. 10,10,13, 13, 45, 21, 67
Answer:
2.) 46.9 3.) 25.6
Step-by-step explanation:
Answer:
2. 46.857
3. 25.571
Step-by-step explanation:
Add all the numbers together and then divide by the number of numbers you added.
12+67+34+10+78+78+49=328
328/7=46.857
10+10+13+13+45+21+67=179
179/7=25.571
Which equation matches this graph ?
Answer:
Wheres the graph??
Step-by-step explanation:
A square pyramid is shown below.
Which shapes could be formed by slicing the square pyramid by a plane? Select all that apply.
A. circle
B. triangle
C. rectangle
D. trapezoid
E. square
Answer:
B and e
Step-by-step explanation:
The shape is a square.
What is a Square Pyramid?'A square pyramid is a three-dimensional geometric shape having a square base and four triangular faces/sides that meet at a single point (called vertex) is called a square pyramid.'
According to the given problem,
If a square pyramid is cut along the plane, then the cross-section of the solid is square. Because it is a square pyramid.
Hence, we concluded that square could be formed by slicing the square pyramid by a plane.
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5k + 9 = 89.............
Answer:
k= 16
Step-by-step explanation:
89-9=80
80/5=16
16=k
Answer:
5k+9=89
5k=89-9
5k=80
k=16
Rewrite the radical as a rational exponent.
Which situation can be solved using the expression shown?
(30)
of the 30 students in the class,
are wearing jackets. How many students in the class are wearing jackets?
of the 30 students in the class, brought their lunch. How many students in the class did not bring their lunch?
In a survey, 2 out of 3 people chose Product A over Product B. If 30 people were surveyed, how many people chose Product B?
In a bag of marbles, 2 out of every 3 marbles are red. If there are 30 red marbles in the bag, what is the total number of marbles in the bag?
Answer:
h
Step-by-step explanation:
2. Which pair of angles is not congruent? F. ∠1 and ∠7 G. ∠3 and ∠5 H. ∠4 and ∠6 I. ∠2 and ∠5
Answer:
I) ∠2 and ∠5
Step-by-step explanation:
A line with a slope of 0 passes through the point (9,5). What is its equation in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
y = 5
Step-by-step explanation:
Any line with a slope of 0 is horizontal, represented by the equation y = a number. That number is the y-value of all the points the line intersects.
We know that that the line intersects (9,5). So, take the y-value of that point and write it into the equation of y = a number. Thus, the answer is y =5.
Suppose a home improvement contractor is painting the walls and ceiling of a rectangular room. The volume of the room is 288 cubic feet. The cost of wall paint is $0.06 per square foot and the cost of ceiling paint is $0.16 per square foot. Let x, y, and z be the length, width, and height of a rectangular room respectively. Identify the room dimensions that result in a minimum cost for the paint and use these dimensions to find the minimum cost for the paint. Round your answer to the nearest cent.
Answer:
The minimum cost is $17.30c
Step-by-step explanation:
Given
[tex]V = 288[/tex] --- Volume
[tex]C_1 = 0.06[/tex] --- cost of wall paint
[tex]C_2 = 0.16[/tex] ---cost of ceiling paint
Required
Minimum cost of paint
The volume is calculated as:
[tex]V =xyz[/tex]
Substitute 288 for V
[tex]288 =xyz[/tex]
Make z the subject
[tex]z = \frac{288}{xy}[/tex]
The surface area is calculated as:
[tex]Area = 2(yz + xz) + xy[/tex]
Because xy represent the dimension of the ceiling and the opposite of the ceiling (the floor) will not be painted. Hence, it does not require a coefficient of 2
The cost is:
[tex]C = 0.06 * 2(yz + xz) + 0.16 * xy[/tex]
Substitute [tex]z = \frac{288}{xy}[/tex]
[tex]C = 0.06 * 2(y*\frac{288}{xy} + x*\frac{288}{xy}) + 0.16 * xy[/tex]
[tex]C = 0.06 * 2(\frac{288}{x} + \frac{288}{y}) + 0.16 * xy[/tex]
[tex]C = 0.12(\frac{288}{x} + \frac{288}{y}) + 0.16 * xy[/tex]
[tex]C = (\frac{34.56}{x} + \frac{34.56}{y}) + 0.16 * xy[/tex]
[tex]C = (\frac{34.56}{x} + \frac{34.56}{y}) + 0.16 xy[/tex]
Differentiate w.r.t x and y
[tex]C_x = -\frac{34.56}{x^2} + 0.16y[/tex]
[tex]C_y = -\frac{34.56}{y^2} + 0.16x[/tex]
By comparison: [tex]x = y[/tex]
Set them equal to 0
[tex]C_y = -\frac{34.56}{y^2} + 0.16x=0[/tex]
[tex]-\frac{34.56}{y^2} + 0.16x=0\\[/tex]
Substitute x for y
[tex]-\frac{34.56}{x^2} + 0.16x=0[/tex]
[tex]0.16x=\frac{34.56}{x^2}[/tex]
Cross multiply
[tex]0.16x^3 = 34.56[/tex]
[tex]x^3 = \frac{34.56}{0.16}[/tex]
[tex]x^3 = 216[/tex]
Take the cube root of both sides
[tex]x = \sqrt[3]{216}[/tex]
[tex]x = 6[/tex]
[tex]x=y= 6[/tex]
Substitute 6 for x and for y in [tex]C = (\frac{34.56}{x} + \frac{34.56}{y}) + 0.16 xy[/tex]
[tex]C = (\frac{34.56}{6} + \frac{34.56}{6}) + 0.16 * 6* 6[/tex]
[tex]C = (\frac{2*34.56}{6}) + 5.76[/tex]
[tex]C = 11.52 + 5.76[/tex]
[tex]C = 17.28[/tex]
[tex]C = 17.3[/tex] --- approximated
Discount, markup, and commission word problems
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A store has a 40% off sale on headphones. With this discount, the price of one pair of headphones is $36.
