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

Answer:

251

Step-by-step 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

$z= \frac{x-\mu}{\sigma} = \frac{57-73}{8}\\=\frac{-16}{8} = -2$

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