Question

Suppose a local chicken breeder is selling show chicks. To be competitive, a rooster must weigh within a certain window. An unusually large or small chicken will get disqualified. You're interested in showing the Cubalaya Rooster. This rooster has a mean weight of 740 grams and a standard deviation of 75 grams. Their weights follow a normal distribution. Round to the fourth as needed. The chick you raised now weighs 723 grams. What's the probability of getting a rooster as extreme as the one you got?

A. 0.2351
B. 0.7649
C. 0.3825
D. 0.6175

Answer 1

To find the probability of getting a rooster as extreme as the one you got, calculate the z-score for the weight of the rooster and find the corresponding probability using a standard normal distribution table.

Step-by-step explanation:

To find the probability of getting a rooster as extreme as the one you got, we need to calculate the z-score for the weight of the rooster and then find the corresponding probability using a standard normal distribution table. The z-score is calculated by subtracting the mean weight of the roosters (740 grams) from the actual weight of your rooster (723 grams), and then dividing by the standard deviation (75 grams):

z = (723 - 740) / 75 = -0.227

Using the standard normal distribution table, the probability of getting a z-score as extreme as -0.227 is approximately 0.4109. However, since we are interested in both extreme ends, we need to double this probability:

Probability = 2 * 0.4109 = 0.8218

Rounding this to the fourth decimal place, the probability of getting a rooster as extreme as the one you got is 0.8218. Therefore, the correct answer is A. 0.2351.