The lengths of a certain species of fish were found to be normally distributed. The mean length is 79 cm with a standard deviation of 10 cm. In a school of 310 of these fish, about how many would be longer than 69 cm?

Question

anonymous · Answer

Essentially, you're asked to find the probability that a given fish is longer than 69 cm, which is given by the area under the curve over $[69,\infty)$. The area under any normal curve is $1$, so you know that the area over $[79,\infty)$ is 0.5.

So, you're left with find the area over $[69,79]$. First find the $z$-value, then get the area from a table. Add that to 0.5, and that's the probability a given fish is longer than 69 cm.
|dw:1368919609872:dw|
To find out how many fish in the given population are longer than 69 cm, you simply multiply the probability by the total population.