A normally distributed population has a mean of 60 and a standard deviation of 10. The probability that the mean of a sample of 25 elements taken from this population will be smaller than 56 is
a.) 0.0166
b.) 0.0228
c.) 0.0394
d.) none of the above
Answers
Answer:
A.
Step-by-step explanation:
How to explain the word problem It should be noted that to determine if Jenna's score of 80 on the retake is an improvement, we need to compare it to the average improvement of the class. From the information given, we know that the class average improved by 10 points, from 50 to 60. Jenna's original score was 65, which was 15 points above the original class average of 50. If Jenna's score had improved by the same amount as the class average, her retake score would be 75 (65 + 10). However, Jenna's actual retake score was 80, which is 5 points higher than what she would have scored if she had improved by the same amount as the rest of the class. Therefore, even though Jenna's score increased from 65 to 80, it is not as much of an improvement as the average improvement of the class. To show the same improvement as her classmates, Jenna would need to score 75 on the retake. Learn more about word problem on; brainly.com/question/21405634 #SPJ1 A class average increased by 10 points. If Jenna scored a 65 on the original test and 80 on the retake, would you consider this an improvement when looking at the class data? If not, what score would she need to show the same improvement as her classmates? Explain.
we need to use the central limit theorem, which states that the distribution of the sample means of a large sample (n > 30) taken from a normally distributed population will also be normally distributed, with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
we have a normally distributed population with a mean of 60 and a standard deviation of 10. We want to find the probability that the mean of a sample of 25 elements taken from this population will be smaller than 56. Using the central limit theorem, we can calculate the standard error of the mean as 10 / sqrt(25) = 2. Therefore, the z-score corresponding to a sample mean of 56 is (56 - 60) / 2 = -2. Therefore, the probability that the mean of a sample of 25 elements taken from this population will be smaller than 56 is 0.0228 or approximately 2.28%. A distributed population refers to a set of data points that follow a specific pattern. In this case, the population is normally distributed with a mean of 60 and a standard deviation of 10. To find the probability that the mean of a sample of 25 elements is smaller than 56, we'll use the concept of standard deviation.
Step 1: Calculate the standard error (SE) using the formula SE = (Standard Deviation) / √(Sample Size), which is SE = 10 / √25 = 2.
Step 2: Compute the z-score using the formula z = (Sample Mean - Population Mean) / SE, which is z = (56 - 60) / 2 = -2.
Step 3: Refer to a standard normal distribution table or use a calculator to find the probability corresponding to the z-score. In this case, the probability is approximately 0.0228 or 2.28%.
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Related Questions
What is the product of 5 and 8√80 in simplest radical form? help plz thank you :)
Answers
Answer:
\(160\sqrt{5}\)
Step-by-step explanation:
357.77 is the product of 5 and 8√80 in simplest radical form.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here , we have,
the product of 5 and 8√80
i.e. 5*8√80
= 40*8.944
=357.77
Hence, 357.77 is the product of 5 and 8√80 in simplest radical form.
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What is 1/100 of 1.9 ?
Answers
Answer:
0.019Step-by-step explanation:
1/100 = 1%
Do 1% of 1.9
and you get =
0.019Hope this helps! <3
Answer:
0.019
Step-by-step explanation:
1/100=0.01
0.01×1.9=0.019
Type of shirt on the clearance rack (long-sleeved with collar, long-sleeved without collar, short-sleeved with collar, or short-sleeved without collar)
Answers
hey there, personally I would choose a short sleeve shirt without a collar bye
The correct categorization for each variable:
(a) Type of shirt on the clearance rack:
Type of variable: CategoricalLevel of measurement: Nominal(b) End-of-year stock classification:
Type of variable: CategoricalLevel of measurement: Ordinal
(c) Amount of coffee in a cup:
Type of variable: QuantitativeLevel of measurement: RatioWhat is the categorizationCategorization is the process of classifying or grouping items, data, or concepts into specific categories or classes based on their shared characteristics or attributes
This variable shows different types of shirts (long sleeves with a collar, long sleeves without a collar, short sleeves with a collar, or short sleeves without a collar).
