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.

x01234 or more%42%37%12%8%1%

(a) Convert the percentages to probabilities and make a histogram of the probability distribution.

(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:

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.

x01234 or more%42%37%12%8%1%

Divide each percentage through by 100

X 0, 1 , 2, 3, 4

P(X) 0.42, 0.37, 0.12, 0.08, 0.01

(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.)

sum up the probabilities of x = 1, x = 2, x = 3, x = 4

P( that a fisherman selected at random fishing from shore catches one or more fish in a 6-hour period) = 0.37 + 0.12 + 0.08 + 0.01

= 0.58

(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.)

sum up the probabilities of x = 2, x = 3, x =4

P( that a fisherman selected at random fishing from shore catches two or more fish in a 6-hour period) = 0.12 + 0.08 + 0.01

= 0.21

(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

multiply each x value by its corresponding frequency and sum them up

mean μ = summation( X* P(X) ) = 0*0.42 + 1* 0.37 + 2* 0.12 + 3*0.08 + 4*0.01

μ = 0.89 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

Square each x value and multiply the result its corresponding frequency and sum them up

summation( X²* P(X) ) = 0²*0.42 + 1²* 0.37 + 2²* 0.12 + 3²*0.08 + 4²*0.01

= 1.73

σ = √ [ ( summation( X²* P(X) ) - μ² ]

= √ ( 1.73 - (0.89)² )

σ = 0.96 fish

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https://helpinhomework.org/blog/how-to-obtain-answer-through-google-drive-link