Which of the following is not true regarding the normal probability distribution? (asymptotic, family of distributions, only two outcomes, 50 percent of the observations greater than the mean)

albiguguiismx 2022-09-13 Answered
Which of the following is not true regarding the normal probability distribution? (asymptotic, family of distributions, only two outcomes, 50 percent of the observations greater than the mean)
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Answers (1)

ignaciopastorp6
Answered 2022-09-14 Author has 14 answers
An asymptotic distribution is a probability distribution that is the limiting distribution of a sequence of distributions. Since normal distributions are the limiting distribution for many other distributions and thus normal distributions are asymptotic.
Normal distributions are considered to be a family of distributions, because you obtain a different normal distribution when you have a different mean and/or a different standard deviation.
A normal distribution is also symmetric about its mean and thus 50% of the observations in a normal distribution are greater than the mean.
The property that does not hold for a normal probability distribution is then "only two outcomes," which is true as a normal probability distribution has infinitely many possible outcomes.
Result:
Only two outcomes.
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