Question 1b.
The distribution is...
i. Reasonably symmetric
ii. Abnormal
iii. Highly Skewed
iiii. Bimodel
Answers
Answer: i) Reasonably symmetric
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Explanation:
The data set is
35,40,45,49,51,54,57,58,58,64,68,68,75,77
Erase the outer pair of values (35 and 77) to end up with this smaller set
40,45,49,51,54,57,58,58,64,68,68,75
Repeat and erase off the outer values (40 and 75) to end up with
45,49,51,54,57,58,58,64,68,68
Keep going until we have either one or two elements left
49,51,54,57,58,58,64,6851,54,57,58,58,6454,57,58,5857,58At this point, we see that the center is between these two last values. So the median is (57+58)/2 = 57.5
--------------------------------
The center is at 57.5
Let L = {35,40,45,49,51,54,57} consist of the set of numbers lower than the median
Let U = {58,58,64,68,68,75,77} be the upper set of values larger than the median.
The middle of set L is 49 and the middle of set U is 68. So Q1 and Q3 are 49 and 68 respectively.
From that, we see the IQR = Q3 - Q1 = 68-49 = 19
Let A and B be the lower and upper fence
We would then say
A = Q1 - 1.5*IQR = 49-1.5*19 = 20.5
B = Q3 + 1.5*IQR = 68 + 1.5*19 = 96.5
Notice how all of the given data values are between A = 20.5 and B = 96.5, which means we don't have any outliers.
Furthermore, if we plotted a box-and-whisker plot (see below), we can see that the two whiskers are fairly the same length. It's not perfect but they're reasonably symmetric. Similarly, the median is somewhat in the middle of the box itself. So this gives a rough idea that the data set we're dealing with is fairly symmetric.
More confirmation can be in the form of a histogram which is also part of the image below. This histogram is fairly symmetric as the left half is nearly (not perfectly) a mirror image of the right half, and vice versa. No one side pulls too far out to create a highly skewed distribution.
Related Questions
How do you simplify 1 1/3
Answers
Answer:
4/3
Step-by-step explanation:
Suppose that the space shuttle has three separate computer control systems: the main system and two backup duplicates of it. The first backup would monitor the main system and kick in if the main system failed. Similarly, the second backup would monitor the first. We can assume that a failure of one system is independent of a failure of another system, since the systems are separate. The probability of failure for any one system on any one mission is known to be 0.01.
(a) Find the probability that the shuttle is left with no computer control system on a mission. (Enter your answer to six decimal places.)
(b) How many backup systems does the space shuttle need if the probability that the shuttle is left with no computer control system on a mission must be
1
one hundred thousand
(Enter your answer as a whole number.)
_____ backup systems.
Answers
Answer:
a) 0.000001 = 0.0001% probability that the shuttle is left with no computer control system on a mission.
b) 3 backup systems are needed.
Step-by-step explanation:
For each system, there are only two possible outcomes. Either it works, or is does not. Systems are independent. This means that we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Three separate computer control systems
This means that [tex]n = 3[/tex]
The probability of failure for any one system on any one mission is known to be 0.01.
So the probability of working is:
[tex]p = 1 - 0.01 = 0.99[/tex]
(a) Find the probability that the shuttle is left with no computer control system on a mission. (Enter your answer to six decimal places.)
This is [tex]P(X = 0)[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{3,0}.(0.99)^{0}.(0.01)^{3} = 0.000001[/tex]
0.000001 = 0.0001% probability that the shuttle is left with no computer control system on a mission.
(b) How many backup systems does the space shuttle need if the probability that the shuttle is left with no computer control system on a mission must be 1 over one hundred thousand
This is n for which:
[tex]P(X = 0) < \frac{1}{100000} = 0.00001[/tex]
With 2 backup systems, the probability is lower than this, so lets see if with only two is possible.
We find [tex]P(X = 0)[/tex] when [tex]n = 2[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{2,0}.(0.99)^{0}.(0.01)^{2} = 0.0001 > 0.00001[/tex]
So 3 backup systems are needed.
