1
$\begingroup$

How do you determine the probability of a sample mean being a certain value?

To make this more concrete, suppose we have a population of 1000 values. the population mean is 50 and the standard deviation is 5.

How do we determine the probability of 20 random individuals from that population having a sample mean of 40, and a standard deviation of 6. What about the probability of them all being less than 40?

No, it's not homework. But I imagine this is a sort of common thing to solve, so if anyone could just point me in the direction of an online resource that talks about the relevant topic, that would be great.

  • 0
    you can also ask it on stats.stackexchange.com2011-07-19
  • 0
    The sample mean and sample standard deviation are statistics, so that they have their distribution, which are used to do confidence intervals.Is that what you're looking for?2011-07-19
  • 0
    The probability that the sample mean is exactly equal to a particular value depends on more information than the mean and standard deviation. But the probability that the sample mean is _between_ two specified values can be approximately found if you know the population mean, the population stadard deviation, and the sample size. That follows from the central limit theorem.2011-07-19

1 Answers 1