The diameter of a brand of tennis balls is approximately normally distributed, with a mean of 2.63 inches and a standard deviation of 0.03 inch. if you select a random sample of 9 tennis balls, what is the probability that the sample mean is between 2.62 and 2.64 inches
Final answer:
The probability that the sample mean diameter is between 2.62 and 2.64 inches is approximately 68.27%, calculated using the Central Limit Theorem to find the standard error and z-scores.
Explanation:
To calculate the probability that the sample mean diameter of the tennis balls is between 2.62 and 2.64 inches, we can use the Central Limit Theorem since we are dealing with a sample of tennis balls rather than just one. The Central Limit Theorem tells us that the sampling distribution of the sample mean will be normally distributed with a mean equal to the population mean (μ) and a standard deviation equal to the population standard deviation (σ) divided by the square root of the sample size (n), which is called the standard error (SE).
Given that the population mean (μ) is 2.63 inches, the population standard deviation (σ) is 0.03 inch, and the sample size (n) is 9, we first calculate the standard error (SE) as follows:
SE = σ / √n = 0.03 / √9 = 0.03 / 3 = 0.01 inch.
Next, we convert the sample mean range (2.62, 2.64) to z-scores, which are measures of how many standard deviations an element is from the mean.
Z for 2.62 = (2.62 - μ) / SE = (2.62 - 2.63) / 0.01 = -0.01 / 0.01 = -1
Z for 2.64 = (2.64 - μ) / SE = (2.64 - 2.63) / 0.01 = 0.01 / 0.01 = 1
Using a standard normal distribution table or calculator, we find the probabilities corresponding to these z-scores. The probability of a z-score being between -1 and 1 is approximately 0.6827 (68.27%).
Therefore, the probability that the sample mean diameter is between 2.62 and 2.64 inches is approximately 68.27%.
Lebron scored a basket 72 times out of 150 shots. what percent of his shots did he score?
a. 42%
b. 50%
c. 48%
d. 63%
square root of 4 plus 45 over 4 plus 125 over 25
I need help with a homework assignment:
Write each series in summation notation beginning with k = 1.
1/2 + 2/3 + 3/4 + 4/5 + 5/6
−11 + 12 − 13 + 14 − 15 + 16
9 − 16 + 25 − 36 + 49 − 64
3 + (3/2) + 1 + (3/4) + (3/5)
I get the numbers that go under and on top of the sigma, I need help deriving the explicit value for the sequence that goes on the right of the sigma.
Thanks
A can in the shape of a right cylinder is filled with 10W-40 oil. The weight of 10W-40 oil is 0.857 gram per cubic centimeter. If the cylinder has a radius of length 5 cm and a height of 10 cm, calculate the weight of the oil (in grams) in the can. Round your answer to the nearest tenth. Use 3.14 for pi
Answer: Weight of the oil is 672.74 grams.
Step-by-step explanation:
Since we have given that
Radius of cylinder = 5 cm
Height of cylinder = 10 cm
Volume of cylinder would be
[tex]\pi r^2h\\\\=3.14\times 5\times 5\times 10\\\\=785\ cm^3[/tex]
Weight of 10W-40 oil = 0.857 grams per cubic cm
So, Weight of the oil in the can would be
Volume × Weight per cm³
[tex]=785.71\times 0.857\\\\=672.74\ grams[/tex]
Hence, Weight of the oil is 672.74 grams.
how do I solve 12-3(x-5)=21
In 1996, funding for a program increased by 0.62 billion dollars from the funding in 1995. In 1997, the funding increased 0.29 billion dollars over the funding in 1996. For those three years, the funding was 11.25 billion dollars. How much was funded in each of these three years?
A triangle is dilated by a scale factor of n = 1/3 . Which statement is true regarding the dilation?
It is a reduction because n > 1.
It is a reduction because 0 < n < 1.
It is an enlargement because n > 1.
It is an enlargement because 0 > n > 1
Answer: The second statement is true. It is a reduction because 0 < n < 1.
Step-by-step explanation:
Given: A triangle is dilated by a scale factor of n = 1/3 .
as n is less than 1 but greater than 0.
A dilation is a rigid transformation that forms an image that is the same shape as of the original figure, but with a different size. A dilation transform a figure by scalar factor 'n' about the center of dilation is a fixed point in the plane which never change.
A dilation that forms a larger image is known as enlargement. A dilation that forms a smaller image is known as reduction.
• If n is greater than 1, then the image is an enlargement.
• If n is between 0 and 1, then the image is a reduction .
• If n is 1, the figure and then the image are exactly same.
Answer:
2nd statement
Step-by-step explanation:
Which is a correct first step for solving this equation?
2x−1(5−3x)=4x+2
Given: F(x) = 3x 2 + 1, G(x) = 2x - 3, H(x) = x
I think it's 2(x+3).
Answer: 2(x+3)
paralyzed;live
Explain why the functions with the given graphs can't be solutions of the differential equation dy dt = et(y − 1)2.
Please see attached document for the graphs:
The functions with the given graphs can't be solutions of
the differential equation dy dt = et(y − 1)2.
(a) won’t work, since it has negative slope on portions of its solutions. The
slope, e t (y − 1)2 , is a nonnegative function.
(b) won’t work, since it has positive slope at y = 1, where the slope must be flat.
Functions with given graphs cannot be solutions to the differential equation dy / dt = e^t(y-1)^2 because their graphs don't satisfy the conditions imposed by the equation, such as non-oscillatory behavior and non-linear variation with time.
Explanation:The question pertains to why certain functions represented by their graphs cannot be solutions to the differential equation dy / dt = et(y-1)2. The explanation lies in the structure of the given differential equation and the properties of function graphs.
