Clearly, life is not distributed evenly around the planet. Each species has a set of environmental conditions - temperature, humidity, salinity, oxygen levels, etc. - that it needs for survival. Of course, there is a certain tolerance range for each of these needs for each species, and the probability of finding members of a given species within this tolerance range is usually approximately normal. Suppose the tolerance range for temperature X in a certain species measured in degrees centigrade is N(35, 17).
(b) Find P(3
5. A laboratory weights filters from a coal mine to measure the amount of dust in the mine atmosphere. Repeated measurements of the weight of dust on the same filter has a standard deviation of σ = 0.08 milligram (mg) and mean 123 mg.

(a) If 3 weightings of this filter are made what is the distribution of this mean? What can be said about the mean and standard deviation of this distribution?

(b) If 32 weightings of this filter are made what is the distribution of this mean? What can be said about the mean and standard deviation of this distribution?