Note that he best estimate of the standard deviation of the population is 75.
Why is this so?The area under the curve in a probability density function indicates likelihood. Because the normal distribution is a probability distribution, the total area under the curve is always one, or one hundred percent. Thus, 25 + 75 = 100.
A normal distribution, often known as a Gaussian distribution, is a form of continuous probability distribution for a real-valued random variable in statistics.
A bell curve is a form of graph used to depict the distribution of a set of chosen values within a specified group that tends to have a middle, normal value as a peak with low and high extremes tapering out pretty symmetrically on each side.
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Full Question:
Although part of your question is missing, you might be referring to this full question:
The normal curve shown represents the sampling distribution of a sample mean for sample size n = 25, selected at random from a population with standard deviation sd. Which of the following is the best estimate of the standard deviation of the population?
3
6
15
30
75
I need help with an AP Calc AB topic. Max/Min, Increasing/Decreasing, Concavity.
I know how to do all of it but when I try this, I am not able to figure it out. Especially when it involves e. Could all work be shown with explanations. Thanks
It should be noted that f(x) is increasing on the interval (-∞, 1).
How to explain the function2e^-x - 2xe^-x > 0
2e^-x > 2xe^-x
Dividing both sides by 2e^-x (which is always positive), we get:
1 > x
Therefore, f(x) is increasing on the interval (-∞, 1).
Also f'(x) = 2e^-x - 2xe^-x
At x = 1, we have:
f'(1) = 2e^-1 - 2e^-1 = 0
Since f'(x) changes sign from negative to positive as we move from x = 1 to x < 1, we conclude that f(x) has a relative minimum at x = 1.
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Scientists theorize that all stars started out as a nebula that
eventually condensed into a protostar, or young star. In three to five sentences, please explain the events that take place for a
protostar to move to the next stage of its life as a glowing star.
The star, at some point, enters the main sequence phase of its life, where it will remain stable for millions to billions of years, depending on its mass.
What is the next stage?The pressure and temperature at the center of a protostar rise as it disintegrates due to its own gravity, which causes hydrogen atoms to undergo nuclear fusion and produce helium atoms. The protostar glows as a result of the massive amount of energy released during this process, which also produces heat and radiation.
The star achieves equilibrium while the fusion reaction continues, with the outward pressure from the reaction counteracting the inward force of gravity.
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What led to the idea that the Universe started out in a big bang?
1.
The observation of the cosmic microwave background
2.
The earliest galaxies observed by the Hubble Space Telescope
3.
Using the Type 1A supernovae in the measurements of the expansion of the universe
4.
The observed expansion of the universe
Answer:
A. The observation of the cosmic microwave background led to the idea that the Universe started out in a big bang.
Explanation:
The cosmic microwave background (CMB) is radiation left over from the Big Bang. It is the oldest light in the Universe and provides a snapshot of the Universe at a very early time. The CMB was discovered in 1964 by Arno Penzias and Robert Wilson, and its existence supports the Big Bang theory. The CMB is nearly uniform in all directions, with small variations that correspond to the density fluctuations in the early Universe that gave rise to the formation of galaxies and other structures. The CMB is one of the strongest pieces of evidence for the Big Bang theory and led to its widespread acceptance among scientists.
Briefly discuss the term symphonic poem. Explain the difference between symphony and symphonic poem, illustrating your discussion with musical examples and relevant composers.
A symphonic poem, also known as a tone poem, is a type of orchestral music that tells a story or evokes a particular mood or image without relying on text or lyrics. The main difference between a symphony and a symphonic poem is that a symphony is a multi-movement work for orchestra that follows a specific structure and is typically abstract example is Franz Liszt.
What is symphonic poem?A symphonic poem, often referred to as a tone poem, is a style of orchestral music that conveys meaning without the use of words or lyrics. Programmatic music, which has a narrative or descriptive nature, is a type of music that normally consists of a single movement, frequently with contrasting passages.
Franz Liszt, a Hungarian composer who produced a number of symphonic poems in the middle of the 19th century, including "Les Préludes," "Mazeppa," and "Tasso, lamento e trionfo," is credited with coining the phrase. Liszt aimed to improve programmatic music, which had been denigrated as merely entertainment, in these compositions.
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