Answer:
hello your question is incomplete below is the complete question
A company's human resources department was interested in the average number of years that a person works before retiring. The sample of size 11 follows: 12 16 18 19,21 21, 21,22 24 24 26What is the arithmetic mean, median and mode? what is the most likely shape of the distribution
answer :
i) mean = 20.36
ii) median = 21
iii) mode = 21
iv) The most likely shape is a Bell - shaped curve
Step-by-step explanation:
sample size = 11
values ( observations ) = 12, 16, 18, 19,21,21,21,22,24,24,26
i) mean
= ∑ values / sample size = 224 / 11 = 20.36
ii) median
median is the value of the data located at the center of the string of data
to determine the middle position = ( n+1 / 2 )
where n = sample size
hence position of median value = 11 + 1 / 2 = 12 / 2 = 6
the value at the 6th position = 21 ( median )
iii) mode
mode = most repeated value in the series of data
hence mode value = 21
Suppose that the distribution of IQ's of North Catalina State University's students can be approximated by a normal model with mean 130 and standard deviation 8 points. Also suppose that the distribution of IQ's of Chapel Mountain University's students can be approximated by a normal model with mean 120 and standard deviation 10 points.
Required:
What is the probability that the mean IQ of the 3 North Catalina students is at least 5 points higher than the mean IQ of the 3 Chapel Mountain students?
Answer:
0.7517 = 75.17% probability that the mean IQ of the 3 North Catalina students is at least 5 points higher than the mean IQ of the 3 Chapel Mountain students
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.
Subtraction of normal variables:
When we subtract normal variables, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.
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.
North Catalina:
Population has mean 130 and standard deviation 8 points. Sample of 3. This means that:
[tex]\mu_{N} = 130, s_{N} = \frac{8}{\sqrt{3}} = 4.6188[/tex]
Chapel Mountain:
Population has mean 120 and standard deviation 10 points. Sample of 3. This means that:
[tex]\mu_{C} = 120, s_{C} = \frac{10}{\sqrt{3}} = 5.7735[/tex]
What is the probability that the mean IQ of the 3 North Catalina students is at least 5 points higher than the mean IQ of the 3 Chapel Mountain students?
We want that: [tex]N - C > 5[/tex]
Distribution N - C:
The mean is:
[tex]\mu = \mu_N - \mu_C = 130 - 120 = 10[/tex]
The standard deviation is:
[tex]s = \sqrt{s_N^2+s_C^2} = \sqrt{4.6188^2+5.7735^2} = 7.3937[/tex]
This probability is 1 subtracted by the pvalue of Z when X = 5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{5 - 10}{7.3937}[/tex]
[tex]Z = -0.68[/tex]
[tex]Z = -0.68[/tex] has a pvalue of 0.2483
1 - 0.2483 = 0.7517
0.7517 = 75.17% probability that the mean IQ of the 3 North Catalina students is at least 5 points higher than the mean IQ of the 3 Chapel Mountain students
Ella ran 6 times around her school building. Then she ran 4 miles home.
Her phone told her that she ran 7 miles total.
Select an equation that represents this situation
A. 6+4x=7 B. 6x+4=7 C. 6 (x+4) =7
Determine the value of x.
Answer:
B.6x+4=7
Step-by-step explanation:
x represents how many miles is around her school building which she did 6 times, 4 miles is for the amount she ran home and 7 miles is the combination of the 6 times the miles around her school, 6x and the miles she ran home 4
making the equation 6x+4=7
Can someone help me
Answer:
sorry sorry sorry
Step-by-step explanation:
I don't know
Can someone please help me with these 2 problems
Answer:
uhururfjfhfufjfjfjfjfjfif
Answer:
I believe the first one is 250
the second one I haven't got a clue
find the difference between 1, 407 and 699
Answer:708
Step-by-step explanation:
URGENT I NEED HELP FIRST PERSON WHO ANSWERS I'LL GIVE BRAINLYEST
A cylindrical vase has a diameter of 6 inches. At the bottom of the vase, there are 9 marbles, each of diameter 3 inches. The vase is filled with water up to a height of 12 inches.
Which of the following could be used to calculate the volume of water in the vase?
