Table 3.9 presents the February rainfalls in Los Angeles for the period 1972–2016.

a. Show that the mean of these data is μ = 3.624 and the population standard deviation is σ = 3.410.

b. Show that the z-score for a rainfall of 0 (rounded to two decimal places) is z = −1.06.

c. Show that the z-score for a rainfall of 7.25 (rounded to two decimal places) is z = 1.06.

d. What percentage of the years had rainfalls of 0?

e. What percentage of the years had rainfalls of 7.25 or more?

f. The z-scores indicate that a rainfall of 0 and a rainfall of 7.25 are about equally extreme. Is a rainfall of 7.25 really as extreme as a rainfall of 0, or is it less extreme?
g. These data are skewed to the right. Explain how skewness causes the z-score to give misleading results.

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Year Table 3.9 Annual Rainfall in Los Angeles During February Rainfall Year Rainfall Year Rainfall Year Rainfall Year Rainfall 1972 0.13 1981 1.48 1990 3.12 1999 0.56 2008 1.64 1973 7.89 1982 0.70 1991 4.13 2000 5.54 2009 3.57 1974 0.14 1983 4.37 1992 7.96 2001 8.87 2010 4.27 1975 3.54 1984 0.00 1993 6.61 2002 0.29 2011 3.29 1976 3.71 1985 2.84 1994 3.21 2003 4.64 2012 0.16 1977 0.17 1986 6.10 1995 1.30 2004 4.89 2013 0.20 1978 8.91 1987 1.22 1996 4.94 2005 11.02 2014 3.58 1979 3.06 1988 1.72 1997 0.08 2006 2.37 2015 0.83 1980 12.75 1989 1.90 1998 13.68 2007 0.92 2016 0.79