Apopulation 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.

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.