Question

According to the Wildlife Service there is a 10% chance that a wolf will howl when the moon light intensity falls to or below 30cd/m. A group of zoologist in Lisbon thinks that the chance is much higher than 10%. In order to conduct a preliminary study they consider a small pack of wolves with 32 wolves in their sample. Answer the following questions.

(a)   According to the Wildlife Service, if the moon light intensity drop to or below 30cd/m, what is the expected number of wolves that will howl in the sample?

(b)   Suppose the moon light intensity did drop to 30F and 5 wolves in the sample howl. What is the sample proportion of howling wolves?

Answer 1

Solution:

We are given that: according to the Wildlife Service there is a 10% chance that a wolf will howl when the moon light intensity falls to or below 30cd/m.

That is: p = 0.10

Sample size = n = 32

Part a) According to the Wildlife Service, if the moon light intensity drop to or below 30cd/m, what is the expected number of wolves that will howl in the sample?

Expected number of wolves that will howl in the sample are:

E(X) = n * p

E(X) = 32 * 0.10

E(X) = 3.2

Thus if the moon light intensity drop to or below 30cd/m, the expected number of wolves that will howl in the sample are 3.2

Part b) Suppose the moon light intensity did drop to 30F and 5 wolves in the sample howl. What is the sample proportion of howling wolves?

x = number of wolves in the sample howl = 5

n = sample size = 32

then the sample proportion of howling wolves is: