##### Question

# estimate

Consider the accompanying observations on stream flow (1000s of acre-feet) recorded at a station in Colorado for the period April 1-August 31 over a 31-yearspan.

155.28 138.84 285.37 203.24 299.87

150.58 94.33 302.74 280.55 125.86

200.19 247.11 62.16 127.96 262.09

446.28 100.85 204.91 311.13 108.91

145.11 66.24 117.64 114.79 185.36

109.11 126.60 210.07 330.33 89.59

63.58

An appropriate probability plot supports the use of the lognormal distribution as a reasonable model for stream flow.

(a) Estimate the parameters of the distribution. [Hint: Remember that X has a lognormal distribution with parameters µ and s2 if ln(X) is normally distributed withmean µ and variance s2.] (Round your estimate for the mean to three decimal places, and round your estimate for the variance to four decimal places.)

mu hat =

sigma hat2 =

(b) Use the estimates of part (a) to calculate an estimate of the expected value of stream flow. [Hint: What is E(X)?] (Round your answer to two decimal places.)

________ thousand acre-feet