At the conclusion of training, all factory workers are timed as they complete a task. The completion times for the task are normally distributed.
Suppose a worker's completion time is 1.1 standard deviations above the mean. What is the worker's percentile score? Round your result to one decimal place.
The annual salaries for people in a particular profession are known to be normally distributed with a mean of $54,800 and a standard deviation of $2,600.
What percentage of people in this profession earn annual salaries between $54,000 and $57,000? Round your result to one decimal place.
Answers
Using the normal distribution, it is found that:
The worker's score is at the 86.4th percentile.42.2% of people in this profession earn annual salaries between $54,000 and $57,000.In a normal distribution with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
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.Question 1:
1.1 standard deviations above the mean, hence, a z-score of Z = 1.1.
Looking at the z-table, z = 1.1 has a p-value of 0.864, hence, the worker's score is at the 86.4th percentile.Question 2:
Mean of 54800, hence \(\mu = 54800\)Standard deviation of 2600, hence \(\sigma = 2600\).The proportion is the p-value of Z when X = 57000 subtracted by the p-value of Z when X = 54000, then:
X = 57000:
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{57000 - 54800}{2600}\)
\(Z = 0.846\)
\(Z = 0.846\) has a p-value of 0.801.
X = 54000:
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{54000 - 54800}{2600}\)
\(Z = -0.307\)
\(Z = -0.307\) has a p-value of 0.379.
0.801 - 0.379 = 0.422
0.422 x 100% = 42.2%
42.2% of people in this profession earn annual salaries between $54,000 and $57,000.
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Related Questions
You conduct a study to determine whether there is a relationship between how old a person is when they divorce and the amount of time before he or she remarries. Some computer output from the analysis and a residual plot of the data are presented below. (Values are in years).Regression Analysis The regression equation is Time = 0.03 + 0.124 Age Predictor Constant Age Coef 0.034 0.123780.04963 2.49 Stdev 1.962 t-ratio 0.02 0.987 0.037 s= 1.659 R-sq=43.7% R-sq(adj)=36.7% 4.0+ i 2.0+ s 0.0+ 2.0+ X --+----Age 24 32 40 48 56What is the predicted number of years a 40 year old will wait before remarrying?
Given that the study found that the average 40 year old waits 4 years before remarrying, what is the value of the residual for a 40 year old?
Based on the printout and the residual plot, does it appear that time and age have a linear relationship? If so, how strong does the predictive relationship appear to be?
Answers
Complete Question
Part of the question is shown on the first uploaded image
The rest of the question
What is the predicted number of years a 40 year old will wait before remarrying?
Given that the study found that the average 40 year old waits 4 years before remarrying, what is the value of the residual for a 40 year old?
Based on the printout and the residual plot, does it appear that time and age have a linear relationship? If so, how strong does the predictive relationship appear to be?
Answer:
a
The predicted number of years a 40 year old will wait before remarrying is \(Time = 4.99\)
b
The value of the residual for a 40 year old is \(t = 0.99 \ years\)
c
Based on the print out , we can say that the time and the age has a linear relationship
And looking the R-sq we can say the 43.7% of time variation is due to age
Step-by-step explanation:
From the regression equation
\(Time = 0.03 + 0.124 Age\)
And from the question we are told that Age is 40 years so
\(Time = 0.03 + 0.124 (40 )\)
\(Time = 4.99\)
Therefore the predicted time 40 year old will wait for 4.99 years before remarrying
From the question,the study found that the average 40 year old waits 4 years before remarrying,
So the residual for a 40 year old is mathematically evaluated as
\(t = 4.99 - 4\)
\(t = 0.99 \ years\)
Based on the print out , we can say that the time and the age has a linear relationship
And looking the R-sq we can say the 43.7% of time variation is due to age
Please help me answer this
Answers
9514 1404 393
Answer:
z^11
Step-by-step explanation:
The applicable rule of exponents is ...
(a^b)(a^c) = a^(b+c)
__
\(z^5\cdot z^6=z^{5+6}=\boxed{z^{11}}\)
__
Additional comment
It might help you to think of an exponent as indicating repeated multiplication. It tells you how many times the factor is repeated. In this case, it means ...
