Question

The Blue Wild Fish Company sells a particular species of fish that live in a local lake. In the entire lake the distribution of fish lengths follows a normal distribution with mean 35 inches and standard deviation 10.5 inches.

a. If the fisherman only catches one fish a day, then approximately the middle 99.7% of those days the fish will have a length between ------------- and ------------inches.
b. If the fisherman catches the usual 40 fish a day, then approximately the middle 99.7% of those days the sample of fish will have an average length between------------ and ----------- inches.

Answer 1

Let X be the fish length

X~ Normal ( 35, 10.5)

Now according to the empirical rule about 99.7% of the middle data lie between 3 standard deviation of the mean i.e,

( )

a) Middle 99.7% of the data will lie between= (( ) = ( )

= ( 3.5 , 66.5)

  If the fisherman only catches one fish a day, then approximately the middle 99.7% of those days the fish will have a length between 3.5  and 66.5 inches.

b) n= 40

Let be the average length of the 40 fish.

  ~ Normal ( 35,   )

Middle 99.7% of the data will lie between () = (   )

= ( 30.0194, 39.9806 )

If the fisherman catches the usual 40 fish a day, then approximately the middle 99.7% of those days the sample of fish will have an average length between 30.0194  and 39.9806 inches.