In the Case Study, we interpreted the phrase “much less than” to mean a measurement that is 2 or more standard deviations below the mean. For Exercises 115–118, suppose we interpret the phrase “much less than” to mean a measurement that is 3 or more standard deviations below the mean.

Question 7.115

115. Use the methods shown in the Case Study to answer the following questions:

  1. What would be the new value of ?
  2. What would be the standard deviation s for each gold piece?
  3. By the Empirical Rule, about what proportion of the mean weights would you now expect to lie between 127.68 and 128.32?

7.1.115

(a) 0.1067 gram (b) 1.067 grams (c) About 0.997