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Q: Is the total area within a continuous probability distribution is equal to 1?

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It depends on the parameter - the mean of the distribution.

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

The sum of proportions computed from a frequency distribution must equal

They are all equal . . . they are the same.(In an asymmetric distribution they are not equal.)

The mean of the sampling distribution is the population mean.

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Yes, but not just continuous prob distribs. It applies to discontinous or discrete distributions as well.

When, over a given range, the probability that a variable in question lies within a particulat interval is equal to the size of that interval as a proportion of the range.

The sum should equal to 1.

For a discrete variable, you add together the probabilities of all values of the random variable less than or equal to the specified number. For a continuous variable it the integral of the probability distribution function up to the specified value. Often these values may be calculated or tabulated as cumulative probability distributions.

A probability is fair if there is no bias in any of the possible outcomes. Said another way, all of the possible outcomes in a fair distribution have an equal probability.

It depends on the parameter - the mean of the distribution.

A uniform distribution.A uniform distribution.A uniform distribution.A uniform distribution.

Don't know what "this" is, but all symmetric distributions are not normal. There are many distributions, discrete and continuous that are not normal. The uniform or binomial distributions are examples of discrete symmetric distibutions that are not normal. The uniform and the beta distribution with equal parameters are examples of a continuous distribution that is not normal. The uniform distribution can be discrete or continuous.

Only the mean, because a normal distribution has a standard deviation equal to the square root of the mean.

-1.43 (approx)

z = 1.52 (approx)

Probability density function (PDF) of a continuous random variable is a function that describes the relative likelihood for this random variable to occur at a point in the observation space. The PDF is the derivative of the probability distribution (also known as cummulative distriubution function (CDF)) which described the enitre range of values (distrubition) a continuous random variable takes in a domain. The CDF is used to determine the probability a continuous random variable occurs any (measurable) subset of that range. This is performed by integrating the PDF over some range (i.e., taking the area under of CDF curve between two values). NOTE: Over the entire domain the total area under the CDF curve is equal to 1. NOTE: A continuous random variable can take on an infinite number of values. The probability that it will equal a specific value is always zero. eg. Example of CDF of a normal distribution: If test scores are normal distributed with mean 100 and standard deviation 10. The probability a score is between 90 and 110 is: P( 90 < X < 110 ) = P( X < 110 ) - P( X < 90 ) = 0.84 - 0.16 = 0.68. ie. AProximately 68%.

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