What is the original price of the pair of headphones?
$
Show Calculator
Stuck? Watch a video or use a hint.
Report a problem
Answer:
90$
Step-by-step explanation:
X(40%) = 36$
X(40/100) =36
40X = 3600
X = 90$
(recheck: 90$ x 40%= 36$)
Susie is paying $568.97 every month for her $150,000 mortgage. If this is a 30 year mortgage, how much interest will she pay over the 30 years of payments?
Answer:
Step-by-step explanation:
Take the paying multiply by months then take the years - the total loan
so you'd have 568.97(12)30-150000=54829.20
I need help with this
Answer:
i need help with this so you can ready
Hi hi dude I just don’t want to play anymore I just don’t want to play
9514 1404 393
Answer:
equation: 8 = v + 5solution: v = 3Step-by-step explanation:
The green line is shown as having a length of 8.
The black line is shown as having two parts that add up to the total length of the black line: v + 5.
The problem statement tells you these are the same length. An equation that says they are equal is ...
8 = v + 5
__
This is solved by subtracting 5 from both sides of the equation.
8 -5 = v +5 -5
Combining like terms gives ...
3 = v
The solution is v = 3.
if 25,m+1,35 are arithmetic sequence then find the value of m
Answer:
m = 29
Step-by-step explanation:
You are counting by fives.
25, 30, 35
m + 1 = 30
m + 1 - 1 = 30 - 1
m = 29
25, (29 + 1), 35
25, 30, 35
The value of m is equal to 29
What is arithmetic sequence?An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.
An arithmetic sequence, therefore, is defined by two parameters, viz. the starting term and the common difference.
We are counting by fives.
m + 1 = 30
Now subtract 1 on both sides;
m + 1 - 1 = 30 - 1
m = 29
Thus substituting the value to find other terms;
25, (29 + 1), 35
The sequence is
25, 30, 35
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HELP PLS WUICK! GIVING OUT BRAINLIST
Answer:
27
reason:
did it recently
Help fjdhddjdhdhhdhdhdufh
What is the recursive formula for the geometric sequence 2, 12, 72, 432,.. ?
[tex]a_{1}=2\\a_{n}=6a_{n-1}[/tex]
The recursive formula is aₙ = 2(6)ⁿ⁻¹.
What is recursive formula?A recursive formula for a geometric sequence with common ratio r is given by aₙ = a₁ rⁿ⁻¹ for n≥2.
Given: 2, 12, 72, 432,..
r= 12/2= 6
a= 2
The recursive formula for the nth term,
aₙ = a₁ rⁿ⁻¹
aₙ = 2(6)ⁿ⁻¹
Hence, the recursive formula is aₙ = 2(6)ⁿ⁻¹
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What is her average?
Answer:
95
Step-by-step explanation:
88 + 95 + 97 + 100 = 380
380 ÷ 4 = 95
To find the average you add all the numbers together and then divide that answer depending on how many numbers there are for example there were 4 numbers in this problem so I divided by 4.
Hoped this helped you!! If you have any other questions about what I said you can ask me :) Have a great day!
find the area of this polygon - PLZZZZZ HELP I WILL GIVE 30 points T^T
Answer:
82 m should be correct i hope
Step-by-step explanation:
I'm in the test and need help please
Graph the solution to the following linear Inequality