Question
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
0.9970
0.003
0.5557
0.4443
0.0287
Answers
GPT 3.5
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.
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.