An automated egg carton loader has a 1% probability of cracking an egg, and a customer will complain if more than one egg per dozen is cracked. Assume each egg load is an independent event.

(a) What is the distribution of cracked eggs per dozen ? Include parame-ter values.

(b) What is the probability that a carton of a dozen eggs results in more than one cracked egg ?

(c) Approximate the probability that among 100 dozen of eggs (i. e. 1200 eggs), there will be at most 1 cracked egg in total.

(d) What is the probability that we need more than 100 loaded eggs to observed a cracked egg?

a) Binomial distribution B(n=12,p=0.01)

b) P=0.007

c) P=0.999924

d) P=0.366

Step-by-step explanation:

a) The distribution of cracked eggs per dozen should be a binomial distribution B(12,0.01), as it can model 12 independent events.

b) To calculate the probability of having a carton of dozen eggs with more than one cracked egg, we will first calculate the probabilities of having zero or one cracked egg.

Then,

c) In this case, the distribution is B(1200,0.01)

d) In this case, the distribution is B(100,0.01)

We can calculate this probability as the probability of having 0 cracked eggs in a batch of 100 eggs.

i used to know but i learned it a long time ago sorry

step-by-step explanation: