Consider a study in which the heights of a sample of 1000 high school seniors were recorded. The mean height is 70' and the standard deviation of the heights is 3". It is observed that the height distribution is approximately normal (a) Approximately what percent of the heights is between 61 and 79 inches? (b) Approximately what percent of the heights is between 67 and 73 inches? (c) Approximately what percent of heights in this sample would exceed 79"? (d) What is the approximate percentile of a senior who is 73" tall? (e) When the data were summarized the value of the first quartile was written down but then smudged. There is general agreement that the writer meant to indicate either 66" or 68". Which of these values is most likely the correct one? Justify your answer with appropriate statistical reasoning.