Question

A population is normally distributed with µ = 100 and σ = 10. a sample of size 9 is selected. the probability that an individual value (from this population) falls between 90 and 110 will be ________ the probability that the sample mean (of this sample) falls between 90 and 110.

Answer 1

a) The empirical rule tells you the probability of being within 1 standard deviation of the mean is 68%.

b) The probability that the sample mean falls within 3 standard deviations* of the mean is 99.7%.

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* The standard deviation of the sample mean is 1/√9 = 1/3 of the standard deviation of an individual sample. Hence the same limits (90-110) now cover 3 standard deviations of the sample mean.