\(z^5\cdot z^6=(z\cdot z\cdot z\cdot z\cdot z)\cdot(z\cdot z\cdot z\cdot z\cdot z\cdot z)\\=z\cdot z\cdot z\cdot z\cdot z\cdot z\cdot z\cdot z\cdot z\cdot z\cdot z = z^{11}\)
Based on data from the American Red Cross, there is a 0.45 probability that a randomly selected American will have Type O blood. This means that:__________
Answers
Answer:
Probability of not an O type blood = 0.55
Step-by-step explanation:
Given:
Probability of O type blood = 0.45
Computation:
Probability of not an O type blood = 1 - Probability of O type blood
Probability of not an O type blood = 1 - 0.45
Probability of not an O type blood = 0.55
This means 0.55 people in america doesn't have O type blood
Solve 5x+7 > 17.
{x1x<2}
O {XIX> 2}
O {xIx>-2}
O {x1x < -2}
Answers
Answer:
The answer is \(x > 2\)
Step-by-step explanation:
to solve this inequality:
\(5x+7 > 17\)
Put "-7" on both sides
\(5x+10\)
divide by 5 on both sides
your answer should be 2.
NEED HELP ASAP!!! will give brian list!
Answers
Answer:
a. 28/143
b. 40/143
Step-by-step explanation:
For both parts, we assume that the teas are selected without replacement. So we start with 13 teas. After one is selected, we have 12 teas left, and then after one more is selected, we have 11 teas left.
a. If all three are sweet:
\( \frac{8}{13} \times \frac{7}{12} \times \frac{6}{11} = \frac{28}{143} \)
b. If exactly one is sweet:
First one sweet, next two unsweet:
\( \frac{8}{13} \times \frac{5}{12} \times \frac{4}{11} = \frac{40}{429} \)
First one unsweet, second one sweet,
third one unsweet:
\( \ \frac{5}{13} \times \frac{8}{12} \times \frac{4}{11} = \frac{40}{429} \)
First two unsweet, third one sweet:
\( \frac{5}{13} \times \frac{4}{12} \times \frac{8}{11} = \frac{40}{429} \)
Adding these probabilities, we have
\( \frac{120}{429} = \frac{40}{143} \)
Sami read 12 books in 7th grade. In 8th grade she read 18 books. What is the percent of increase on the number of books that Sami read
Answers
Answer:
50% Increase
Step-by-step explanation:
first you can find half the number of the first amount
then in the case it is 6 so 12+6=18.
Answer:
20
Step-by-step explanation:
The percent of increase is 20%.
In order to solve this problem you have to solve this equation:
18-15/15
3/15
0.2 = 20%
five eighths of x is 2 1/2. what is x?
Answers
4
Step-by-step explanation:
8/5(put 8 as numerator becuz we need to find all x from 5/8) x 2 1/2＝4
If 1/2 of a loaf of brown bread costs R6,how much will 2 halves cost
Answers
Step-by-step explanation:
1/2 is equal to R6.
So 2 halves mean R6+R6=R12
Or
R6×2= R12
Answer:R12
Weekly demand for a certain brand of a golf ball at The Golf Outlet is normally distributed with a mean of 35 and a standard deviation of 5. The profit per box is $5.00. Write an Excel formula that simulates the weekly profit:
= 5 * 35 * NORMSINV(RAND())
= 5* NORMINV(RAND(), 35, 5)
= 5 * RANDBETWEEN(5, 35)
= NORMINV(RAND(), 5 * 35, 5)
Answers
Answer:
= 5 * NORMINV(RAND(), 35, 5)
Step-by-step explanation:
From the given information:
The total weekly profit is achieved by the multiplication of the unit profit (5) and the weekly demand.
Here, the weekly demands obey a normal distribution where the mean = 35 and the standard deviation = 5.
Using the Excel Formula:
The weekly profit can be computed as:
= 5 * NORMINV(RAND(), 35, 5)
find the number of books at $3.95 each that can be bought with a $10 note
Answers
Answer:
2 books
Step-by-step explanation:
10/3.95 = 2.53
Complete the proof.
Given ΔNOP≅ΔNMP ,∠NOM≅∠PMN
Prove MNOP is a rhombus.
Answers
NO = NM and PO = MN, meaning that all four sides of MNOP are equal. So MNOP is a rhombus.
Describe the rhombus.A rhombus is a quadrilateral with all facets of equal length and each pair of opposite faces parallel, making it an equilateral parallelogram. A rhombus is occasionally referred to as a rhomb, while a rhombus is occasionally referred to as a diamond.
We must demonstrate that MNOP has four equal sides and that the opposite angles are equal in order to establish that it is a rhombus.
Given NOP, NMP, and NOM, PMN, we can infer that:
Because their corresponding angles are equal, the triangles NOP and NMP are comparable.
