Question

Entomologist heinz kaefer has a colony of bongo spiders in his lab. there are 1000 adult spiders in the colony, and their weights are normally distributed with mean 11 grams and standard deviation 2 grams. about how many spiders are there in the colony which weigh more than 12 grams?

Answer 1

The probability that a spider selected at a random from the colony weighs more than 12 grams is given by:

$P(x\ \textgreater \ 12)=1-P(x\ \textless \ 12) \\ \\ =1-P\left(z\ \textless \ \frac{x-\mu}{\sigma} \right)=1-P\left(z\ \textless \ \frac{12-11}{2} \right) \\ \\ =1-P(z\ \textless \ 0.5)=1-0.69146=0.30854$

Thus, given that there are 1000 adult spiders in the colony, the number of spiders in the colony that weigh more than 12 grams is given by 0.30854 * 1000 ≈ 309

Answer 2

We have to find the probability N(11,2)>12, wherein N(11,2)
is the normal law with mean 11 and standard deviation 2. 
Using a scientific calculator we get the probability 0.3. 

Now multiply by the population which is 1000 like this:
0.3*1000=300.

There is 300 spiders  in the colony which weigh more than 12 grams