Question

When dragons on planet Dathomir lay eggs, the eggs are either green or yellow. The biologists have observed over the years that 29% of the eggs are yellow, and the rest green. Next spring, the lead scientist has permission to randomly select 44 of the dragon eggs to incubate. Consider all the possible samples of 44 dragon eggs. What is the mean (μ) number of yellow eggs in samples of 44 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 44 ? σ=

Answer 1

The mean number of yellow eggs in a sample can be found by multiplying the sample size by the probability of getting a yellow egg. The sample size is 44 and the probability of getting a yellow egg is 0.29 (29%). So, to calculate the mean number of yellow eggs, we multiply 44 by 0.29:

44 * 0.29 = 12.8

So, the mean number of yellow eggs in a sample of 44 eggs is 12.8 (to one decimal place).

The standard deviation in the number of yellow eggs can be found by taking the square root of the product of the sample size, the probability of getting a yellow egg, and the probability of not getting a yellow egg. The probability of not getting a yellow egg is 1 - 0.29 = 0.71. Therefore, to calculate the standard deviation, we take the square root of 44 * 0.29 * 0.71:

sqrt(44 * 0.29 * 0.71) = 3.0

So, the standard deviation in the number of yellow eggs in samples of size 44 is 3.0 (to one decimal place).

In conclusion, out of 44 randomly selected dragon eggs from planet Dathomir, we would on average expect to find about 12.8 yellow eggs (mean), with a standard deviation of 3.0 eggs.