The nominal level of measurement is the basic level where data is placed into separate groups without any particular order or ranking.
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See full text below
For each of the variables described below, indicate whether it is a quantitative or a categorical (qualitative) variable. Also, indicate the level of measurement for the variable: nominal, ordinal, interval, or ratio. Make sure your responses are the most specific possible.
Variable
Type of variable
Level of measurement
(a) Type of shirt on the clearance rack (long-sleeved with collar, long-sleeved without collar, short-sleeved with collar, or short-sleeved without collar)
Quantitative
Nominal
Ordinal
Categorical
Interval
Ratio
(b) End-of-year stock classification (high yield, medium yield, or low yield)
Quantitative
Nominal
Ordinal
Categorical
Interval
Ratio
(c) Amount (in fluid ounces) of coffee in a cup dispensed by a vending machine
Quantitative
Nominal
Ordinal
Categorical
Interval
Ratio
Can anybody solve this?
Answers
Answer:
the answer is 1
Step-by-step explanation:
mark brainliest, thankyou
If the two lines below are perpendicular and the slope of the red line is -7, what is the slope of the green line?
Answers
Answer:
1/7
Step-by-step explanation:
negative reciprocal
Solve the inequality:
2(x = 5) > 4
Answers
Answer:
x>-3 (if the = is meant to be +)
Step-by-step explanation:
Distribute the 2: 2x+10>4
Subtract 10 from both sides: 2x>-6
Divide both side by 2: x>-3
Solving algebraic equationsSolve:3z + 5 (2-z) =2z-10
Answers
distribute the 5 to whats inside the parentheses
\(3z+10-5z=2z-10\)simplify the common factors on both sides
\(-2z+10=2z-10\)bring all algebraic expressions to one side, and to the other all constant numbers
\(-2z-2z=-10-10\)simplify both sides
\(\begin{gathered} -4z=-20 \\ \end{gathered}\)divide both sides by 4
\(\begin{gathered} z=\frac{-20}{-4} \\ z=5 \end{gathered}\)What is the solution set for this inequality?
-8x + 40>-16
Answers
Answer:
x<7
Step-by-step explanation:
hope this helps :)
the hypotenuse of a right triangle is 11 inches. if one leg is 10 inches, find the degree measure of each angle
Answers
The measure of angles are
∠A = 24.61 degrees∠B = 90 degrees∠C = 65.39 degreesThe length of the hypotenuse of the right triangle = 11 inches
The length of the one leg = 10 inches
Then the length of the other leg is the square root of the sum of the hypotenuse square and one leg square
Then the equation will be
The length of the other leg = \(\sqrt{11^2-10^2}\)
= \(\sqrt{121-100}\)
= 4.58 inches
Therefore AC = 11 inches
AB = 10 inches
BC = 4.58 inches
The angle B = 90 degrees
Consider the angle A
cos θ = Adjacent side / hypotenuse
cos θ = 10 /11
θ = 24.61 degrees
Consider the angle C
cos θ = Adjacent side / Hypotenuse
cos θ = 4.58 / 11
θ = 65.39 degrees
Hence, the measure of angles are
∠A = 24.61 degrees∠B = 90 degrees∠C = 65.39 degreesLearn more about right triangle here
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What is the answer ?
Answers
\(a^{2} - b ^{2} + 4b - 4\)
Answers
Answer:
\(\left(a+b-2\right)\left(a-b+2\right)\)
Step-by-step explanation:
\(a^2-b^2+4b-4\)
\(a^2-\left(b^2-4b+4\right)\)
\(a^2-(b^2-2b-2b+4)\)
\(a^2-\left(b-2\right)\left(b-2\right)\)
\(a^2-\left(b-2\right)^2\)
Apply the difference of two squares formula.
