The data set below is a random sample of the heights (in meters) of women belonging to a certain ethnic subgroup. Assume the population is normally distributed 1.63 1.62 1.61 162 1.39 1.55 a) Find the mean and standard deviation of the data.
Answers
The mean of the data set is approximately 1.57 meters. The standard deviation of the data set is approximately 0.0968 meters, indicating the average deviation of data points from the mean.
To compute the mean and standard deviation of the data set, we'll use the following formulas:
Mean (μ) = (sum of all data values) / (total number of data values)
Standard Deviation (σ) = sqrt((sum of squared differences from the mean) / (total number of data values))
Let's calculate the mean and standard deviation for the given data set:
Data set: 1.63, 1.62, 1.61, 1.62, 1.39, 1.55
Mean (μ) = (1.63 + 1.62 + 1.61 + 1.62 + 1.39 + 1.55) / 6 = 9.42 / 6 ≈ 1.57
Next, we calculate the sum of squared differences from the mean:
(1.63 - 1.57)^2 + (1.62 - 1.57)^2 + (1.61 - 1.57)^2 + (1.62 - 1.57)^2 + (1.39 - 1.57)^2 + (1.55 - 1.57)^2 ≈ 0.0666
Finally, we calculate the standard deviation:
Standard Deviation (σ) = sqrt(0.0666 / 6) ≈ 0.0968
Therefore, the mean of the data set is approximately 1.57 meters and the standard deviation is approximately 0.0968 meters.
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Related Questions
Jake had 11 comic books. Rowan has 6 more comic books than jake
Answers
Rowan has 17 comic books
8) A dress normally sells for $35.85. How much does the dress cost after a 15% discount??
Answers
Answer:
$30.47
Step-by-step explanation:
100%-15%=85%
85%=0.85
$35.85*0.85=30.47 (to 2d.p)
Hope this helps
Sarah is creating a triangular birthday card for her teacher. In order to glue lace
around the outside of the card, Sarah needs to know the length of each side. She
knows that two of the sides measure 4 inches and 9 inches. Between which two
numbers must the third side of the card fall?
Answers
Answer:
6-12.
Step-by-step explanation:
Between 6 to 12 two numbers must the third side of the card fall.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
We are given that Sarah is creating a triangular birthday card for her teacher.
Thus in order to glue lace around the outside of the card, Sarah needs to know the length of each side.
It should be known that two of the sides measure 4 inches and 9 inches.
Therefore, in between 6 to 12 the third number must be lie.
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Is 6 a factor of 20 yes or no
Answers
Answer:
no 6 aint no factor of 20
Step-by-step explanation:
Solve the equation for x. −0.24x − 16.4 = 1.48 x = −62.2 x = 62.2 x = −74.5 x = 74.5
hurry pls
Answers
The solution of the given linear equation is x = -9.53
How to solve the equation for x?Here we have the linear equation:
-0.24*x - 16.4 = 1.48*x
To solve this, first we need to move all the terms with x to the left and the terms without x to the right.
-0.24*x - 1.48*x = 16.4
(-0.24 - 1.48)*x = 16.4
-1.72*x = 16.4
Now we can divide both sides by -1.72 to get:
x = 16.4/-1.72 = -9.53
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Answer: c) (is it c?)
Step-by-step explanation: c) x= - 74.5
0.24x+16.4=-1.48 step 1- subtract: -1.48- 16.4
0.24x= -17.88 (divide)
x= −74.5
there
i hope this helps!!
Find the side x, giving answer to 1 decimal place
Answers
Answer:
Set your calculator to degree mode.
Using the Law of Sines:
7/sin(40°) = x/sin(81°)
x = 7sin(81°)/sin(40°) = 10.8
Answer:
10.8=x
Step-by-step explanation:
Using the Law of Sines, we can put together the fact that
\(\frac{sin A}{a} =\frac{sinB}{b}\)
Substitute our given values from the triangle:
\(\frac{sin 81}{x} =\frac{sin40}{7}\)
Turn the sines into a decimal:
\(\frac{0.9876}{x} =\frac{0.6427}{7}\\\)
cross multiply using butterfly method
0.988·7=0.643x
solve for x
6.916=0.643x
divide both sides by 0.643
10.8=x (round to nearest tenth)
Hope this helps! :)
For the normal distribution with parameters µ= 4, ϭ= 3, calculate p(x >1)
Answers
Therefore , the solution to this problem of probability of P(x > 1) = 0.8413 .
