A lepidopterist is studying changes in butterfly flight patterns in the first 30 days after metamorphosis. For

every cocoon collected for the study, there is a 20% chance in lab conditions that the butterfly will not

complete metamorphosis.

a)

What probability distribution can be used to model the number of butterflies that can be used for the

study from an initial batch of cocoons?

b)

If the researcher starts with 50 cocoons, what is the probability she will have at least 48 surviving

butterflies?

c)

The lepidopterist must have at least 60 surviving butterflies to find significant results in her research on

flight behavior. To have a comfortable margin of error, she will collect enough cocoons such that the

expected

number of surviving cocoons is 80. How many cocoons should she collect?

d)

Unfortunately, the lepidopterist is only able to collect 40 cocoons on her own. She calls a friend in

another lab who is willing to collect additional cocoons (and data). Her friend collects 50 cocoons.

The rate of successful metamorphosis in her friend's lab is 75%. What is the expected total number of

surviving butterflies from both labs?