Equation dy / dt = et(y-1)2 is a non-linear first order differential equation. To be a solution to this equation, a function's graph must satisfy certain conditions imposed by the equation. However, if certain function graphs represent an undefined curve or if their graphs demonstrate oscillatory behavior, they do not satisfy these criteria.
For instance, the differential equation demands non-oscillatory behavior as seen in the general solution provided in the reference: Yn(x) = Ce-Bx +De+Bx. This form describes a gradual attenuation of y(x), i.e., it does not oscillate. Similarly, if a graph represents a function that varies non-linearly with time (like In[A] vs. Time), it does not represent a solution to the differential equation as well.
Thus, the inability of certain function graphs to satisfy the conditions required by the given differential equation is the reason they cannot be its solutions.
Learn more about Differential Equations here:https://brainly.com/question/33433874
#SPJ3
If the odds of the steelers beating the chiefs are 7 to 4, what is the probability of this event happening?
Among 170 households surveyed, 44 have a video camera, 40 have a snapshot camera, 51 have binoculars, 9 have a video camera and a snapshot camera, 8 have a snapshot camera and binoculars, and 5 have all three products. what is the probability that a household will have a snapshot camera or binoculars? express the answer as a fraction.
The assembly department started the month with 17,500 units in its beginning work in process inventory. an additional 288,000 units were transferred in from the prior department during the month to begin processing in the assembly department. there were 29,250 units in the ending work in process inventory of the assembly department. how many units were transferred to the next processing department during the month?
How many ounces are there in a gallon?
and how would I come about solving this?..
A _____ is the composition of a translation and a reflection across a line parallel to the direction of translation. glide reflection tessellation rotation dilation
Answer:
Glide reflection
Step-by-step explanation:
A glide reflection is a composition of a translation and a reflection across a line parallel to the direction of translation. A glide reflection requires a translation on a figure, which is then reflected over a line. This is a symmetry operation that requires a translation rule and a line to reflect over. A common example of this are footsteps in the sand.
In 2008, there were 6.7 × 109 people living on earth. What is that number in standard notation?
A.) 6,700,000
B.)6,700,000,000
C.)67,000,000
D.)67,000,000,000
Answer:
B) 6,700,000,000 people.
Step-by-step explanation:
We have been given that in 2008, there were [tex]6.7\times 10^9[/tex] people living on earth. We are asked to convert our given population in standard notation.
While changing scientific notation to standard notation we just move the decimal as many times as the exponent indicates. We can see that our exponent is 9, so we will move the decimal to 9 places right.
[tex]6.7\times 10^9=6.7\times 1000000000[/tex]
[tex]6.7\times 10^9=6700000000[/tex]
Therefore, there were 6,700,000,000 people living on earth and option B is the correct choice.
Answer:
B.)6,700,000,000
Step-by-step explanation:
SO when you have to transform from the scientific notation into standar notation, you just have to move the decimal point to the right the number of positions that the scientific notation has as the exponent, in this case it is 9, so you move one position the decimal point to the right to make the number 67, and then add 8 zero´s to the right:
6,700,000,000
As you can see you moved the decimal point 9 positions to the right.
So that´s how you can convert scientific notation to standard notation.
Let f(x) = -10x-18 and g(x) = -3x, find (f-g)(x)
1 gallon of paint pour the paint into a paint tray that measures 10 inch wide 10 inch long and 7 cm deep what will happen
1 gallon = 231 cubic inches
7cm = 2.75591 inches ( round to 2.76 )
10 x 10 x 2.76 = 276 cubic inches
there will be more than enough room for the gallon of paint
276-231 = 45 cubic inches of space left over
A computer printer can print a 800-word document in 32 seconds. At this rate, how many seconds are required to print a document that contains 880 words?
how to write 293,805 in standard and expanded form
karens penny bank is 1/5 full. after she adds 280 pennies it is now 7/10 full how many pennies can karens bank hold?
7/10-1/5 = 7/10-2/10 = 5/10 = 1/2
so 280 pennies fills 1/2 of her piggy bank
so 280*2 = 560
her piggy bank can hold 560 pennies
A 8.5
B 8.1
C 12.5
D 12.9
you are dealt one card from a standard 52 card deck. Find the probability of being dealt a heart
13 hearts
a 13/52 probability.
that reduces to a 1/4 probability of getting a heart
Ellen has $75 in her savings account. She deposits $25 every week. Her father also deposits $35 into the account every time Ellen mows the lawn. Her savings account balance can be shown with the following expression: 75 + 25w + 35m Part A: Identify a coefficient, a variable, and a constant in this expression. (3 points) Part B: If Ellen saves for 8 weeks and mows the lawn 2 times, how much will she have in her account? Show your work to receive full credit. (4 points) Part C: If Ellen had $95 in her savings account, would the coefficient, variable, or constant in the expression change? Why?
If a pitcher strikes out 5 batters in 4 innings how many batters is it likely he will strike out in, 9 innings round to the nearest whole number
Process average or mean: is computed by dividing the total of the measurements made on the process by the number of measurements used to compute the total approximates the center of the distribution of measurements made on the process a measure of
Y=0, what is x when y=x^2-6x+9
05.01)A company makes triangular plates for individual slices of pizza. For each plate, the base is 5 inches and the height is 16 inches. The area of the top of the plate is ____ inches squared
Answer: 40 inches squared
Step-by-step explanation:
1. first, you multiply, do 5*16 what does that give you? (80)
2. then, divide your answer by 2 what do you get? (40)
3. lastly, it should look like this: 5*16=(answer)/2=(answer)
hope this helps
Simplify 1/3(9a+b)-1/2(4a+2b)