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Mathematics & Economics
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Area Under a Normal Distribution Curve Research Assignment (Math Problem Sample)

Instructions:

Take a position on whether or not the total area under a normal distribution is infinite. Provide an example to support your response.

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Content:

Area under a Normal Distribution Curve
Student’s Name
Institutional Affiliation
Area under a Normal Curve
The area under a normal distribution curve is one. Definition of normal distribution, normal distributed data occurs when the frequencies fall off at a rate that is proportional to the space of the score from the mean, and to the frequencies CITATION Sub14 \l 1033 (Subotic, 2014). A normal distribution also means a family of probability distributions that are continuous which can be described the normal equation. The bell shaped curve helps in finding the percentage of data that is found in a certain interval. In a typical calculus problem, this is the area under the curve over the interval. This is seen in a probability distribution. The normal equation of a variable N:
N= {1/ [ σ * √ (2π)]}*e-y-μ)2/2σ2
Where y- the normal random variable,
μ - The mean,
σ -The standard deviation.
The following is observed about a normal distribution curve as seen below; area is equally distributed under the normal curve. The probability that a certain value is equal to a random variable is zero. There is equal probability that d is more than X and the area that is bounded by normal curve d and infinity. There is equal probability X and d equals the area that is bounded by the normal curve d subtracted from infinity. Every curve that is normal obeys the following rule,
* Approximately 68percent of the area is within one standard deviation of the mean where the curve falls.
* Approximately 95 percent of the area is within two standards of deviation of the mean where the curve falls.
* Approximately 99 percent of the area is within thre...
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