What defines probability?The mathematical formula known as a probability calculation, which is described by that mathematical formula, determines all the probabilities for a thing to occur under specific random events. The closer a probability is to the unit value, the less confident one may be in the outcome; on the other side, the closer it is to zero, the less confident one can be in the outcome. The degree of certainty is determined by the proximity of the probability value, which is calculated using a number between 0 and 1.
Here,
Given : µ= 4, ϭ= 3
Thus,
=> P(x > 1) = P(x-4/3 , 1-4/3 )
= P( Z > -1)
By using standard normal table
we get , = 0.8413
So,
We get , P(x > 1) = 0.8413
Therefore , the solution to this problem of probability of P(x > 1) = 0.8413 .
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a candy bar cost ninety-five cents, which is 19 times the price of a piece of hard candy. what is the price of hard candy?
Answers
If a candy bar cost 95 cents which is 19 times the price of a piece of hard candy, then the price of hard candy is 5 cents
The cost of a candy bar = 95 cents
The cost of the candy bar is 19 times the price of a piece of hard candy
Assume that the cost of one hard candy is x
Then the equation will be
The cost of hard candy × 19 = The cost of a candy bar
Substitute the values in the equation
x × 19 = 95
Move the 19 to the right hand side of the equation
x = 95 / 19
Use the division
x = 5 cent
Therefore, the price of hard candy is 5 cent
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Yolanda wants to replace the grass in this triangular section of her yard with mulch. A bag of mulch costs $4.85 and covers 3 square feet. Which of the following statements accurately describe this situation? Select all that apply.
Yolanda wants to replace the grass in this triangular section of her yard with mulch. A bag of mulch costs $4.85 and covers 3 square feet. Which of the following statements accurately describe this situation? Select all that apply.
Answers
Answer:
Step-by-step explanation:
A grade 7 student does jumping jacks at a constant rate. If the student does 40 jumping jacks in one minute, how many jumping jacks does the student do in 15 seconds?
Answers
If the student does 40 jumping jacks in one minute, 10 jumping jacks does the student do in 15 seconds.
Given Information:
Student does jumping jacks at a constant rate.
If the student does 40 jumping jacks in one minute.
To determine how many jumping jacks does the student do in 15 seconds.
40 jumping jacks = 1 minute
1 minutes = 60 second
60 second = 40 jumping jacks
15 seconds = 40/ 60 * 15
= 0.666 * 15
= 10
Therefore, 10 jumping jacks does the student do in 15 seconds.
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Find the Surface area
Answers
Answer:
A=l×w×h
Step-by-step explanation:
5×5×6×7
1050. or if we add 4 in the solution part 2400
Study the sentence below and select the best answer:
Peter receives a basic salary of £150 a weekly plus a 15% commission on all sales. Peter sold exactly
£3,000 this week. How much did he make in total?
£600
£700
£450
£500
Answers
you roll a 6-sided die with faces numbered 1 through 6, and toss a coin what is the probability of rolling a 2 or getting heads
Answers
Answer:
2/3
Step-by-step explanation:
You have 6 possible outcomes. Getting 1 outcome is 1/6. You have 2 possible outcomes. Getting 1 outcome is 1/2.
Add 1/2 and 1/6 to get 2/3
ratio of 3 boys and 4 girls there are now 12 boys
Answers
Answer:
There are 16 girls.
Step-by-step explanation:
3 : 4
12 : x
Now if we cross multiply:
3(x) = 12(4)
3x = 48
x = 16
SAT scores are normally distributed with a mean of 500 and a standard deviation of 100. Find each of the following.
