FWT wrote:Given a normal distribution of values for weight having a mean of 140 Pounds and a standard deviation of 6 pounds, what is the range of weights which would represent the middle 95% of the distribution? (Use the 68-95-99.7 standard deviation rule.)
Review
the rule to determine the number of standard deviations (to either side of the mean) is indicated by "the middle 95%".
Then take the mean value and the standard-deviation value they gave you, and add this number of standard deviations to the mean, and also subtract this number of standard deviations from the mean. The sum and difference demark the range of values they're looking for.
For instance, if you were dealing with, say, IQ tests, which generally have a mean of 100 and a standard deviation of 15, "the rule" says that 68%, or just over two-thirds, of the population is within one standard deviation of the mean. This says that 68% fall between 100 - 15 = 85 and 100 + 15 = 115 for their measured IQ.
That's all there is to it!