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Do some normal probability distributions have different means and different standard deviations?
Yes. Normal (or Gaussian) distribution are parametric distributions and they are defined by two parameters: the mean and the variance (square of standard deviation). Each pair of these parameters gives rise to a different normal distribution. However, they can all be "re-parametrised" to the standard normal distribution using z-transformations. The standard normal distribution has mean 0 and variance 1.
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Do normal probability distributions have different arithmetic means and different standard deviations?
Yes. And that is true of most probability distributions.
Do some normal probability distributions have different arithmetic means and different standard deviations?
Yes. Most do.
What percentage of observations of a normal distribution is reprented by the mean plus or minus 1.96 standard deviations?
The probability of the mean plus or minus 1.96 standard deviations is 0. The probability that a continuous distribution takes any particular value is always zero. The probability between the mean plus or minus 1.96 standard deviations is 0.95
How many standard deviations is 16.50 from the mean?
How many standard deviations is 16.50 from the mean?
What is the difference between t-distribution and standard normal distribution?
the t distributions take into account the variability of the sample standard deviations. I think that it is now common to use the t distribution when the population standard deviation is unknown, regardless of the sample size.
