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 $0123$ at least $4$

$\%45\%35\%14\%5\%1\%$

A button hyperlink to the SALT program that reads: Use SALT.

$($a$)$

Convert the percentages to probabilities and make a histogram of the probability distribution. $($Because the data table has summarized the data into categories, use SALT to create a bar chart.$)$

A histogram has a horizontal axis labeled x and a vertical axis labeled P$($x$)$ with values from $0$ to $0\mathrm{.}53.$ The histogram has $5$ bars. Each bar is associated with a label and an approximate value as listed below.

$0$: $0\mathrm{.}45$

$1$: $0\mathrm{.}35$

$2$: $0\mathrm{.}05$

$3$: $0\mathrm{.}14$

at least $4$: $0\mathrm{.}01$

A histogram has a horizontal axis labeled x and a vertical axis labeled P$($x$)$ with values from $0$ to $0\mathrm{.}53.$ The histogram has $5$ bars. Each bar is associated with a label and an approximate value as listed below.

$0$: $0\mathrm{.}45$

$1$: $0\mathrm{.}05$

$2$: $0\mathrm{.}35$

$3$: $0\mathrm{.}14$

at least $4$: $0\mathrm{.}01$

A histogram has a horizontal axis labeled x and a vertical axis labeled P$($x$)$ with values from $0$ to $0\mathrm{.}53.$ The histogram has $5$ bars. Each bar is associated with a label and an approximate value as listed below.

$0$: $0\mathrm{.}45$

$1$: $0\mathrm{.}35$

$2$: $0\mathrm{.}14$

$3$: $0\mathrm{.}05$

at least $4$: $0\mathrm{.}01$

A histogram has a horizontal axis labeled x and a vertical axis labeled P$($x$)$ with values from $0$ to $0\mathrm{.}53.$ The histogram has $5$ bars. Each bar is associated with a label and an approximate value as listed below.

$0$: $0\mathrm{.}45$

$1$: $0\mathrm{.}14$

$2$: $0\mathrm{.}05$

$3$: $0\mathrm{.}35$

at least $4$: $0\mathrm{.}01$

$($b$)$

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

$($c$)$

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

$($d$)$

Compute $,$ the expected value of the number of fish caught per fisherman in a $6-$hour period $($round $"$at least $4"$ to $4).$

$=$ fish

$($e$)$

Compute $,$ the standard deviation of the number of fish caught per fisherman in a $6-$hour period $($round $"$at least $4"$ to $4).($Round your answer to three decimal places.$)$

$=$ fish