\(x^2-y^2=(x+y)(x-y)\)
\(\left(a+\left(b-2\right)\right)\left(a-\left(b-2\right)\right)\)
\(\left(a+b-2\right)\left(a+2-b\right)\)
The speed limit on the Princes Highway in Victoria is 110km/hour.
What is this speed limit, rounded to the nearest whole number, in m/s?
Answers
Answer:
31m/s
Step-by-step explanation:
110km/h
110 × 1000m / 3600s
110000m/3600s
30.55m/s
*Rounding up to nearest whole number*
31m/s ( I hope it helps )
i need help plsss
Given: m <1=110°
m< 2=70°
Prove:
angle 2 is supplementary to angle 3
<1~<3
Answers
Step-by-step explanation:
if <1 is congruent with < 3 in. you know congruent means if the two triangles have the same shape and size so <1 and < 3 are the same size means < 3 is 110°
if < 2 is 70° and < 3 is 110° that are supplementary the total is 180°
Classify each variable according to the set of numbers that best describes itsvalues.
1.the area of the circleAfound by using the formulaπr2
2.the number n of equal slices in a pizza; the portion p of the pizza in one slice
3. the air temperaturetin Saint Paul, MN, measured to the nearest degreeFahrenheit
4. the last four digitssof a Social Security number
Answers
The variable "area of the circle" would likely be classified as a continuous variable, as it can take on any value within a certain range (e.g. 0 to infinity), and the difference between any two values within that range can be any positive value.
The variable "number of equal slices in a pizza" would likely be classified as a discrete variable, as it can only take on certain integer values (e.g. 1, 2, 3, etc.). Similarly, the variable "portion of the pizza in one slice" would also be classified as a discrete variable, as it can only take on certain values (e.g. 1/2, 1/3, 1/4, etc.).
The variable "air temperature in Saint Paul, MN" would likely be classified as a continuous variable, as it can take on any value within a certain range (e.g. -40 to 120 degrees Fahrenheit), and the difference between any two values within that range can be any positive value.
The variable "last four digits of a Social Security number" would likely be classified as a discrete variable, as it can only take on certain integer values (e.g. 0001 to 9999).
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Bethany made a sketch of a mural she is going to paint. The sketch is a rectangle that is 8 inches by 11 inches. What is the percent increase of the perimeter of the mural from the sketch?
Answers
The percent increase of the perimeter of the mural from the sketch is 20%.
The sketch of a mural that Bethany is going to paint is a rectangle of 8 inches by 11 inches.
We can use the formula for the perimeter of a rectangle to find its perimeter.
Perimeter of a rectangle = 2 × (length + width)
So, the perimeter of the sketch is:
Perimeter of the sketch = 2 × (8 + 11)
= 2 × 19
= 38 inches
Now, let's find the perimeter of the actual mural.
We don't know the exact dimensions of the mural, but we do know that it will be bigger than the sketch.
Let's say that the dimensions of the mural will be 120% of the dimensions of the sketch.
We can use this to find the dimensions of the mural:
Length of mural = 1.2 × 8
= 9.6 inches
Width of mural = 1.2 × 11
= 13.2 inches
Now we can use the formula for the perimeter of a rectangle to find the perimeter of the mural:
Perimeter of the mural = 2 × (length + width)
= 2 × (9.6 + 13.2)
= 2 × 22.8
= 45.6 inches
The percent increase of the perimeter of the mural from the sketch can be found using the formula:
Percent increase = ((new value - old value) / old value) × 100
We want to find the percent increase of the perimeter, so:
Old value = 38 inches
New value = 45.6 inches
Percent increase = ((45.6 - 38) / 38) × 100
= (7.6 / 38) × 100
= 20%
Therefore, the percent increase of the perimeter of the mural from the sketch is 20%.
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A researcher is studying the relation between sleep and mood. The researcher asked 20 people how many hours of sleep each had last night and had each rate how happy each felt at that moment on a scale from 0 ("Not at all happy") to 100 ("Extremely happy"). The following summary statistics are from the researcher’s study:
∑sleep = 144 ∑mood = 1,410
∑(sleep2) = 1,114 ∑(mood2) = 108,394
∑(sleep * mood) = 10,742
a. What is the correlation between hours of sleep and mood score?
b. What is the regression equation for predicting mood score from hours of sleep? (This means to compute a and b and write the regression equation using those values.)
