Question

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 = fish

Answer 1

a)

P(X >= 1) = 1 - P(X = 0)

= 1 - 0.42

= 0.58

b)

P(X >= 2) = 1 - P(X < = 1 )

= 1 - [ P( X = 0) + P(X = 1) ]

= 1 - [ 0.42 + 0.37 ]

= 0.21

c)

E(X) = = X * P(X)

= 0 * 0.42 + 1 * 0.37 + 2 * 0.14 + 3 * 0.06 + 4 * 0.01

= 0.87

d)

Standard deviation = sqrt [ X² * P(X) - ² ]

= sqrt [ 0² * 0.42 + 1² * 0.37 + 2² * 0.14 + 3² * 0.06 + 4² * 0.01 - 0.87² ]

= 0.934