Statistics and probability : Prediction Interval of a Future Observation

• Probability and Statis...
Statistics and probability : Prediction Interval of a Future Observation .
Assume that the random sample comes from a normal population with unknown mean μ and known variance . A natural point estimator of a new observation is sample average.
To predict a new observation, not only do we need to account for the variation of a future random observation, but also we should account for the variation due to estimating the mean.
As a result, if we use the probability statement with the z-statistic from standard normal distribution and place x0 in the center of the probability statement, we have the following event occurring with probability 1 − α.
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