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.

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 46 of the dragon eggs to incubate. Consider all the possible samples of 46 dragon eggs.

What is the mean number of yellow eggs in samples of 46 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 = 14.72(already figured this out)

What is the standard deviation in the number of yellow eggs in samples of size 46?

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

standard deviation =?

I just need help finding the standard deviation

Answer 1

Let's call the population proportion of yellow eggs p = .32. For sufficiently large sample sizes, the sampling distribution for the sample proportion is approximately normally distributed, with mean p and standard deviation sqrt(pq/n), where q = 1-p and n is the sample size. Thus we calculate the standard deviation to be sqrt(.32*.68/46) = .069.