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. A study in Science revealed that the supercooling temperature of terrestrial frogs frozen at -6ºC has a relative frequency distribution with a mean of –2ºC and a standard deviation of .3ºC. Consider the mean supercooling temperature x-bar of a random sample of n = 42 terrestrial frogs frozen at –6ºC.
a. Find the probability that x exceeds – 2.05ºC.
b. Find the probability that x falls between –2.20ºC and –2.10ºC.