NOM and PMN have proportional comparable sides since they are equivalent.
The matching sides of NOP and NMP are proportionate since the triangles are comparable. As a result, NP = PM, NO = NM, and NP/NO = PM/NM.
Since NP/PO = PM/PM and NP = PM, we obtain PO = MN because NOM and PMN are equivalent and their respective sides are proportional.
As a result, NO = NM and PO = MN, indicating that MNOP's four sides are equal. Additionally, since corresponding angles of identical triangles are equal and opposite angles of rhombuses are equal, we can infer that MNOP's opposite angles are also equal.
MNOP is therefore a rhombus.
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Solve by substitution
2 x + 3y = 5
2x + 3y = 4
Answers
Answer:
2(1)+3(1)Is 5 2(2)+ 3(0) is 4
Step-by-step explanation:
Please mark brainlest
What is the constant up a proportionally in a equation y=x/g
Answers
Answer:
Step-by-step explanation:
\(y=(\frac{1}{g} )x\)
Constant up a proportionally is \(\frac{1}{g}\).
HURRY!!!
What is the value of |243| + |−23| − |−16|?
Answers
Answer:
250
Step-by-step explanation:
everything u need is in the picture
A realtor is decorating some homes for sale, putting a certain number of decorative pillows on each twin bed and a certain number on
each queen bed. In one house, she decorated 1 twin bed and 2 queen beds and used a total of 27 pillows. At another house, she used
37 pillows to spruce up 3 twin beds and 2 queen beds. How many decorative pillows did the realtor arrange on each bed?
Answers
Answer:
Each of the twin beds: 5 decorative pillows
Each of the queen beds: 11 decorative pillows
Step-by-step explanation:
Let the number of pillows used for each twin bed be x
Let the number of pillows used for each queen bed be y
she decorated 1 twin bed and 2 queen beds and used a total of 27 pillows. Thus;
x + 2y = 27 - - - (eq 1)
Also, she used
37 pillows to spruce up 3 twin beds and 2 queen beds. Thus;
3x + 2y = 37 - - - (eq 2)
From eq 1, x = 27 - 2y
Thus;
3(27 - 2y) + 2y = 37
81 - 6y + 2y = 37
81 - 4y = 37
4y = 81 - 37
4y = 44
y = 44/4
y = 11
x = 27 - 2(11)
x = 27 - 22
x = 5
Thus, she used 5 decorative pillows for each of the twin beds and 11 decorative pillows for each of the queen bed
Determine the monthly payment for the installment loan.
Amount Financed (P) = $15,000
Annual Percentage Rate (R) = 5%
Number of Payments per Year (N) = 12
Time in Years (T) = 3
The monthly payment is $_____?
(Round to the nearest cent as needed.)
Answers
The monthly payment is $453.125.
How to calculate simple interest amount?If the initial amount (also called as principal amount) is P, and the interest rate is R% annually, and it is left for T years for that simple interest, then the interest amount earned is given by:
\(I = \dfrac{P \times R \times T}{100}\)
Given;
Amount Financed (P) = $15,000
Annual Percentage Rate (R) = 5%
Number of Payments per Year (N) = 12
Time in Years (T) = 3
Now, monthly payment;
=(p*i*(1+i)^n)/((1+i)^n-1)
=15000(0.05/12)(1+0.05/12)^36/(1+0.05/12)^36-1
= 72.5/0.16
=453.125
Therefore, the monthly payment by 5% interest will be $453.125.
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Greatest error of 4.052 lb
Answers
The Greatest error is equal to the absolute value of δ, which is 0.048 lb.
In the given question, we are asked to find the greatest error of 4.052 lb. We can find the error in this case by taking the difference between the measured value and the actual value.
The greatest error can be found by assuming that the actual value is the maximum value and the measured value is the minimum value.
Therefore, we can assume that the actual value is 4.052 + δ and the measured value is 4.052 - δ, where δ is the error.In order to find the value of δ, we need to use the concept of significant figures. Significant figures are the digits that carry meaning in a number.
For example, in the number 4.052 lb, all digits are significant because they all carry meaning. However, if we add a zero after the decimal point, as in 4.0520 lb, the zero is not significant because it does not carry any meaning. Therefore, we can say that the number 4.052 lb has four significant figures.
To find the value of δ, we need to use the rule that the error should be rounded to one significant figure. Therefore, we can round the number 4.052 to 4.1 and subtract it from 4.052 to get the value of δ:δ = 4.052 - 4.1 = -0.048 lb
Since the error is negative, it means that the measured value is less than the actual value.
