How to determine the probability using normal distribution.
Several species of terrestrial tree frogs that hibernate at or near the ground surface can survive prolonged exposure to low winter temperatures. In cold conditions the frog's body temperature called its super-cooling temperature remains relatively higher for the reason of an accumulation of glycerol in its body fluids. Recent studies have presented that the super-cooling temperature of terrestrial frogs frozen at -6°C has a relative occurrence distribution with a mean of - 2°C and a standard deviation of 0.3°C (The first of these research was reported in Science May 1983.) Ponder the mean super cooling temperature x of a random sample of n = 42 terrestrial frogs frozen at -6°C.
a. Define the probability that x exceeds -2.05°C.
b. Define the probability that x falls between -2.20°C and -2.10°C.