Somebody help me with this?
Answers
Answer:
2
Step-by-step explanation:
The solutions of a quadratic graph are the x-intercepts. As you can see from the graph, the only place that it intercepts the x axis is at 2, so the solution is 2.
Calculator
A worker at a computer factory can assemble 8 computers per hour.
How long would it take this worker to assemble 200 computers?
08h
o 20 h
0 25 h
0 200 h
Answers
Answer:
25 Hours
Step-by-step explanation:
200 computers divided by 8 an hour gives you 25 hours to assemble the computers.
200 ÷ 8 = 25
I hope this helps. ^^
What is the solution of the inequality shown below X-3>7
Answers
Step-by-step explanation:
x-3>7 =>
x>10
hope this helps
What percent of 38 is 23
Answers
This mean 23 is 60.5% of 38
The percentage of 38 that is 23 is = 60.5%
Percentage of a given quantity:To calculate the percentage of a given quantity, the quantity is taken to be =100%
That is ; 38 = 100%
Therefore, 23 = X
make X the subject of formula,
[tex]x = \frac{23 \times 100}{38} [/tex]
[tex]x = \frac{2300}{35} [/tex]
X = 60.5%
Therefore, 60.5% of 38 is 23.
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PLEASEEEE HELP!!!! (Multiplying/Dividing Fractions Word Problems) An auto shop installed a new automatic system to do paint jobs for cars. The system can paint 6 cars in an hour. How long does it take to paint one car?
Answers
Answer:
10 minutes.
Step-by-step explanation:
Note the amount of minutes in an hour.
1 hour = 60 minutes.
The system can paint 6 cars in an hour. Divide 60 minutes with 6 cars:
60/6 = 10
Each car takes 10 minutes to get fully painted.
~
A square pyramid and a cube have the same total surface area. The width of the cube is 8 centimeters. The base of the pyramid is equal to base of the cube. What is the slant height of the square pyramid?
Answers
Answer:
Step-by-step explanation:
surface area of cube = 6×8² = 384 cm²
lateral area of pyramid = surface area of pyramid - base area
= 384 - 8²
= 320 cm²
area of triangular face = 320/4 = 80 = ½(base)(slant height) = ½(8)(slant height)
slant height = 20 cm
Under a periodic inventory system, closing entries will include
debits to Sales, Purchases Returns and Allowances, and Purchases Discounts
credits to the Allowance for Doubtful Accounts
adjustments to the merchandise inventory account to match physical inventory
all of these
Answers
Answer:
0.285714285 nearest thousandth
Which shapes can the composite figure be divided into to find the area?
O a rectangle and a triangle
O a rectangle and two triangles
O a trapezoid and a rectangle
O a trapezoid and two triangles
Answers
Somebody help me with this
40 points ☺️
Answers
Function lis defined by the equation r
R=5/8t - 9
Function 2 is defined by the following table,
I
Which function has a greater y-intercept?
Answers
Answer:
Both have the same y-intercept (-9)
Step-by-step explanation:
✔️Function 1, r = ⅝t - 9, is given in the slope-intercept form, y = mx + b.
b = y-intercept = -9
y-intercept for Function 1 = -9
✔️Function 2, using the table given, the y-intercept is the value of r when t = 0.
Thus, r = -9 when t = 0.
y-intercept for Function 2 = -9
✔️Both functions has the same y-intercept. None is greater than the other.
Solve the proportion
Answers
Let’s say you have these fractions:
A / B = C / D
To cross multiply, multiply the denominator of the first fraction (B) by the numerator of the second fraction (C). Multiply the numerator of the first fraction (A) by the denominator of the second fraction (D).
You get B x C = A x D
After cross multiplying your fractions, you get 63 = 7(c +4)
Distributing the 7 into c+4 gives you this:
63 = 7c + 28
Now solve this like a normal equation with a variable
63 = 7c + 28
35 = 7c
5 = c
To double check that, plug c = 5 into the original equation.
