Question

# Movie stars and U.S. presidents have fished Pyramid Lake. It is one of the best places...

Movie stars and U.S. presidents have fished Pyramid Lake. It is one of the best places in the lower 48 states to catch trophy cutthroat trout. 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 % 44% 35% 14% 6% 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 =

(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 two decimal places.)
σ =

B)

Probabality that a fisherman selected at random fishing from shore catches one or more fish in a 6 hour period

= P(x = 1) + P(x = 2) + p(x = 3) + p( x >= 4)

= 0.35 + 0.14 + 0.06 + 0.01

= 0.56

C)

Probabality that a fisherman selected at random fishing from shore catches two or more fish in a 6 hour period

= P(x = 2). + P(x = 3) + p(x >= 4)

= 0.14 + 0.06 + 0.01

= 0.21

D)

Expected value = μ

= x p(x)

= 0 x 0.44 + 1x 0.35 + 2 x 0.14 + 3 x 0.06 + 4 x 0.01

= 0.85

E)

Variance =Σ[x^2 * p(x)] - μ^2

= [0^2 x 0.44 +1^2 x 0.35 +2^2 x 0.14 +3^2 x 0.06 +4^2 x 0.01]- 0.85^2

= 1.61 - 0.7225

= 0.8875

Standard deviation = √(variance)

= √0.8875

= 0.94