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
%	43%	35%	15%	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. (Enter a number. 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. (Enter a number. 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). (Enter a number. 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). (Enter a number. Round your answer to three decimal places.)
σ =  fish

Answer 1

SOLUTION:

From given data,

(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.

the probability that a fisherman selected at random fishing from shore catches one or more fish in a 6-hour period.

= 0.35+0.15+0.06+0.01 =0.57

(c) Find the probability that a fisherman selected at random fishing from shore catches two or more fish in a 6-hour period.

the probability that a fisherman selected at random fishing from shore catches two or more fish in a 6-hour period.

= 0.15+0.06+0.01 =0.22

(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). (Enter a number. Round your answer to two decimal places.) μ = fish

We simplify the value of

x=4 or more as x=4

Hence,

X	Probability (p)	P*X	X2	P*X2
0	0.43	0	0	0
1	0.35	0.35	1	0.35
2	0.15	0.3	4	0.6
3	0.06	0.18	9	0.54
4	0.01	0.04	16	0.16
Total	1	0.87		1.65

Expected value =

(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). (Enter a number. Round your answer to three decimal places.) σ = fish

Standard deviation =

=