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%

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

A histogram with 5 bars is given. The horizontal axis is labeled: x. The vertical axis is labeled: P(x). The leftmost bar is centered on the value 0 and is 0.43 units tall. Moving to the right, the second bar is centered on the value 1 and is 0.35 units tall. The third bar is centered on the value 2 and is 0.06 units tall. The fourth bar is centered on the value 3 and is 0.15 units tall. The fifth bar is centered on the value 4, with the label "4 or more", and is 0.01 units tall.

A histogram with 5 bars is given. The horizontal axis is labeled: x. The vertical axis is labeled: P(x). The leftmost bar is centered on the value 0 and is 0.43 units tall. Moving to the right, the second bar is centered on the value 1 and is 0.15 units tall. The third bar is centered on the value 2 and is 0.35 units tall. The fourth bar is centered on the value 3 and is 0.06 units tall. The fifth bar is centered on the value 4, with the label "4 or more", and is 0.01 units tall.

A histogram with 5 bars is given. The horizontal axis is labeled: x. The vertical axis is labeled: P(x). The leftmost bar is centered on the value 0 and is 0.43 units tall. Moving to the right, the second bar is centered on the value 1 and is 0.35 units tall. The third bar is centered on the value 2 and is 0.15 units tall. The fourth bar is centered on the value 3 and is 0.06 units tall. The fifth bar is centered on the value 4, with the label "4 or more", and is 0.01 units tall.

A histogram with 5 bars is given. The horizontal axis is labeled: x. The vertical axis is labeled: P(x). The leftmost bar is centered on the value 0 and is 0.43 units tall. Moving to the right, the second bar is centered on the value 1 and is 0.06 units tall. The third bar is centered on the value 2 and is 0.15 units tall. The fourth bar is centered on the value 3 and is 0.35 units tall. The fifth bar is centered on the value 4, with the label "4 or more", and is 0.01 units tall.

(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 , 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.)

=

fish

(e) Compute , 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.)

=

fish