1/(5) + 4 = 7/63
1/9 = 7/63
7/63 simplifies into 1/9 (7:7 = 1, 63/7 = 9)
1/9 = 1/9 so c = 5 is correct
The sum of 25 and h is divided by f cubed.
Answers
Graph f(x)=|x+1|+2. Shows vertex and 4 points.
Answers
Answer:
[tex](-1,2)[/tex]
Step-by-step explanation:
The vertex of [tex]f(x)=|x|[/tex] is [tex](0,0)[/tex]
The +1 inside the absolute value horizontally shifts the graph 1 unit to the left.
The+2 outside the absolute value vertically shifts the graph 2 units upward.
So, the vertex of the graph of [tex]f(x)=|x+1|+2[/tex] is [tex](-1,2)[/tex]
Here’s the graph
Advertising expenses are a significant component of the cost of goods sold. Listed below is a frequency distribution showing the advertising expenditures for 60 manufacturing companies located in the Southwest. Estimate the mean and the standard deviation of advertising expenses. (Round squared deviations to nearest whole number and final answers to 2 decimal places.) Advertising Expenditure ($ millions) Number of Companies 25 up to 35 5 35 up to 45 10 45 up to 55 21 55 up to 65 16 65 up to 75 8 Total 60
Mean
Standard deviation
Answers
The estimated mean of advertising expenses is $52 million, and the estimated standard deviation is $11.23 million.
To estimate the mean and standard deviation of advertising expenses, we need to calculate the midpoint of each class interval, the product of the midpoint and the frequency, and the squared deviation from the mean.
Here's a table to organize the calculations:
Class Interval (x) Frequency (f) Midpoint (x) fx
25 up to 35 5 30 150
35 up to 45 10 40 400
45 up to 55 21 50 1,050
55 up to 65 16 60 960
65 up to 75 8 70 560
To calculate the mean, we need to find the sum of the products of the midpoint and the frequency, divided by the total frequency.
Mean = (fx) / Total Frequency
Mean = (150 + 400 + 1,050 + 960 + 560) / 60
Mean = 3,120 / 60
Mean = 52
Calculate the squared deviation from the mean for each class interval.
(x - mean)² × f
(30 - 52)² × 5 = 484 × 5 = 2,420
(40 - 52)² × 10 = 144 × 10 = 1,440
(50 - 52)² × 21 = 4 × 21 = 84
(60 - 52)² × 16 = 64 × 16 = 1,024
(70 - 52)² × 8 = 324 × 8 = 2,592
Calculate the sum of the squared deviations.
Sum of (x - mean)× f = 2,420 + 1,440 + 84 + 1,024 + 2,592
= 7,560
Standard Deviation =√(Sum of (x - mean)² × f / Total Frequency)
Standard Deviation = √(7,560 / 60)
Standard Deviation = √(126)
Standard Deviation = 11.23
Hence, the estimated mean of advertising expenses is approximately $52 million, and the estimated standard deviation is approximately $11.23 million.
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Complete question
Advertising expenses are a significant component of the cost of goods sold. Listed below is a frequency distribution showing the advertising expenditures for 60 manufacturing companies located in the Southwest. Estimate the mean and the standard deviation of advertising expenses. (Round squared deviations to nearest whole number and final answers to 2 decimal places.)
Advertising Expenditure ($ millions) Number of Companies
25 up to 35 5
35 up to 45 10
45 up to 55 21
55 up to 65 16
65 up to 75 8
Total 60
Which of the following measures of variability can be used to compare two data sets? Select all that apply.
A.
Mean
B.
Interquartile range
C.
Median
D.
Mean Absolute Deviation (MAD)
E.
Range
Answers
Answer:
B. Interquartile range
E. Range
Step-by-step explanation:
When the variability is to be used for comparing the two data sets so the measures that should be considered is range & interquartile range as it shows the difference also it compared the two different data sets
Therefore option B and E is correct
And, the rest of the options are wrong
Here are two similar rectangles.
