A Yellow Lobster! As reported by the Associated Press, a veteran lobsterman recently hauled up a yellow lobster less than a quarter mile south of Prince Point in Harpswell Cove, Maine. Yellow lobsters are considerably rarer than blue lobsters and, according to B. Ballenger’s The Lobster Almanac (Darby, PA: Diane Publishing Company, 1998), roughly 1 in every 30 million lobsters hatched is yellow. Apply the Poisson approximation to the binomial distribution to answer the following questions: a. Of 100 million lobsters hatched, what is the probability that between 3 and 5, inclusive, are yellow? b. Roughly how many lobsters must be hatched in order to be at least 90% sure that at least one is yellow?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 33PPS
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A Yellow Lobster! As reported by the Associated Press, a veteran lobsterman recently hauled up a yellow lobster less than a quarter mile south of Prince Point in Harpswell Cove, Maine. Yellow lobsters are considerably rarer than blue lobsters and, according to B. Ballenger’s The Lobster Almanac (Darby, PA: Diane Publishing Company, 1998), roughly 1 in every 30 million lobsters hatched is yellow. Apply the Poisson approximation to the binomial distribution to answer the following questions:

a. Of 100 million lobsters hatched, what is the probability that between 3 and 5, inclusive, are yellow?

b. Roughly how many lobsters must be hatched in order to be at least 90% sure that at least one is yellow?

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