A drought is a period of abnormal dry weather that causes a serious hydrologic imbalance in an area. The Palmer Drought Index (PDI) is designed to quantitatively measure the severity of a drought. A PDI value of -1 or less indicates a dry (drought) period. A PDI value greater than -1 indicates a wet (non drought) period. Civil engineers at the University of Arizona used paleontology data and historical records to determine PDI values for each of the past 400 years in Texas (Journal of Hydrologic Engineering, Sept./Oct. 2003). The researchers discovered that the number Y of years that need to be sampled until a dry (drought) year is observed follows an approximate geometric distribution. A graph of the distribution is shown at the top of the page.
a. From the graph, estimate E(Y).
b. Use the result, part a, to estimate the value of p for the geometric distribution.
c. Estimate the probability that 7 years must be sampled in order to observe a drought year.