Suppose the mass of gorillas, in kg, are N(155; 400) distributed. Find the probability of gorillas with mass between 150 and 175 kg.
0.5987
0.8413
0.44
0.2426
0.3985
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.