Answers
a.The correlation between hours of sleep and mood score is approximately 0.707. b.The regression equation for predicting mood score from hours of sleep is: Mood score ≈ 15.496 + 7.641 * Hours of sleep
a. To calculate the correlation between hours of sleep and mood score, as well as the regression equation for predicting mood score from hours of sleep, we can use the following formulas:
Correlation (r):
r = (n∑(sleep * mood) - ∑sleep * ∑mood) / √((n∑(sleep^2) - (∑sleep)^2) * (n∑(mood^2) - (∑mood)^2))
Regression equation:
Mood score = a + b * Hours of sleep
Where:
n = number of observations (in this case, 20)
∑ represents the sum of the values
Let's plug in the given values and calculate the correlation and regression equation:
∑sleep = 144
∑mood = 1,410
∑(sleep^2) = 1,114
∑(mood^2) = 108,394
∑(sleep * mood) = 10,742
n = 20
Calculating the correlation (r):
r = (20 * 10,742 - 144 * 1,410) / √((20 * 1,114 - 144^2) * (20 * 108,394 - 1,410^2))
r = (214,840 - 203,040) / √((22,280 - 20,736) * (2,167,880 - 1,988,100))
r = 11,800 / √(1,544 * 179,780)
r ≈ 11,800 / √277,964,320
r ≈ 11,800 / 16,670.37
r ≈ 0.707
The correlation between hours of sleep and mood score is approximately 0.707.
b. To find the regression equation, we need to calculate the coefficients a and b.
b = (n∑(sleep * mood) - ∑sleep * ∑mood) / (n∑(sleep^2) - (∑sleep)^2)
b = (20 * 10,742 - 144 * 1,410) / (20 * 1,114 - 144^2)
b = 214,840 - 203,040 / (22,280 - 20,736)
b = 11,800 / 1,544
b ≈ 7.641
a = (∑mood - b * ∑sleep) / n
a = (1,410 - 7.641 * 144) / 20
a = 1,410 - 1,099.104 / 20
a ≈ 15.496
Therefore, the regression equation for predicting mood score from hours of sleep is:
Mood score ≈ 15.496 + 7.641 * Hours of sleep
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I NEED ANSWERS ASAP!!! PLEASE
Answers
Answer:
10 in by 48 in
Step-by-step explanation:
The volume (V) of a rectangular solid is calculated as
V = Ah ( A is the area of the base and h the height )
Here h = 3 and V = 1440 , then
3A = 1440 ( divide both sides by 3 )
A = 480 in²
The area of a rectangle = length × breadth
From the give options
10 × 48 = 480 ← is the only option
help me 7th grade mathh
Answers
Answer:
The 3rd answer, 1 pound of blueberry's is $2.75
Step-by-step explanation:
6 x 2.75 is equal to 16.5
Identify the smallest relation containing the relation R = {(a, b) | a > b} on the set of positive integers that is both reflexive and symmetric.
a. A.R = {(a, b) | a ≥ b}
b. B.R = {(a, b) | a = b and a ≠ b}
c. C.R = {(a, b) | a = b or a ≠ b}
d. D.R = {(a, b) | a > b or a < b}
Answers
C.R = {(a, b) | a = b or a ≠ b} is the smallest relation containing the relation R = {(a, b) | a > b} on the set of positive integers that is both reflexive and symmetric. Therefore, the correct option is c.
The relation R = {(a, b) | a > b} on the set of positive integers is a non-reflexive relation because there are no elements in R that are of the form (a, a). To make it reflexive, we need to add elements of the form (a, a) to the relation R. However, we also need to ensure that the relation remains symmetric.
