Snowfall in the City of Cleveland for the winter months (defined as January, February, and March)...

Snowfall in the City of Cleveland for the winter months (defined as January, February, and March) is distributed as a Poisson random variable, with an average of 5 inches per month.

What is the probability that there will be at least 13 inches of snow in the City of Cleveland next March? ANSWER: (Use only the appropriate formula and/or statistical table in your textbook to answer this question. Report your answer as to 4 decimal places, using conventional rounding rules.

What is the probability that there will be at least 7 but less than 11 inches of snow in the City of Cleveland next January? ANSWER: (Use only the appropriate formula and/or statistical table in your textbook to answer this question. Report your answer as to 4 decimal places, using conventional rounding rules.

What is the probability that there will be exactly 6 inches of snow in the City of Cleveland next January, February, and March combined? ANSWER: (Use only the appropriate formula and/or statistical table in your textbook to answer this question. Report your answer as to 4 decimal places, using conventional rounding rules.

Solutions

Expert Solution

µ = 5 inches per month

P(X = x) = e^-µ * µ^x / x!

a) P(X > 13) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 12))

= 1 - (e^-5 * 5⁰ / 0! + e^-5 * 5¹ / 1! + e^-5 * 5² / 2! + ... e^-5 * 5¹² / 12! )

= 1 - 0.998

= 0.0020

b) P(7 < X < 11) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)

= e^-5 * 5⁷ / 7! + e^-5 * 5⁸ / 8! + e^-5 * 5⁹ / 9! + e^-5 * 5¹⁰ / 10!

= 0.2241

c) P(X = 6) = e^-5 * 5⁶ / 6! = 0.1462

orchestra answered 1 year ago

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