Question

The lengths of a certain species of fish were found to be normally distributed. The mean length is 93 cm with a standard deviation of 12 cm. In a school of 360 of these fish, about how many would be longer than 81 cm?

Answer 1

Number of fish having a length greater than 81 cm out of 360 `=304`

Explanation:

Given -
Mean length of fish `=barx=93` cm
SD `sigma=12 cm`

Number of fish having a length greater than 81 cm out of 360.

Find the value of `z` at `x=81`

`z=(x-barx)/sigma=(81-93)/12=(-12)/12=-1`

Find the Area between `z=-1` and `z=oo`

Area between `z=-1` and `z=oo` = Area between `z=-1` and `z=0+` Area between `z=0` and `z=oo`
Area between[ `z=-1` and `z=oo]= 0.3413 + 0.5 = 0.8413`

Number of fish having a length greater than 81 cm out of 360 `=0.8413 xx 360 = 303.868=304`