For a Normally Distributed Population of Observations

Short Answer

For a normally distributed population of observations,

and

For a randomly selected sample of size 36, what is the probability that the sample mean
(a) will fall above 91
(b)will fall more than 10 points above the population mean of 100
(c)will differ (in either direction) from the population mean by 10 points or more
(d)What sample mean has such a high value that the probability is .01 of obtaining one as high or higher
(e)Within what limits would the central 95% of all possible sample means fall