Using the normal distribution, it is found that:
a) There is a 0.0228 = 2.28% probability that a randomly chosen salary exceeds $35,000.
b) There is a 0.3085 = 30.85% probability that a randomly chosen salary is less than $22,500.
c) There is a 0.4938 = 49.38% probability that a randomly chosen salary lies between $25,000 and $37,500.
d) The 15th percentile of the sociology salaries is of $19,825.
e) The salaries are $20,800 and $29,200.
Normal Probability DistributionIn a normal distribution 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]
It 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, which is the percentile of X.In this problem:
The mean is of [tex]\mu = 25000[/tex].The standard deviation is of [tex]\sigma = 5000[/tex].Item a:
The probability is 1 subtracted by the p-value of Z when X = 35000, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{35000 - 25000}{5000}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a p-value of 0.9772.
1 - 0.9772 = 0.0228.
There is a 0.0228 = 2.28% probability that a randomly chosen salary exceeds $35,000.
Item b:
The probability is the p-value of Z when X = 22500, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{22500 - 25000}{5000}[/tex]
[tex]Z = -0.5[/tex]
[tex]Z = -0.5[/tex] has a p-value of 0.3085.
There is a 0.3085 = 30.85% probability that a randomly chosen salary is less than $22,500.
Item c:
This probability is the p-value of Z when X = 37500 subtracted by the p-value of Z when X = 25000, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{37500 - 25000}{5000}[/tex]
[tex]Z = 2.5[/tex]
[tex]Z = 2.5[/tex] has a p-value of 0.9938.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{25000 - 25000}{5000}[/tex]
[tex]Z = 0[/tex]
[tex]Z = 0[/tex] has a p-value of 0.5.
0.9938 - 0.5 = 0.4938
There is a 0.4938 = 49.38% probability that a randomly chosen salary lies between $25,000 and $37,500.
Item d:
This is X when Z has a p-value of 0.15, so X when Z = -1.035.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.035 = \frac{X - 25000}{5000}[/tex]
[tex]X - 25000 = -1.035(5000)[/tex]
[tex]X = 19825[/tex]
The 15th percentile of the sociology salaries is of $19,825.
Item e:
Due to the symmetry of the normal distribution, it is the 20th percentile and the 80th percentile, that is, X when Z = -0.84 and X when Z = 0.84.
20th percentile:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.84 = \frac{X - 25000}{5000}[/tex]
[tex]X - 25000 = -0.84(5000)[/tex]
[tex]X = 20800[/tex]
80th percentile:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.84 = \frac{X - 25000}{5000}[/tex]
[tex]X - 25000 = 0.84(5000)[/tex]
[tex]X = 29200[/tex]
The salaries are $20,800 and $29,200.
More can be learned about the normal distribution at https://brainly.com/question/24663213
Can someone help me pls
Answer: The second option would be the answer
Step-by-step explanation:
Factoring the number is just listing all the whole numbers it can be divided by, and in this case it includes the variable. 16a is dividable by 1, 2, 4, 8, 16, and a; since 16a / a = 16. Apply this to 18b, and 1, 2, 3, 6, 9, 18, and b.
Mr. Malone made a graph to represent the time his students spent studying for their tests throughout the unit and their actual test scores Use the two points that are marked on the line of best fit to answer the following questions .
Answer:
a. 4/3
b. Test scores in percentage
c. y=4/3x +50
d. 78
Use substitution to solve the system of equations.
y=×+1.75
4×-2y=4
(4,4)
(3.75, 5.5)
(3.75, 0)
(5.5, 4)
evaluate if x=5 xsquard+10=
Answer:
35!
Step-by-step explanation:
5squared is 25 so you then do 25+10 wich = 35!
Which polygon has parallel sides and at least one acute angle?
Answer: A
Step-by-step explanation:
I believe it is a the parallelogram because it has at least one acute angle on the bottom and at least 2 parallel sides
Can someone help me please
9 bags sorry for the other answer
she has 7 boxes at home, then she goes and buys 6 more from the store, now she has 7 + 6 = 13 boxes of chips, each box of chip has 13 bags, so the total amount of potato chips I guess is 13 * 13 = 169 bags total.
So she split it even among her 9 students, so how many times does 9 go into 169? 169 ÷ 9, has a quotient of 18 with a remainder of 7.
18 * 9 = 162, plus 7 = 169, which is the total amount of potato chips bags.
The area of the triangle below is 38.28 square meters. What is the length of the base?
Answer:
8.8 m
Step-by-step explanation:
Area of triangle = 38.28 = * b * 8.7b = 38.28 * 2 / 8.7b = 8.8 m
Are all prime numbers greater than 2 odd numbers? Are all composite numbers even numbers? Justify your response with examples.
Answer:
Yes and no
Step-by-step explanation:
Prime numbers greater than 2 are always odd because if they were even they would be divisible by 2, becoming composite. Not all composite numbers are even, some may be a multiple of two odd numbers. For example, 21 = 3*7
How many places do you need to move the decimal to the left to write the
number below in scientific notation?
