Chickens at a farm are processed when they are 20 weeks old. The distribution of

Question

Chickens at a farm are processed when they are 20 weeks old. The distribution of their weights is normal with mean 1.7 kg, and standard deviation 0.250kg. The farm has created three categories for these chickens according to their weight: PETITE (weight less than 1.5 kg), STANDARD (weight between 1.5kg and 2.2kg), and BIG (weight above 2.2kg).

6- Chickens are selected randomly and their weights is verified, what is the probability to find a BIG chicken for the first time at exactly the fifth trial?  

Explanation / Answer

Mean = 1.7kg

Standard deviation = 0.25kg

P(X < A) = P(Z < (A - mean)/standard deviation)

P(Big Chicken) = P(X > 2.2)

= 1 - P(X < 2.2)

= 1 - P(Z < (2.2 - 1.7)/0.25)

= 1 - P(Z < 2)

= 1 - 0.9772

= 0.0228

6 - P(finding a BIG chicken for the first time at exactly the fifth trial) = First 4 chicken are not big and fifth one is big)

= (1-0.0228)4 x 0.0228

= 0.0208

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