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-year span. 150.58 66.24 117.64 89.59 204.91 108.91 185.36 210.07 109.11 117.70 285.37 280.55 299.87 58.86 100.85 94.33 125.86 302.74 311.13 151.32 247.11 203.24 127.96 330.33 114.79 145.11 262.09 200.19 493.80 111.78 133.86 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 u and o? if In(X) is normally distributed with mean u and variance o2.] (Round your estimate for the mean to three decimal places, and round your estimate for the variance to four decimal places.) û = a2 = (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

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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-year span.
150.58
66.24
117.64
89.59
204.91
108.91
185.36
210.07
109.11
117.70
285.37
280.55
299.87
58.86
100.85
94.33
125,86
302.74
311.13
151.32
247.11
203.24
127.96
330.33
114.79
145.11
262.09
200.19
493.80
111.78
133.86
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 u and o? if In(X) is normally distributed with
mean u and variance o2.] (Round your estimate for the mean to three decimal places, and round your estimate for the variance to four decimal places.)
62 =
(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
Transcribed Image Text: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-year span. 150.58 66.24 117.64 89.59 204.91 108.91 185.36 210.07 109.11 117.70 285.37 280.55 299.87 58.86 100.85 94.33 125,86 302.74 311.13 151.32 247.11 203.24 127.96 330.33 114.79 145.11 262.09 200.19 493.80 111.78 133.86 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 u and o? if In(X) is normally distributed with mean u and variance o2.] (Round your estimate for the mean to three decimal places, and round your estimate for the variance to four decimal places.) 62 = (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
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