Option a, A.R = {(a, b) | a ≥ b}, contains all the elements of R, including those of the form (a, b) where a > b, and also includes elements of the form (a, a). However, it is not symmetric because if (a, b) is in A.R, then (b, a) is not necessarily in A.R.
Option b, B.R = {(a, b) | a = b and a ≠ b}, only contains elements of the form (a, a) where a is a positive integer. It is reflexive but not symmetric because (a, a) is in B.R but (a, b) or (b, a) is not in B.R for any a and b where a ≠ b.
Option c, C.R = {(a, b) | a = b or a ≠ b}, is the smallest relation that contains R and is both reflexive and symmetric. It contains all elements of R as well as elements of the form (a, a) for all positive integers a. Since it includes both (a, b) and (b, a) for any two positive integers a and b, it is also symmetric.
Option d, D.R = {(a, b) | a > b or a < b}, contains all elements of R and also includes elements of the form (a, b) where a < b. It is not reflexive because it does not contain any elements of the form (a, a) for any positive integer a.
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asapppp help me someone please
Answers
Answer:
3/5
Step-by-step explanation:
P ( walks or takes the bus) = walks or takes the bus/ total
walks = 10
takes the bus = 25+ 20+5 = 50
There is no overlap
P ( walks or takes the bus) = walks or takes the bus/ total
= (10+ 50)/ 100
= 60/100
=3/5
Answer:3/5
Step-by-step explanation:
Just put the answer in and it’s right
QP=
Help please thanks so much
Answers
Answer:
QP = | a - d |
Step-by-step explanation:
since the y- coordinates of P and Q are equal , both b
then PQ is the absolute value of the difference of the x- coordinates, that is
QP = | a - d | = | d - a |
Tariq went shopping for a new pair of pants. Sales tax where he lives is 4%. The price of the pair of pants is $30. Find the total price including tax. Round to the nearest cent.
Answers
Answer:
Step-by-step explanation:
4% = 4/100
4/100 x 30 = 1.2
30 + 1.2 = 31.20 (nearest cent)
Answer:
31.20
Step by step explanation: I got it from delta
In a continuous review policy with R=1500,σ2
R=200, and L=3, what is the reorder point at a cycle service level of 95% ? 1) 4,070 2) 4,470 3) 5,970 4) 5,070
Answers
The correct option from the given choices is 4) 5,070. Determine the reorder point in a continuous review policy with a cycle service level of 95%,
We can use the following formula:
Reorder Point = R + Z * sqrt(L * \(σ^2_R\))
Where:
- R is the average demand during lead time
- Z is the Z-score corresponding to the desired service level (95% corresponds to a Z-score of approximately 1.645)
- L is the lead time
- \(σ^2_\)R is the variance of demand during lead time
Given:
R = 1500
\(σ^2\)R = 200
L = 3
Using the formula, we can calculate the reorder point:
Reorder Point = 1500 + 1.645 * sqrt(3 * 200)
Reorder Point ≈ 1500 + 1.645 * sqrt(600)
Reorder Point ≈ 1500 + 1.645 * 24.4948974
Reorder Point ≈ 1500 + 40.2570784
Reorder Point ≈ 1540.2570784
Rounding the reorder point to the nearest whole number, we get:
Reorder Point ≈ 1540
Therefore, the correct option from the given choices is 4) 5,070.
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(solve the literal equation for y.)
6 - 3y = -6
Answers
Answer:
4
Step-by-step explanation:
SCOOBY+DOOO=BUSTED;
FIND THE VALUE OF B+U+S+T+E+D ?
Answers
The value of B+U+S+T+E+D is 20. B represents the number 2, U represents the number 3, S represents the number 19, T represents the number 20, E represents the number 5, and D represents the number 4. When these numbers are added together, they equal 20.
BUSTED is an acronym for 'Believing Uncovering Solving Troubles Everywhere Dynamicly'. It is a popular phrase used by the characters in the Scooby-Doo cartoons. It is a phrase used to express the moment when the mystery is solved and the bad guy is caught.