1) The minimum score to put you in the upper 25% of scores
2) The z-score of an SAT score of 670
3) The percentage of scores between 420 and 620
4) The percentage of scores below 350
Answers
Answer:
i dont know
Step-by-step explanation:
write the sequence of natural numbers which leaves the remainder 3 on didvidng by 10
Answers
The sequence of natural numbers that leaves a remainder of 3 when divided by 10 is:
3, 13, 23, 33, 43, 53, 63, 73, 83, 93, 103, 113, ...
\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)
♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)
Its midpoint i need help
Answers
Answer:
(3.5, 4.8)
Step-by-step explanation:
2.6 - 1.7 = 0.9, 2.6 + 0.9 = 3.5
3 - 1.2 = 1.8, 3 + 1.8 = 4.8
Answer:
\(thank \: you\)
Triangle a is reflected in the x-axis to give b which is the reflected in the line y=x.
Answers
Triangle a is reflected in the x-axis to give b which is reflected in the line y=x. The coordinates of triangle C are (-5,4) , (-2,2) and (-2,4)
Coordinates for Triangle A are (4,5), (2,2), and (4,2)
Triangle B is created by reflecting triangle A along the x-axis.
The x-axis coordinates stay the same after reflection in the x-axis, while the y-axis coordinates go negative with the same magnitude.
Consequently, triangle B's coordinates are (4, -5), (2, -2), and (4,-2)
The x and y coordinates of triangle B are now reversed as it is reflected by the line y = x to create triangle C.
Triangle C's coordinates are (-5,4), (-2,2), and (-2,4)
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!!20 Points!! Solve using augmented matrices.
x+y=1
3x-y=7
Answers
y=-1
You have to do subtitution
The marked price of an article is rs 10000 . If he discounted rate and VAT rate are equal and the price with VAT is 9900 find the vat rate .
Answers
The rate of VAT is 10%.
In the question, we are asked to find the VAT rate, given that the market price of an article is Rs. 10000, the rate of discount and the rate of VAT are equal, and the price after VAT is Rs. 9900.
We assume the rate of discount and the rate of VAT to be r%.
Thus, discount = r% of Rs. 10000 = Rs. r/100 * 10000 = Rs. 100r.
Thus, the price after discount = Rs. 10000 - 100r = Rs. 100(100 - r)
Then, VAT = r% of (Rs. 100(100 - r)) = Rs. r/100 * 100(100 - r) = Rs. r(100 - r).
Thus, the price after VAT = Rs. 100(100 - r) + Rs. r(100 - r) = Rs. (100 + r)(100 - r).
The price after VAT is given to be Rs. 9900.
Thus, (100 + r)(100 - r) = 9900,
or, 100² - r² = 9900,
or, r² = 100² - 9900,
or, r² = 10000 - 9900 = 100,
or, r = ±√100 = ±10.
Since r is the rate of VAT, it cannot be negative, making r = 10.
Thus, the rate of VAT is 10%.
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Plz help please
Is the relation shown in the arrow diagram a function?
Answers
Answer:
The answer is A
Step-by-step explanation:
In order for it to be a function every x value has to have a different y value or every input has to have a different output.
find the quotient.
Answers
Answer:11 to the 15th power :)
Step-by-step explanation:
you subtract the lower number from the higher number and in this case since the higher number is on top, the answer goes on top which means it’s positive
Andres is going to invest in an account paying an interest rate of 4% compounded
continuously. How much would Andres need to invest, to the nearest dollar, for the
value of the account to reach $4,700 in 11 years?
Answers
\(~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 4700\\ P=\textit{original amount deposited}\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &11 \end{cases} \\\\\\ 4700=Pe^{0.04\cdot 11} \implies 4700=Pe^{0.44}\implies \cfrac{4700}{e^{0.44}}=P\implies 3027\approx P\)
Which of the following sets is not finite?
{ x | x is a natural number less than 10}
{ x | x is an integer that is less than 0}
{ x | x is a whole number between 0 and 10}
Answers
The following sets:
finitefiniteNot finiteWhat is function?
