A particular lake is known to be one of the best places to catch a certain type of fish. In this table, x = number of fish caught in a 6-hour period. The percentage data are the percentages of fishermen who caught x fish in a 6-hour period while fishing from shore.
x | 0 | 1 | 2 | 3 | 4 or more |
% | 42% | 37% | 14% | 6% | 1% |
(b) Find the probability that a fisherman selected at random
fishing from shore catches one or more fish in a 6-hour period.
(Round your answer to two decimal places.)
(c) Find the probability that a fisherman selected at random
fishing from shore catches two or more fish in a 6-hour period.
(Round your answer to two decimal places.)
(d) Compute μ, the expected value of the number of fish caught per
fisherman in a 6-hour period (round 4 or more to 4). (Round your
answer to two decimal places.)
μ = fish
(e) Compute σ, the standard deviation of the number of fish caught
per fisherman in a 6-hour period (round 4 or more to 4). (Round
your answer to three decimal places.)
σ
Solution:-
(b) P(X >= 1) = P(1) + P(2) + P(3) + P(4)
= 0.37+ 0.14 + 0.06 + 0.01
= 0.58
(c) P(X >= 2) = P(2) + P(3) + P(4)
= 0.14 + 0.06 + 0.01
= 0.21
(d) μ = 0.87
(e) σ = 0.9344 = 0.934 (rounded)
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