11.10 The rainfall measured by each of 12 gauges was recorded for 20 successive days. The average results for each day are as follows:

Day Rainfall Day Rainfall April 1 0.00 April 11 2.10 April 2 0.03 April 12 2.25 April 3 0.05 April 13 2.50 April 4 1.11 April 14 2.50 April 5 0.00 April 15 2.51 April 6 0.00 April 16 2.60 April 7 0.02 April 17 2.50 April 8 0.06 April 18 2.45 April 9 1.15 April 19 0.02 April 10 2.00 April 20 0.00 Use an appropriate test to determine whether these data exhibit some sort of pattern. Find the P value:

(a) Using tests based on runs with both the exact distribution and the normal approximation.

(b) Using other tests that you may think are appropriate.

(c) Compare and interpret the results of

(a) and (b).