Question

when dragons on planet dathomir lay eggs, the eggs are either green or yellow. the biologists have observed over the years that 21% of the eggs are yellow, and the rest green. next spring, the lead scientist has permission to randomly select 47 of the dragon eggs to incubate. consider all the possible samples of 47 dragon eggs.
what is the mean (μ) number of yellow eggs in samples of 47 eggs?
μ = (please show your answer to 1 decimal place)
what is the standard deviation (σ) in the number of yellow eggs in samples of size 47?
σ = (please show your answer to 1 decimal place)
check answer

Explanation:

Step1: Calculate the mean

The mean formula for a binomial distribution is $\mu = np$, where $n = 47$ (sample size) and $p=0.21$ (probability of yellow eggs).
$\mu=47\times0.21 = 9.87\approx9.9$

Step2: Calculate the standard deviation

The standard deviation formula for a binomial distribution is $\sigma=\sqrt{np(1 - p)}$.
Substitute $n = 47$ and $p = 0.21$:
$\sigma=\sqrt{47\times0.21\times(1 - 0.21)}=\sqrt{47\times0.21\times0.79}=\sqrt{7.7973}\approx2.8$

Answer:

$\mu = 9.9$
$\sigma = 2.8$