Johnny Ray has 1000 egg-laying chickens at Eggstravagant Poultry Company. Histor
ID: 3131936 • Letter: J
Question
Johnny Ray has 1000 egg-laying chickens at Eggstravagant Poultry Company. Historically, each chicken lays an average of 260 eggs per year of 5 per week, per chicken, That comes to an average of 5000 eggs per week of 260,000 total eggs laid per year, which can be considered a steady stream of egg production. Historically, 15% of the eggs are damaged before Johnny Ray can gather them. a) If 20 eggs are samples, how many would you expect to be damaged? b) What is the probability that a sample of 20 eggs produced will have 3 or more damaged? Comment
Explanation / Answer
a)The expected number of eggs to be damaged is:
n*p
=20*0.15
=3
b)Using binomila theorem find the probability that a sample of 20 eggs produced will have 3 or more damaged is:
P(X>=3), where X follows Bin(20,0.15)
P(X>=3)
=1-P(X<2)
=1-[P(X=0)+..+P(X=2)]
=1-[20C0*0.15^0*0.85^20+...+20C2*0.15^2*0.85^18]
=0.595
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