Final answer:
The standard deviation in the number of yellow dragon eggs in samples of size 52 from planet Pern is approximately 3.04, and the variance is 9.2292. These calculations are based on the binomial distribution formula because the outcome (color of the eggs) follows two possibilities with consistent probabilities.
Step-by-step explanation:
The question asks about the standard deviation and variance of yellow dragon eggs from the planet Pern. Given that 23% of the eggs are yellow, we can calculate these statistics using the binomial distribution formula since we're dealing with two outcomes (yellow or green eggs) that are consistent across all the samples. For a binomial distribution, the formula for standard deviation is √(np(1-p)) and for variance, it is np(1-p), where 'n' is the number of trials and 'p' is the probability of success (in this case, an egg being yellow).
Let's calculate the standard deviation:
- Number of eggs (n) = 52
- Probability of yellow egg (p) = 0.23
- Standard deviation (σ) = √(52*0.23*(1-0.23))
- σ = √(52*0.23*0.77)
- σ = √(9.2292)
- σ ≈ 3.04
Now, let's calculate the variance:
- Variance (σ^2) = 52*0.23*(1-0.23)
- σ^2 = 9.2292
Therefore, the standard deviation of the number of yellow eggs in samples of size 52 is approximately 3.04, and the variance is 9.2292.