Suppose the mass of students, in kg is N(68; 9) distributed. Find the probability of students with the mass between 64 and 67 kg.
0.9082
0.6293
0.2789
0.5375
0.3879
To find the probability of students with a mass between 64 and 67 kg, first we need to find the z-scores for those weights using the formula:
z = (X - μ) / σ
where X is the weight, μ is the mean (68 kg) and σ is the standard deviation (9 kg).
For X = 64 kg:
z1 = (64 - 68) / 9 = -0.4444
For X = 67 kg:
z2 = (67 - 68) / 9 = -0.1111
Next, we look up the probabilities associated with these z-scores in the standard normal distribution table.
The probability of a z-score of -0.1111 is 0.4562
The probability of a z-score of -0.4444 is 0.3289
Then, we find the difference between these probabilities:
0.4562 - 0.3289 = 0.1273
Therefore, the probability of students with a mass between 64 and 67 kg is 0.1273.
None of the given options match this result. So, the correct answer may not be included here.