An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable)
First,
{x| x∈ N ∧ x<10} = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9} which is finite
Next,
{x| x∈ Z ∧ 0<x<10} = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9} which is finite
Last,
{x| x∈ Z ∧ x<10} = { ........,-4 ,-3 ,-2 ,-1} which is not finite
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One endpoint on GH is G(–7, 24). The midpoint is M(3, 4). Find the coordinates of the endpoint H. ( , )
Please help find endpoint H
Answers
Answer:
H (13, -16)
Step-by-step explanation:
\(\boxed{\begin{minipage}{7.4 cm}\underline{Midpoint between two points}\\\\Midpoint $=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the endpoints.\\\end{minipage}}\)
Given:
Endpoint (x₁, y₁) = G (-7, 24)Endpoint (x₂, y₂) = H Midpoint = M (3, 4)Substitute the given endpoint G and midpoint M into the midpoint formula:
\(\implies M=\left(\dfrac{x_H+x_G}{2},\dfrac{y_H+y_G}{2}\right)\)
\(\implies (3, 4)=\left(\dfrac{x_H-7}{2},\dfrac{y_H+24}{2}\right)\)
x-value of endpoint H:
\(\implies 3=\dfrac{x_H-7}{2}\)
\(\implies 6=x_H-7\)
\(\implies x_H=13\)
y-value of endpoint H:
\(\implies 4=\dfrac{y_H+24}{2}\)
\(\implies8=y_H+24\)
\(\implies y_H=-16\)
Therefore, the coordinates of endpoint H are:
(13, -16)Answer: 13 -16
Step-by-step explanation: Edge 2023
Han calculated the volume of a cylinder. Han said, “I used the formula V=\(\pi r^{2} h."\)
Do you agree with Han's strategy? Explain your reasoning.
Answers
Han's strategy is correct, as V = πr²h is the exact formula for the volume of a cylinder of radius r and height h.
How to obtain the volume of a cylinder?The volume of a cylinder of radius r and height h is given by the equation presented as follows:
V = πr²h.
This is the exact formula used by Han, hence the strategy is correct.
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The equation of circle D is (x + 2)2 + y² = 32.
Select all the points that lie on circle D.
□ (-6,-4)
□ (-2,16)
□ (-4,6)
□ (0,14)
□ (2,4)
Answers
The equation of circle D is (x + 2)2 + y² = 32 then the points (-6,-4) and (-4,6) lie on circle D
The equation of a circle with center (h,k) and radius r is (x - h)² + (y - k)² = r².
This is called the standard form of the equation of a circle.
In the given equation, (x + 2)² + y² = 32, we can see that the center of the circle is (-2, 0) and the radius is √32 = 4√2.
To determine which points lie on the circle, we substitute the x and y coordinates of each point into the equation and check if the equation is true.
If it is true, then the point lies on the circle.
Let us check if (-6, -4) lies on the circle, we substitute x = -6 and y = -4 into the equation:
(-6 + 2)² + (-4)² = 32
(-4)² + (-4)² = 32
16 + 16 = 32
32 = 32
Since the equation is true, (-6, -4) lies on the circle.
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Write the equation of the line with a slope of 5 and a y-intercept of (0, -3)
Answers
Answer:
y = 5x - 3
Step-by-step explanation:
equation of a straight line is y = mx + b where m=slope and b=y-intercept
in this case m=5 and b= -3
y = mx + b
y = 5x - 3
Consider the graph. Which inequality best represents the graph?
Answers
Answer:
y >= x/2 - 1
Step-by-step explanation:
the slope (rise/run) is 1/2 and the y-intercept is -1 so in point-slope form
y = x/2 - 1 but everything above the line (unshaded part) is valid so y is equal to or greater than.
3) 8x = 72
It’ll help
Answers
Answer:
9
Step-by-step explanation:
×=72/8
×=9
Hope it helps
Answer: 9
Step-by-step explanation: First, look for the value of x. A number with a variable in front of it means that you’ll be multiplying, but you can use division which makes it easier to find x. SO, DIVIDE 72 by 8 (82 ÷ 7), which equals to 9. (8 x 9 = 72)