BUSTED is an important part of the Scooby-Doo cartoon series. It expresses the moment when the mystery is solved and the bad guy is caught. It is also a great way to encourage children to believe in themselves and to use their own detective skills to solve a mystery. The value of B+U+S+T+E+D is 20, and it is a fun way to teach kids math and problem solving skills.
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instructions: for profit/loss, round your answers to two decimal places. if you are entering any negative numbers be sure to include a negative sign (-) in front of those numbers. a loss should be entered as a negative number. b. given a price of $11 per gift box, how many boxes of chocolate should choco lovers produce? gift boxes what will the profit or loss be per gift box? $ per gift box c. suppose that choco lovers raises the price to $13 per gift box. now how many boxes should choco lovers produce? gift boxes what will the new profit or loss be per gift box?
Answers
Choco Lovers will face a loss of 5.625 per gift box.
Choco Lovers will face a loss of 18 per gift box.
Gift boxes = (Fixed Cost + Profit) / Profit per unit
11 = (30,000 + Profit) / 8
Profit = 8 × Gift boxes – 30,000
Profit = 8G – 30,000
Here, Profit per unit = 8
Fixed Cost = 30,000
By substituting the values in the formula, we get:
8G – 30,000 = Profit
G = (30,000 + Profit) / 8 At 11 per gift box, Choco Lovers should produce 4375 boxes of chocolate.
per gift box Profit per unit = Selling price per unit – Variable cost per unit
Selling price per unit = 11
Variable cost per unit = 8
Profit per unit = 11 – 8 = 3
Profit/Loss per box = 3 × 4375 – 30,000
Profit/Loss per box = -5625
Suppose that Choco Lovers raises the price to 13 per gift box.
Now,
Gift boxes = (Fixed Cost + Profit) / Profit per unit
13 = (30,000 + Profit) / 10
Profit = 10 × Gift boxes – 30,000
Profit = 10G – 30,000
Here, Profit per unit = 10
Fixed Cost = 30,000
By substituting the values in the formula, we get:
10G – 30,000 = Profit
G = (30,000 + Profit) / 10
At 13 per gift box, Choco Lovers should produce 4000 boxes of chocolate.
Profit per unit = Selling price per unit – Variable cost per unit
Selling price per unit = 13
Variable cost per unit = 10
Profit per unit = 13 – 10 = 3
Profit/Loss per box = 3 × 4000 – 30,000
Profit/Loss per box = -18000
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ADHE - ADGF below. Find the value of 'x'.
X
H н
E
8
2.
12
Answers
Given:
\(\Delta DHE\sim \Delta DGF\)
To find:
The value of x.
Solution:
We know that, corresponding sides of similar triangles are proportional.
Since,\(\Delta DHE\sim \Delta DGF\), therefore
\(\dfrac{HE}{GF}=\dfrac{DE}{DF}\)
On substituting the values from the figure, we get
\(\dfrac{8}{12}=\dfrac{x}{x+2}\)
\(\dfrac{2}{3}=\dfrac{x}{x+2}\)
On cross multiplication, we get
\(2(x+2)=3x\)
\(2x+4=3x\)
\(4=3x-2x\)
\(4=x\)
Therefore, the value of x is 4.
How many different triangles can you make if you are given the measurements for 2 sides and a angle that is not between those sides?
Answers
Th different triangles that can you make if three property of the triangle is known and one side must be known, will be one.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
To specify the triangle, atleast one of the sides must be known and any other two property like side-angle, side-side, and angle-angle.
Th different triangles that can you make if three property of the triangle is known and one side must be known, will be one.
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a container hold 6 cups of yogurt. The nutrition label reads that a serving size is 1/3 cup. How many servings are there in the container?
Answers
Answer:
18 servings
Step-by-step explanation:
If one serving is 1/3 cup, one cup is 3 servings. Therefore, we can multiply 3 x 6 for an answer of 18 servings
Can somebody plz help tell me how to find the people who surveyed like where do u find it? Thx!
WILL MARK BRAINLIEST WHOEVER CAN HELP WITH THIS :DDD
