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