Example 7.9 from Statistics, 7.3 Using the Central Limit Theorem

Using the clt to find percentiles (part 2)

Find the 95^th percentile for the sample mean excess time for a sample of 80 customers who exceed their basic contract time allowances. Draw a graph.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
Let k = the 95^th percentile. Find k where P( $\bar{x}$ < k) = 0.95.

k = 26.0 using invNorm $(0 .95,22, \frac{22}{\sqrt{80}})$ = 26.0

Figure 7.9

The 95^th percentile for the sample mean excess time used is about 26.0 minutes for a random sample of 80 customers who exceed their contractual allowed time.
95 percent of such samples would have means under 26 minutes; only five percent of such samples would have means above 26 minutes.

How did it go?

Solution

Solution