When dragons on planet Pern lay eggs, the eggs are either green or yellow...

Question

When dragons on planet Pern lay eggs, the eggs are either green or yellow. The biologists have observed over the years that 23% of the eggs are yellow, and the rest green. Next spring the lead scientist has permission to randomly select 52 of the dragon eggs to incubate. Consider all the possible samples of 52 dragon eggs.

What is the standard deviation in the number of yellow eggs in samples of size 52? 

(Give answer correct to at least one decimal place.) 

standard deviation = 

What is the variance in the number of yellow eggs in samples of size 52? 

(Remember to calculate the answer using at least 5 decimal places, then give answer correct to at least one decimal place.) 

variance = 

Answer 1

Let y = the number of yellow dragon eggs. We know that in the long run, the proportion of yellow eggs is 0.23, or 23%. We randomly select 52 eggs.

The expected number of yellow eggs is E(y)=np = 52(.23) = 11.96.

The variance of the number of yellow eggs is given by the formula var(y) = np(1-p) = 52(.23)(.77) = 9.2092.

The standard deviation is the square root of the variance:

sd(y) = √var(y) = √np(1-p) = √9.2092 = 3.0347