π(3in)2(12in) − 1.5(four over threeπ(9in)3)
π(12in)2(3in) − 1.5(four over threeπ(9in)3)
π(3in)2(12in) − 9(four over threeπ(1.5in)3)
π(12in)2(3in) − 9(four over threeπ(1.5in)3)
Answer:
C. π(3in)2(12in) − 9(four over threeπ(1.5in)3)Step-by-step explanation:
Volume of water is the difference of volume of vase at 12 in height and the total volume of marbles.
Volume of cylinder up to water level:
Vs = πr²h = π(6/2)²(12) = π×(3 in)²×(12 in)Volume of marbles:
Vm = 9(4/3πr³) = 9×(4/3×π(3/2)³) = 9×(4/3×π×(1.5 in)³)Volume of water:
Vw = Vs - Vm = π×(3 in)²×(12 in) - 9×(4/3×π×(1.5 in)³)Correct choice is C
Answer:
C. π(3in)2(12in) − 9(four over threeπ(1.5in)3)
Step-by-step explanation:
Volume of water is the difference of volume of vase at 12 in height and the total volume of marbles.
Volume of cylinder up to water level:
Vs = πr²h = π(6/2)²(12) = π×(3 in)²×(12 in)
Volume of marbles:
Vm = 9(4/3πr³) = 9×(4/3×π(3/2)³) = 9×(4/3×π×(1.5 in)³)
Volume of water:
Vw = Vs - Vm = π×(3 in)²×(12 in) - 9×(4/3×π×(1.5 in)³)
Correct choice is C
Helpp with math!!!!!!!!
I think the area is 63. Sorry if it is incorrect.
help with math please will give 5 stars and brainlyist
k+12=23
plsssss help
A rectangular piece of metal is 30 in longer than it is wide. Squares with sides 6 in long are cut from the four corners and the flaps are folded upward to form an open
box. If the volume of the box is 1050 in3, what were the original dimensions of the piece of metal?
What is the original width? in
What is the original length in
breadth= X
L= x+30
after you cut a square with 6in from the corners, the length becomes x+30-6 =x+24 and breadth becomes x-6.
The eqn for volume of box is Length x Breadth x height
it's given that LxBxH = 1050
here height is 6, because u are folding the edge where it's been cut off and that side becomes the height.
rewrite with the given information we get
(x+24)*(x-6)*6 = 1050
divide both sides with 6
(x+25)*(x-6) = 175
distribute the brackets we get,
x^2 -18x -144 =175
x^2 -18x-319 = 0
solve for x using quadratic formula.
we get x= 29, -11
since length cannot be negative x= 29
B= 29, L=59.
I will give brainiest to the person who answers this
Find the length of arc AB. Use 3.14 for 7.
Round to the nearest tenth.
h 7.9 cm
B
66 49
D
[? ]cm
Answer:
12.4
Step-by-step explanation:
[tex]AL= 2r\pi (\frac{angle}{360} )[/tex]
[tex]AL= 2(7.9)(\pi )(\frac{90}{360})\\[/tex]
Helping to give out points!! Whoever solves the math riddle correctly with a brief explanation will get brainliest and a thanks (the other answers will just get a thanks).
Riddle: I have a big family. I am 16 years old. My sister Reina is 22 years old. The twins are 14 years old. Susana is 10 years old and my brother Robert is 7 years old. If the total number of our ages added together is 100, how old is Albert?
Answer:
Robbert is 7
Step-by-step explanation:
because you already said it
What percent 39 is 26
Answer: 66.67
Step-by-step explanation:
lisa spent $21 on diapers. if they cost $7 package, how many packages did she buy
Answer:
3 packages
Step-by-step explanation:
first we need to make this into a equation that we can solve!
x = 21/7
if we use our times tables then we know that
7 * 3
= 21
so knowing what we know, lets go back to the question/ equation!
21/7
= 3
( if you wanted, that could also be a way to double check you answer :)
hope this helped you and if you have any more questions then please ask me! :)
a shark is located 45 feet directly below a swimmer on the surface of the water. the angle of depression from a boat nearby to the shark is 64 degrees. how far is the swimmer from the boat
Using the slope concept, it is found that the swimmer is 21.95 feet from the boat.
