Suppose the masses of gorillas, in kg, are N(155; 400) distributed. Find the probability of gorillas with masses less than 100 kg.


0.9970


0.003


0.5557


0.4443


0.0287

1 answer

0.003

To find this probability, we need to use the z-score formula:

z = (X - μ) / σ

where z is the z-score, X is the value we want to find the probability for (in this case 100kg), μ is the mean (155kg), and σ is the standard deviation (20kg).

Plug in the values:

z = (100 - 155) / 20
z = -55 / 20
z = -2.75

Now, we look up the z-score -2.75 in the standard normal distribution table to find the corresponding probability. The probability of getting a z-score of -2.75 or below is 0.003, which is the probability of gorillas with masses less than 100 kg.