Almost all of the rain in Los Angeles falls in the winter, so a season of rainfall is measured from July 1 through the end of June. Display 9.44 gives a summary of the rainfall in Los Angeles for the last 128 seasons.

a. You want to estimate mean seasonal rainfall in a confidence interval and can afford to check a random sample of only seven seasons. If you suspect that the population has a shape like that in the histogram in Display 9.44, can you proceed, or should you consider a transformation?

b. Display 9.45 shows a reciprocal transformation of the rainfall data. The mean of the distribution is about 0.081. Does this mean have a meaningful interpretation? Are you satisfied with the conditions for inference now?

c. Display 9.46 shows a log transformation of the rainfall data. Does this transformation do a better or worse job than the reciprocal transformation in satisfying the conditions for inference?

d. If, instead of taking a random sample of size 7, you were able to consider these 128 seasons to be a random sample of Los Angeles rainfall over, say, the last 2000 seasons, would you be concerned about constructing a confidence interval for the mean seasonal rainfall directly from the original data (with no transformation)?

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