Agrocery supplier believes that the mean number of broken eggs per dozen is 0.8 with a standard deviation of 0.6. you buy 8 dozen eggs without checking them.
a) how many broken eggs do you expect to get?
b) what's the standard deviation?
c) is it necessary to assume the cartons of eggs are independent? why?

Step-by-step explanation:

Given that a grocery supplier believes that the mean number of broken eggs per dozen is 0.8 with a standard deviation of 0.6.

Here we assume the cartons of eggs are independent

a) Mean value of eggs in 8 dozens = 8 Expected value in 1 dozen

b) Var (8x) (Here 8 dozens)

 (assuming independent)

Otherwise we have Var(x1+x2+x3+...)=sum of var of xis + cov (xi,xj)

Thus we have to assume independent to avoid covariance

So Var(8x)=64 Var(x)

STd dev for 8 dozens = 8(0,6) = 4.8

c) To avoid covariance i.e. variance among pairs of dozens we assume independence.