Question

When dragons on planet Pern lay eggs, the eggs are either green or yellow. The biologists have observed over the years that 26% 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.
1. What is the mean number of yellow eggs in samples of 67 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 =
2. What is the standard deviation in the number of yellow eggs in samples of size 67?
(Give answer correct to at least one decimal place.)
standard deviation =
3. What is the variance in the number of yellow eggs in samples of size 67?
(Remember to calculate the answer using at least 5 decimal places, then give answer correct to at least one decimal place.)

Answer 1

Answer:

μ=  17.42

var=  12.891= 12.9

σ = 3.59

Explanation:

As the number of trials are fixed  i.e 67 and the success is also fixed i.e 26% or 0.26 this is treated as a binomial experiment.

The mean of the binomial experiment is calculated as

μ= np = 67*0.26= 17.42

This is the same as the expected value of number of yellow eggs.

E(y)= np=μ=  67*0.26= 17.42

The variance  of the binomial experiment is calculated as

var= npq  = 67*0.26(1-0.26)= 67*0.26(0.74)= 12.8908= 12.891

The standard deviation  of the binomial experiment is calculated as

σ =√npq= √12.8908= 3.590376  = 3.59038= 3.5904 = 3.590= 3.59