Therefore, the greatest error is equal to the absolute value of δ, which is 0.048 lb.
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8The coordinates ofpoint A are (-6, 4). The coordinates ofpoint B are (3, 4)>Which expressionrepresents thedistance, in units,between points Aand B ?
Answers
Given the following coordinates of A and B below,
\(\begin{gathered} A(x_1,y_1)=(-6,4) \\ B(x_2,y_2)=(3,4) \end{gathered}\)To find the distance between coordinates A and B, the formula is,
\(d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}\)Substituting the points into the formula given above,
\(\begin{gathered} d=\sqrt[]{(3-(-6)^2+(4-4)^2} \\ d=\sqrt[]{9^2+0^2}=\sqrt[]{81+0}=\sqrt[]{81}=9\text{ units} \end{gathered}\)Since the distance between the two points is 9 units,
\(\begin{gathered} \lvert-6\rvert\text{ is 6 because the absolute value of a number is always positive} \\ \lvert3\rvert\text{ is} \\ \lvert-6\rvert+\lvert3\rvert=9\text{ units} \end{gathered}\)Hence, A is the right option.
2. 28 - 3t = 10
Work out the value of t.
Answers
Answer:
t = 6
Step-by-step explanation:
28 - 3t = 10
-3t = 10 - 28
-3t = -18
t = -18/-3
t = 6
Note: (-)/(-) = +
Answer:
t=6
Step-by-step explanation:
—3t=—18
t=6
Answer this question please
Answers
All the functions which are bounded below and bounded above are,
⇒ Absolute value function.
⇒ sine function function
⇒ cosine function
We have to given that;
To check all the functions which are bounded below and bounded above.
Here, All the functions are,
⇒ Absolute value function.
⇒ sine function function
⇒ cosine function
⇒ Square root function
⇒ natural logarithmic function
Since, The Absolute value function is defined as;
⇒ | f (x) |
And,
⇒ | f (x) | ≤ M ; for M > 0
⇒ - M ≤ f (x) ≤ M
Hence, It is a bounded function.
Since, Sine and cosine function are defined in between 1 and - 1.
Hence, Both are bounded below by - 1 and bounded above by 1.
So, Both function are bounded.
Since, Square root function is defined as,
⇒ √ f (x) ≥ 0
Hence, It is only bounded below.
Since, When the base of the logarithm is greater than 1, log(x) approaches negative infinity as x approaches 0.
Hence, It is not bounded.
Thus, All the functions which are bounded below and bounded above are,
⇒ Absolute value function.
⇒ sine function function
⇒ cosine function
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Margo borrows $200, agreeing to pay it back with 4% annual interest after 16 months. How much interest will she pay? Round your answer to the nearest cent, if necessary.
Answers
Answer:
Interest I = $10.67
Step-by-step explanation:
Simple interest I = principal × rate × time
I = Prt
Given;
Principal P = $200
rate r = 4% = 0.04
time t = 16 months = 16/12 years
Substituting the given values;
I = $200 × 0.04 × 16/12
I = $10.66666666666
I = $10.67
She will pay $10.67 interest.
The amount of money that Mary earns varies directly with the number of hours worked. If Mary earns $320 for working 40 hours,
determine the constant of variation
A)
6
B)
7
C)
8
D
9
Answers
Answer:
(c) 8
Step-by-step explanation:
Simplify the slope of AC
Answers
Answer:
\( \frac{c}{a + b} \)
Step-by-step explanation:
Point A is on the origin, hence its coordinates would be (0, 0). Coordinates of point C are (a + b, c)
Slope of AC
\( = \frac{c - 0}{a + b - 0} \\ \\ = \frac{c}{a + b} \\ \)
Answer:
In the green box of the numerator, enter "c"
In the gray bax in the denominator, there should be "a"
Step-by-step explanation:
Slope is Rise/Run.
Here the rise is "c" because the base is at 0, and the top of the parallelogram is at "c"
Solve for x.
