Question

Suppose the mass of gorillas, in kg, are N(155; 400) distributed. Find the probability of gorillas with mass more than 200 kg.

Answer 1

[AI-generated answer — Bot GPT 3.5]

First, we need to standardize the distribution of gorilla masses by calculating the z-score:

z = (X - μ) / σ
where:
X = 200 kg
μ = 155 kg
σ = √400 = 20 kg

z = (200 - 155) / 20
z = 45 / 20
z = 2.25

Next, we need to find the probability that a gorilla has a mass greater than 200 kg, which corresponds to finding the area under the standard normal curve to the right of z = 2.25. Using a standard normal distribution table or a calculator, we find that the probability of z > 2.25 is approximately 0.0122.

Therefore, the probability of gorillas with mass more than 200 kg is approximately 0.0122 or 1.22%.