60,000,000,000
O A. 11
B. 12
C. 9
D. 10
75% of the students are boys. There are 24 boys. What is the total number of students?
Answer: 32
Step-by-step explanation:
We can write the problem like this:
[tex]\frac{75}{100}x=24[/tex]
Then, we can multiply 100 to the equation:
[tex]75x=2400[/tex]
Now, we can divide 2400 and 75:
[tex]x=32[/tex]
Now we can conclude that the amount of students is 32.
evestigation Grade 10 2.3 Suppose x represents the unit of calculating the resale in plot million of rands . Which of the following values of x gives the best value of the plot? Substantiate your answer with an appropriate calculation. x = 2 x. = 5 .x= -3
Conclusion:
Graphs are used to represent functions and equations
The best value of x is x = 5
How to determine the best value of xFrom the question, we understand that x represents the unit of calculating the resale in plot million of rands
This means that x cannot be negative.
So, we have x = 2 and x = 5
The graph is not given.
So, we can assume that the graph is a linear function with a positive slope
For a linear function with a positive slope, the higher the x value, the higher the output value
Hence, the best value of x is x = 5
Read more about graphs and functions at:
https://brainly.com/question/14323743
Use the drop-down menus below to state the sequence of transformations that maps Figure K onto Figure L in the animation below. Then use those transformations to determine: are the two figures congruent? Use the drop-down menus to explain why or why not.
Answer:
1)Reflection,reflection
2)are congruent because reflections are used
Step-by-step explanation:
You reflect figure K so it's upside down.
Then reflect over the y-axis to make it to figure L
The process of two reflections, one horizontally, then vertically will map the two figures
-Chetan K
Let V = {(x, y, 2x - 3y)|x, yeR}. Prove that V is closed for addition and scalar multiplication i.e. that V is the subspace of R.
The original question got deleted for "not having enough information". Ironic how this is the whole question. Mod must've not understood. Here's a repost with my answer.
Answer:
To prove V is a subspace of R, you must show:
(1) It is not empty
(2) Adding vectors returns real numbers
(3) Multiplying by scalars return real numbers
2 & 3 follow the conditions that x,y must be real.
===
(1):
0 = 0 + 0 , therefor V cannot be an empty set. Really thats it.
===
(2)
Let u=(u1, u2 , 2u1-3u2)
Let v *lowercase =(v1, v2, 2v1-3v2)
Great, now lets add them. This isn't intuitive unless you finish reading it all.
u+v = ( u1 + v1 , u2 + v2 , 2u1 - 3u2 + 2v1 - 3u2 )
--> u + v = [ (u1+v1), (u2+v2) , (2u1 + 2v1) + (-3u2 - 3v2) ] (got like terms kinda)
====> All must equal (x,y, 2x-3y)
... which means x=u1+v1 & y=u2+v2 (you compare u+v to V for this)
===
(3)
Let c be a real number.
C(u) = (Cu1, Cu2, C2u1 - C3u2)
====> Must equal (x,y, 2x-3y)
... which means Cu1 = x & Cu2 = y
Cu is in V (because x,y are)
-> V is a subspace of R3.
i need help with this can you help me please
Answer:
B
Step-by-step explanation:
The volume of the cube is the total amount of cubes in the box.
Because the box is a cube, and you know the formula for volume of cube is L³
L³=125
∛L³=∛125
L=5
there would be 25 cubes in each layer, not 125. Because one layer is L²
How to do the math for 2d -9= -29
Answer:
d = -10
Step-by-step explanation:
Hey there!
Let's Solve:
2d - 9 = -29 => Step 1: Add 9 to both sides(becasue we are subtracting 9)2d = -20 =>Step 2: Divide both sides by 2(because we are multiplying by 2 in 2d)d = -10-Chetan K
eight more than three times a number is equal to the sum of the number and 10. find the number
Answer:
8+3x=x+10
2x=2
x=1
The number is 1
Let I stand for radiation experienced by the person, r stand for distance, and k be the constant of variation. Write an equation of variation representing the relationship between I, r, and k.
The radiation experienced is inversely proportional to distance, Therefore the required equation will be l = k/r
Equation of variationsVariation is defined as the changing of variable parameters. In problems relating to two or more variables, it is seen that the value of variable changes with respect to the other.
Variation can be direct, inverse, partial and joint in nature
Given the following parameters
Let I stand for radiation experienced by the personr stands for distancek be the constant of variation.The radiation experienced is inversely proportional to distance, Therefore the required equation will be l = k/r
learn more on variation here: https://brainly.com/question/6499629
Choose all numbers that are divisible by 2 and 5
A 88520
B 76023
C 95067
D 74076
E 58453
F47650
Step-by-step explanation:
numbers divisible by 2 end with an even number (2,4,6,8,0)
numbers divisible by 5 end with either 5 or 0
Answer:
A,D, and F
Step-by-step explanation:
Any number that is even is divisible by 2.