3(-2x - 1) = 2(x + 5)
Answers
Answer:
x= − 8 /13 = −1 8 /5 = −1.625
Step-by-step explanation:
either one is the answer
<3 Enjoy,
Dea
Answer:
x=-1.625 Decimal form
x= -13/8 Fraction form
Step-by-step explanation:
3(-2x-1)=2(x+5)
Use distributive property to solve-
-6x-3=2x+10
Now add like terms
-6x-3=2x+10
+3 +3
-6x=2x+13 (get the x by itself)
-2x -2x
-8x=13 Divide
x= -1.625 Decimal form
x=-13/8 Fraction form
When Jonas becomes the Receiver of Memory, he gets a rule that he may not tell his dreams. He wants to know how many of his 505050 classmates have the same rule. He asks 555 friends from his class whether they may tell their dreams. Of those, 444 say that they may.
Answers
Answer:
101010 classmates can't tell their dreams.
Step-by-step explanation:
I'm not sure what the question is, but if it is an average thing than 444 of 555 is 80 percent, so if that is what it wants 404040 of the students can share their dreams, and 101010 can't.
Hope this helps!
A bank loaned out 20,500, part of it at the rate of 9% annual interest, and the rest at 11% annual interest the total interest earned for both loans was 2,225.00 how much was loaned at each rate
Answers
The money loaned at 9% annual interest was 1500 and the money loaned at 11% annual interest was 19000.
Let the amount of money loaned at 9% be x
the amount of money loaned at 11% be y
According to the question,
Total money loaned = 20,500
Thus the equation formed is,
x + y = 20,500 ------ (i)
Simple interest is calculated by
I = P * r * t
where I is the simple interest
r is the rate of interest
t is the time
Thus, the interest on x = 0.09x
the interest on y = 0.11y
Total interest gained = 2,225
Thus the equation formed is,
0.09x + 0.11y = 2225 -------(ii)
Multiply (i) by 0.09
0.09x + 0.09y = 1845
Subtract the above from (ii)
0.02y = 380
y = 19000
x = 1500
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let C be the curve y=5sqrtx for 1.1
Answers
We can integrate this S = 2π ∫(1.1 to 4.4) (5√(4x + 25))/(2√x) dx over the given interval (1.1 to 4.4) to find the surface area.
We can evaluate the integral using numerical methods or a calculator to find the final answer.
We have,
To find the surface area of the revolution about the x-axis of the function f(x) = 5√x over the interval (1.1 to 4.4), we can use the formula for the surface area of revolution:
S = ∫(a to b) 2πy√(1 + (f'(x))²) dx
In this case,
f(x) = 5√x, so f'(x) = (d/dx)(5√x) = 5/(2√x).
Let's calculate the surface area:
S = ∫(1.1 to 4.4) 2π(5√x)√(1 + (5/(2√x)²) dx
Simplifying the expression inside the integral:
S = ∫(1.1 to 4.4) x 2π(5√x)√(1 + 25/(4x)) dx
Next, we can integrate this expression over the given interval (1.1 to 4.4) to find the surface area.
To find the surface area of revolution about the x-axis of the function
f(x) = 5√x over the interval (1.1 to 4.4), we need to evaluate the integral:
S = ∫(1.1 to 4.4) 2π(5√x)√(1 + 25/(4x)) dx
Let's calculate the integral:
S = 2π ∫(1.1 to 4.4) (5√x)√(1 + 25/(4x)) dx
To simplify the calculation, let's simplify the expression inside the integral first:
S = 2π ∫(1.1 to 4.4) (5√x)√((4x + 25)/(4x)) dx
Next, we can distribute the square root and simplify further:
S = 2π ∫(1.1 to 4.4) (5√(4x + 25))/(2√x) dx
Thus,
We can integrate this expression over the given interval (1.1 to 4.4) to find the surface area.
We can evaluate the integral using numerical methods or a calculator to find the final answer.
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Adjust to compatible numbers that count by 25s, and then subtract to estimate the difference. 252 - 23 =
Answers
Answer:
252
l----------l----------l----------l 252 changes to 250
225 250 275 300
23
l----------l---------l---------l 25 changes to 23
0 25 50 75
250-25=225
Step-by-step explanation:
solve for θ. sinθ = cos(θ+10)
a. 6°
b.66°
c.84°
d.40°
Answers
Answer: d. 40°
Step-by-step explanation:
Use the Cofunction Identity: sin Ф = cos (90° - Ф)
sin Ф = cos (Ф + 10) = cos (90° - Ф)
⇒ Ф + 10 = 90 - Ф
2Ф + 10 = 90
2Ф = 80
Ф = 40
17. Find the missing angle(s).
soto
\b
Omg pls hurry I need help
Answers
Answer:
B = 50 & C = 130
Step-by-step explanation:
I really don't know how to explain but 180 - 50 = 130 for C and 50 is the measurement for B