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?

1 Answer
Apr 21, 2017

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#

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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#