Question 8.100

69. Averages of several measurements are less variable than individual measurements. The true mass of the whiskey sample in Exercise 67 is 4.6 grams, or 4600 mg. Antonio’s measurements have the normal distribution with mean 4600 mg and standard deviation 10 mg. In this case, the mean of his three measurements also has a normal distribution.

  1. Sketch on the same graph the two normal curves, for individual measurements and for means of three measurements. Figure 8.24 (page 382) is an example of this kind of graph.
  2. What interval of values covers the middle 95% of Antonio’s individual measurements?
  3. What interval of values covers the middle 95% of averages of three measurements?

69.

(a)

image

(b) Use the 95 part of the rule with results in the interval (4580, 4620).

(c) Now the standard deviation is 5.77, so we have the following: results in the interval (4588.46, 4611.54).