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Q: Is total area under a normal distribution finite?

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100%

Look in any standard normal distribution table; one is given in the related link. Find the area for 2.43 and 1.52; then take the area for 2.43 and subtract the area for 1.52 and that will be the answer. Therefore, .9925 - .9357 = .0568 = area under the normal distribution curve between z equals 1.52 and z equals 2.43.

sigma represents standard deviation. In a normal distribution, +/- 1 sigma from the mean, for instance, corresponds to approximately 67% of the area under the normal distribution. +/- 2 sigma corrresponds to 95% of the area and +/- 3 sigma from the mean corresponds to 99% of the area under a normal distribution. The area that is covered under +/- six sigma from the mean corresponds to nearly 100% -- that is, the part of the area NOT under that +/- 6 sigma is in the 10^-15 range or 1/1,000,000,000,000,000. The six sigma name borrows from this to suggest that the method gives this degree of certainty: that in 999,999,999,999,999 in 1,000,000,000,000,000 cases the result will be predictable. It does nothing, however, to explain how an agricultural process management methodology applies to other fields.

I am under the assumption that in statistics, if the ten percent condition is not met, meaning that the sample size is more than 10% of the population, then the result is not a normal distribution.

0.0124

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The total area under a normal distribution is not infinite. The total area under a normal distribution is a continuous value between any 2 given values. The function of a normal distribution is actually defined such that it must have a fixed value. For the "standard normal distribution" where μ=0 and σ=1, the area under the curve is equal to 1.

100%

The distribution of sample means will not be normal if the number of samples does not reach 30.

yes because 1 = 100% so the entire area under the curve is 100%

One.

Yes. The total area under any probability distribution curve is always the probability of all possible outcomes - which is 1.

1.it is bell shaped.2.m.d=0.7979 of s.d 3.total area under the normal curve is equal to 1.

The area under a normal distribution is one since, by definition, the sum of any series of probabilities is one and, therefore, the integral (or area under the curve) of any probability distribution from negative infinity to infinity is one. However, if you take an interval of a normal distribution, its area can be anywhere between 0 and 1.

0.1972

~0.0606

Approx 0.0606

Yes, it is true; and the 2 quantities that describe a normal distribution are mean and standard deviation.

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