Gribbles are small, Pale White, Marine worms that bore through wood. While sometime considered a pest since they can wreck wooden docks and piers, they are now being studied to determine whether the enzyme they secrete will allow us to turn inedible wood and plant waste into bio-fuel. Suppose that the length of a gribble is normally distributed with an average length of 3.1 mm and a standard deviation of 0.52 mm.

Requirements:

a) Find the probability that a randomly selected gribble has a length less than 2.0 mm. Be sure to define your random variable and use proper statistical notation when stating your result.

b) Find the probability that a randomly selected gribble has a length between 2.5 and 3.5 mm.

c) Find the probability that a randomly selected gribble has a length greater than 3.6 mm. Suppose we randomly select 8 gribbles and measure their lengths.

d) Find the probability that the sample mean length of these 8 gribbles is less than 2.0 mm. Be sure to define your random variable and use proper statistical notation when stating your result.

e) Explain why your answer to part d) is different from your answer in part a).

f) Find the probability that the sample mean length of these 8 gribbles is between 2.5 and 3.5 mm.

g) Find the probability that the sample mean length of these 8 gribbles is greater than 3.6 mm.