What is a slope?The slope is given by the vertical change divided by the horizontal change.It's also the tangent of the angle of depression.In this problem:
A shark is located 45 feet directly below a swimmer on the surface of the water, hence the vertical change is 45.The distance d is the horizontal change, which we want to find.The angle is of 64º.Hence:
[tex]\tan{64^{\circ}} = \frac{45}{d}[/tex]
[tex]d = \frac{45}{\tan{64^{\circ}}}[/tex]
[tex]d = 21.95[/tex]
The swimmer is 21.95 feet from the boat.
You can learn more about the slope concept at https://brainly.com/question/26342863
For the function f(x) = 5x + 4
Find f(6)
Answer:
f(6) =34
Step-by-step explanation:
f(x) = 5x + 4
Let x= 6
f(6) = 5*6 +4
= 30 +4
= 34
Which set of sides will make a triangle? 1 cm, 3 cm, Icm 10 cm, 5 cm, 9 cm 5 cm, 2 cm, 3 cm 10 cm, 3 cm, 4 cm
Answer:
5cm, 9cm, 10cm
Step-by-step explanation:
Please help me on this answer I am 1 week behind
what is the value of p in 24 = 2p
write 11.3826 to the nearest thousand
Answer:
11.383
Step-by-step explanation:
the third place is the thousandths.
By rounding 11.3826 to the nearest thousand, we get 11.383.
What is the method of rounding a number?The number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.
Example: 0.2358 rounded to the nearest thousand is 0.236.
If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.
Example: 0.7231 rounded to the nearest thousand is 0.723.
Given number is 11.3826.
Rounding to nearest thousand, we get:
11.3826 ⇒ 11.383.
Learn more about rounding a number to nearest thousand here: https://brainly.com/question/24234983
#SPJ2
A snack is 5 parts peanuts and 2 parts raisins. How many pounds of peanuts should be mixed with one-half pound raisins
find the area under the standard normal curve to the right of z=−2.28 z = − 2.28 .
If I save 500$ per month, for 12 years how much money will I have ?
Answer:
I think its 72,000
Step-by-step explanation:
there's 144 months in 12 years and i just multiplied it by 500
Bryce grew
33 inches each year for the past 4 years. How many inches total has Bryce grown in the
past 4 years ?
Answer:
132 inches
Step-by-step explanation:
33 x 4 = 132 inches
Find the greatest common factor of 28 and 35
Answer:
7
Step-by-step explanation:
Factors for 28: 1, 2, 4, 7, 14, and 28
Factors for 35: 1, 5, 7, and 35
The perimeter of a rectangular painting is 340cm. If the width of the painting is 74cm, what is its length?
Answer:
96
Step-by-step explanation:
Answer:
96 cm
Step-by-step explanation:
Length + Width + Length + Width = Perimeter
Length + 74 cm + Length + 74 cm = 340 cm
74 + 74 = 148
340 - 148 = 192
192 ÷ 2
96
Check:
74cm + 96cm + 74cm + 96cm = 340 cm
Suppose the probability that it will rain tomorrow is 0.59. What is the probability that it will not rain tomorrow?
Answer:
0.41
Step-by-step explanation:
All probability equals 1. So if the probability that something will happen is x, then the probability that it will not happen is 1-x
y∝1√x
If
y=7 when x=64
find,
x when y=8
Answer:
uhm im really sorry about this but i really need points i would help but id get it wrong im bad aat math
Step-by-step explanation:
Whichever answer is correct will get brainliest!
Find the value of x. Round to the nearest tenth. 35 12. х x = [?] Enter
Answer:
Round to the nearest tenth. 35 12. х x = [?] Enter
Step-by-step explanation:
Four teams will receive prize money based on their ticket sales. The total prize amount to be apportioned is $63. Determine the standard divisor based on the ticket sales. The ticket sales are: Applejacks: 66 tickets sold Broncos: 769 tickets sold Colts: 652 tickets sold Deers: 556 tickets sold Calculate the standard divisor to two decimal places.
Answer:
32.43
Step-by-step explanation:
To get the standard divisor
We sum up the tickets sold
Applejack's = 66 tickets
Broncos = 769 tickets
Colts = 652 tickets
Deers = 556 tickets
The total prize amount = $63
Total tickets = 66 + 769 + 652 + 556 = 2043
Standard divisor = 2043/63
= 32.43
The standard divisor to two decimal places is 32.43