Question

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 1

Probability that a randomly selected broiler weighs more than 1454 g is 0.3372 or 34% (approx.)

Explanation:

Given:

Weights of Broilers are normally distributed.

Mean = 1387 g

Standard Deviation = 161 g

To find: Probability that a randomly selected broiler weighs more than 1454 g.

we have ,

`Mean,\,\mu=1387`

`Standard\,deviation,\,\sigma=161`

X = 1454

We use z-score to find this probability.

we know that

`z=(X-\mu)/(\sigma)`

`z=(1454-1387)/(161)=0.416=0.42`

P( z = 0.42 ) = 0.6628 (from z-score table)

Thus, P( X ≥ 1454 ) = P( z ≥ 0.42 ) = 1 - 0.6628 = 0.3372

Therefore, Probability that a randomly selected broiler weighs more than 1454 g is 0.3372 or 34% (approx.)