Question

. Suppose that a discrete random variable is the number of broken eggs in a randomly selected carton of one dozen

eggs. The expected value for the number of broken eggs is 0.48 eggs. Which of the following statements is a
correct interpretation of this expected value? Explain why the others are wrong.
a. The probability that an egg will break in one-dozen cartons is 0.48, on average.
b. When a large number of one-dozen cartons of eggs are examined, the average number of broken eggs in a
one-dozen carton is 0.48 eggs.
c. The mean number of broken eggs in one-dozen cartons is 0.48 eggs

Answer 1

b. When a large number of one-dozen cartons of eggs are examined, the average number of broken eggs in a

one-dozen carton is 0.48 eggs

Explanation:

given that a discrete random variable is the number of broken eggs in a randomly selected carton of one dozen eggs. The expected value for the number of broken eggs is 0.48 eggs.

Here expected value we mean average and when we take a large number of one dozen eggs, the broken eggs would be approximately 0.48 eggs.

This is the application of central limit theorem to mean of sample of a random varaible.

Hence correct option is

b. When a large number of one-dozen cartons of eggs are examined, the average number of broken eggs in a

one-dozen carton is 0.48 eggs