1 cm
2 cm
4 cm
Work out the area of the larger rectangle.
Answers
Answer:
40.32
Step-by-step explanation
4*1.2=4.8
7*1.2=8.4
8.4*4.8
=40.32
Solve and graph the inequality.
−x4−6≥−8
Answers
Answer:
Inequality Form: − 4 √ 2 ≤ x ≤ 4 √ 2 Interval Notation: [ − 4 √ 2 , 4 √ 2 ]
Answer:
-4x ≥ 14
x ≥ -3.5
Graphed (numberline):
<-----------3.5---0------------->
could be x
In which rainforest three layer would you most expect to spot a harpy eagle
Answers
Answer:
canopy layer
Step-by-step explanation:
A television originally cost t dollars, including tax. Ricardo purchased the television when it was on sale for 35% off its original cost. Which of the following expressions represents the final cost, in dollars, of the television Ricardo purchased?
A. t - 0.35
B. t + 0.65
C. 0.35t
D. 0.65t
Answers
The cost of the television Ricardo purchased is A = 0.65t , where t is the initial cost
What is Percentage?A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %
The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.
Percentage change is the difference between the measured value and the true value , as a percentage of the true value
Percentage change =( (| Measured Value - True Value |) / True Value ) x 100
Given data ,
Let the initial cost of television be = t
Let the percentage of discount on television = 35 %
If the original cost of the television was t dollars, then the sale price would be 65% of the original cost, or 0.65t dollars (since the television is on sale for 35% off).
However, this sale price still includes tax, so we need to subtract the tax from the sale price to get the final cost.
Let's say the tax rate is r (as a decimal), then the final cost would be:
A = 1 - ( 0.35 )t
A = 0.65t
Hence , the expression that represents the final cost of the television that Ricardo purchased is (D) 0.65t
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5.2 divided by what equals 0.052
Answers
Simplify the following proper fraction by reducing to lowest terms. 2/18
Answers
Answer:1/9
Step-by-step explanation: divide both sides of the fraction by 2
Answer:
1/9
both divide by 2 then 2/2=1 and 18/2=9 so that the answer will be 1/9
20 points to answer !!
In your own words, describe a situation in your own life that involves quadrilaterals..... (see picture above)
Answers
the burger king sign is a rectangle i had burger king last week
what is a equivalent expressions 3(6x+4)
Answers
Answer: 18x + 12
Step-by-step explanation:
3 ( 6x + 4 )
3 x 6x = 18x
3 x 4 = 12
18x + 12
ill mark brainlistnplss help
Answers
Hope this helps.
What is the answer for this 5c + 9 -2c -7
Answers
Step-by-step explanation:
Given
5c + 9 - 2c - 7
= 3c + 2
Hope it will help :)❤
Find the mean: 17.4 mm, 20.3 mm, 84.1 mm, 31.2 mm, 53.7 mm, 11.7 mm
Answers
Can the sides of a triangle have lengths 2, 6, and 9
Answers
Answer:
no.
Step-by-step explanation:
the sum of the two smallest sides of the triangle must be greater than the largest side in order to form a triangle. 2+6<9
please help if you do thanks :) question 2
Answers
Answer:
When we have a random function like:
y = f(x)
If there is no clarification, the domain will be the set of all real numbers except the ones that may make a problem.
For example, if there is some value of x such that there is a denominator equal to zero, then that particular value of x is not in the domain of f(x) (because we can not divide by x)
Something similar happens when we have a square root, remember that:
√x
Is a complex number if x < 0.
Then if we have a function like:
y = √x
The domain will be the set of all reals such that x ≥ 0.
Then the procedure to find the domain is to find the inputs that may have problems, and "remove" them from the domain.
For the range, we need to first know the domain, then we can evaluate the function in different points of the domain and see the outputs. Once we know all the outputs, we know the range of the function.
Usually, when working with continuous functions, these may have a global maximum M and a global minimum m, then the range is:
m ≤ Y ≤ M
if not, then the range is the set of all real numbers.