Elementary Statistics

Question

When dragons on planet Pern lay eggs, the eggs are either green or yellow. The biologists have observed over the years that 19% of the eggs are yellow, and the rest green. Next spring the lead scientist has permission to randomly select 67 of the dragon eggs to incubate. Consider all the possible samples of 67 dragon eggs.

What is the usual number of yellow eggs in samples of 67 eggs? (Give answers as SENSIBLE whole numbers.)

minimum usual number of yellow eggs = 

maximum usual number of yellow eggs =

Answer 1

This question is effectively asking you to apply the Normal Approximation to the Binomial Distribution

μ = np, ο = √(npq)

Where in this problem, `n=67` and `p=0.19`.

When the question asks for "the usual" number of yellow eggs, they are asking for a range.

Such a range can be obtained by e.g. a 95% confidence interval describing where we believe the true number of yellow eggs to lie.

Plugging in the problem-details into the 95% Confidence Interval formulae:

[lower-bound, upper-bound] = μ ± 1.96 * ο

So we see that the usual range is given by 67 * 0.19 ± 1.96 * sqrt(67 * .19 * (1 - .19)) = [6.43, 19.02]

Since we can never observe a fractional number eggs, only whole eggs, I would say that we can be reasonably confident that we observe between 6 and 20 yellow eggs within a sample of 67.

https://stats.libretexts.org/Courses/Las_Positas_ollege/Math_40%3A_Statistics_and_Probability/06%3A_Continuous_Random_Variables_and_the_Normal_Distribution/6.04%3A_Normal_Approximation_to_the_Binomial_Distribution#:~:text=Then%20the%20binomial%20can%20be,0.5%20or%20x%E2%88%920.5).