Question: Supercooling temperature of frogs. Many species of terrestrial tree frogs that hibernate at or near the ground surface can survive prolonged exposure to low winter temperatures. In freezing conditions, the frog's body temperature, called its supercooling temperature, remains relatively higher because of an accumulation of glycerol in its body fluids. Recent studies have shown that the supercooling temperature of terrestrial frogs frozen at -6"C has a relative frequency distribution with a mean of -2'C and a standard deviation of .3"C. (The first of these studies was reported in Science, May 1983.) Consider the mean supercooling temperature T, of a random sample n:42 terrestrial frogs frozen at -6"C.

a.) Find the probability that \(\bar{X}\) exceeds -2.05'C.

b.) Find the probability that \(\bar{X}\) falls between -2.20"C and -2.10'C.