The weights of broilers (commercially raised chickens) are approximately normally distributed with mean 1387 grams and standard deviation 161 grams. What is the probability that a randomly selected broiler weighs more than 1,454 grams?

Answer:Probability that a randomly selected broiler weighs more than 1454 g is 0.3372 or 34% (approx.)Step-by-step explanation:Given:Weights of Broilers are normally distributed.Mean = 1387 gStandard Deviation = 161 gTo find: Probability that a randomly selected broiler weighs more than 1454 g.we have ,[tex]Mean,\,\mu=1387[/tex][tex]Standard\,deviation,\,\sigma=161[/tex]X = 1454We use z-score to find this probability.we know that [tex]z=\frac{X-\mu}{\sigma}[/tex][tex]z=\frac{1454-1387}{161}=0.416=0.42[/tex]P( z = 0.42 ) = 0.6628   (from z-score table)Thus, P( X ≥ 1454 ) = P( z ≥ 0.42 ) = 1 - 0.6628 =  0.3372Therefore, Probability that a randomly selected broiler weighs more than 1454 g is 0.3372 or 34% (approx.)