Question

When dragons on planet Pern lay eggs, the eggs are either green or yellow. The biologists have observed over the years that 32% of the eggs are yellow, and the rest green. Next spring the lead scientist has permission to randomly select 45 of the dragon eggs to incubate. Consider all the possible samples of 45 dragon eggs. What is the usual number of yellow eggs in samples of 45 eggs

Answer 1

Answer:

The usual number of yellow eggs in samples of 45 eggs is 14.4.

Step-by-step explanation:

For each egg, there are only two possible outcomes. Either they are yellow, or they are not. The probability of an egg being yellow is independent of other eggs, so we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

$E(X) = np$

32% of the eggs are yellow

This means that $p = 0.32$

45 eggs

This means that $n = 45$

What is the usual number of yellow eggs in samples of 45 eggs

$E(X) = np = 45*0.32 = 14.4$

The usual number of yellow eggs in samples of 45 eggs is 14.4.