Suppose the mass of gorillas, in kg, are N(155; 400) distributed. Find the probability of gorillas with mass between 150 and 175 kg.

Question

0.5987


0.8413


0.44


0.2426


0.3985

Answer 1

To find the probability of gorillas with mass between 150 and 175 kg, we need to calculate the z-scores for both 150 kg and 175 kg using the mean and standard deviation given.

Z-score for 150 kg:
Z = (X - mean) / standard deviation
Z = (150 - 155) / sqrt(400)
Z = -5 / 20
Z = -0.25

Z-score for 175 kg:
Z = (X - mean) / standard deviation
Z = (175 - 155) / sqrt(400)
Z = 20 / 20
Z = 1

Now, we look up the cumulative probabilities for these z-scores using a standard normal distribution table.

P(Z < -0.25) = 0.4013
P(Z < 1) = 0.8413

Therefore, the probability of gorillas with mass between 150 and 175 kg is:
P(-0.25 < Z < 1) = P(Z < 1) - P(Z < -0.25) = 0.8413 - 0.4013 = 0.44

So the correct answer is 0.44.