A D and F are even numbers. If a number ends in 2,4,6,8, or 0 then it is an even number, so you can just look at the last number and determine weather it is divisible by 2.
Pls help me I don’t know
Answer: Please give me more information, I am sorry :(
Step-by-step explanation: Please give me more information, I am sorry :(
( But I think is the length of the prism is 2cm ......)
Answer:
Step-by-step explanation:
The length of the prism is 2cm
Hope this helps!
Use the graph to solve the system of equations.
Answer:
( -2 , 1 )
Step-by-step explanation:
Add the 2 equations downwards.
( -x+4y=6 ) + ( 2x-y=-5 )...consider the sign of each term.
= x + 3y = 1
Put -2 in x because that's where the graph above shows an intersection of the 2 equations.
-2 + 3y = 1
3y = 3
y = 1.
( x , y) = ( -2 , 1 )
PLS HELP ME, PLS THIS IS DUE FIRST CORRECT ANSWER GETS BRAINLIEST
Answer:
c
Step-by-step explanation:
the number goes to both of the numbers in the equation
Consider the equation below.
-2(5x + 8) = 14 + 61
The equation was solved using the following steps.
-10r - 16 = 14 + 6r
Step 1:
Step 2:
Step 3:
-163 – 16 = 14
-16= 30
Step 4:
30
=
-16
Step 5:
1 =
Complete the statements below with the process used to achieve steps 1-4.
Answer:
x = -91/10
Step-by-step explanation:
-2(5x + 8) = 14 + 61
-10x -16 = 75
-10x = 91
-10x/-10 = 91/-10
x = -91/10
How to divide 400 by 40
Answer:
10 ez
Step-by-step explanation:
400÷40 it like. 10 ÷ into 100
Which degrees are more advanced than a four year bachelor's degree? Check all that appe
O a doctoral degree
a master's degree
D a high school degree
an associate degree
Answer:
A doctoral degree
A masters degree
Answer:
A,B
Step-by-step explanation:
What is the area of a circle whose radius is 15 inches? Round your answer to the nearest tenth of a square inch.
Answer:
706.86 in^2
Step-by-step explanation:
The formula for the area of a circle is [tex]A = \pi r^{2}[/tex]
Since your radius was given (15 in) the area is:
[tex]A=\pi (15)^{2} =225\pi =706.86 in^2[/tex]
11+20+?-2=45 what is the missing number?
Answer:
16 i think hehe is it?.....
Answer:
16
Step-by-step explanation:
let ? be x then
11+20+x-2=45
29+x = 45
x = 45-29
x = 16
A rectangle is drawn so that the width is 2 feet shorter than the length. The area of the rectangle is 48 square feet. Find the length of the rectangle.
Given :
Rectangle is drawn so that the width is 2 feet shorter than the length.The area of the rectangle is 48 sq feet.⠀
To Find :
The Length of the rectangle⠀
Solution :
We know that,
[tex]\qquad { \pmb{ \bf{Length \times Width = Area_{(rectangle)}}}}\: [/tex]
So,
Let's assume the width of the rectangle as x and the length will be (x + 2).
⠀
Now, Substituting the given values in the formula :
[tex]\qquad \sf \: { \dashrightarrow (x + 2) \times x = 48 }[/tex]
[tex]\qquad \sf \: { \dashrightarrow {x}^{2} + 2x = 48 }[/tex]
[tex]\qquad \sf \: { \dashrightarrow {x}^{2} + 2x - 48 = 0 }[/tex]
[tex]\qquad \sf \: { \dashrightarrow {x}^{2} +8x -6x- 48 = 0 }[/tex]
[tex]\qquad \sf \: { \dashrightarrow {x} (x +8) -6(x+8) = 0 }[/tex]
[tex]\qquad \sf \: { \dashrightarrow (x +8) (x - 6) = 0 }[/tex]
[tex]\qquad \sf \: { \dashrightarrow x = -8, \: \: x = 6 }[/tex]
⠀
Since, The width can't be negative, so the width will be 6 which is positive.
⠀
[tex]\qquad { \pmb{ \bf{ Width _{(rectangle)} = 6\:ft}}}\: [/tex]
[tex]\qquad { \pmb{ \bf{ Length _{(rectangle)} = 6+2=8 \: ft}}}\: [/tex]
A tree grows at the rate of 1½ inches every week. At this rate, how many weeks will it take the tree to grow 20.25 inches?
please help me I need help
Answer:
23.16 your welcome
Step-by-step explanation:
Help me please.......
Answer:
decompose
numerator
mixed number
Step-by-step explanation:
1. To DECOMPOSE is to break apart a number.
e.g. to decompose 853: 800 + 50 + 3
2. The NUMERATOR is the top number in a fraction (the bottom number is the denominator).
3. A number that has whole number part and fraction part is a MIXED NUMBER, e.g. [tex]6\frac23[/tex]
