Question

When dragons on planet Pern lay eggs, the eggs are either green or yellow. The biologists have observed over the years that 31% of the eggs are yellow, and the rest green. Next spring the lead scientist has permission to randomly select 65 of the dragon eggs to incubate. Consider all the possible samples of 65 dragon eggs.

What is the mean number of yellow eggs in samples of 65 eggs? (that is the same as asking for the expected value of the number of yellow eggs)
(Give answer correct to at least one decimal place.)
mean =

What is the standard deviation in the number of yellow eggs in samples of size 65?
(Give answer correct to at least one decimal place.)
standard deviation =

Answer 1

Solution :

Given that,

p = 0.31

q = 1 - p =1-0.31=0.69

n = 65

Using binomial distribution,

Mean = = n * p = 65*0.31=20.2

Standard deviation = = n * p * q =  65*0.31*0.69=3.7