Question

1. Torpor is a type of deep sleep in which an animal lowers its metabolic rate by as much as 95%. Animals often use torpor to survive during periods of colder temperatures because they require up to 50% less energy when torpid. On a given winter day, groundhogs can be classified as either in torpor or not in torpor. The probability of a groundhog not being in torpor on a given winter day is 3/20 or 0.15.

It is February 2nd (Groundhog Day) and you are a local weather forecaster living in Punxsutawney, Pennsylvania. There are 75 groundhogs living in the Punxsutawney area. You are interested in knowing the probability that more than 20 groundhogs are not in torpor. Find p(x > 20).

Answer 1

The number of groundhogs not in torpor follows a binomial distribution.This distribution can be approximated by a normal distribution with

mean = np = 75*0.15= 11.25

standard deviation = sqrt root (npq) = sqrt root(75*0.15*0.85) = 3.0923 because both np [11.25] and n(1-p) [63.75] are greater than 5.