Question

The lengths of a certain species of fish were found to be normally distributed. The mean length is 73 cm with a standard deviation of 8 cm. In a school of 480 of these fish, about how many would be longer than 57 cm?

Answer 1

251

Explanation:

Given - Mean length of fish = μ= 73 cm

SD σ =8 c m

Number of fish having a length greater than 57 cm out of 480.

Find the value of z at x = 57

`z= (x-\mu)/(\sigma) = (57-73)/(8)\\=(-16)/(8) = -2`

Area between z = − 2 and z = ∞

= Area between z = − 1 and z = 0 +

Area between z = 0 and z = ∞

=0.02275+0.5= 0.52275

Therefore number of fish having teeth greater than 57 cm

= 0.52275*480 = 5.2275*48 = 250.92 ≅251