Suppose the mass of students, in kg is N(68; 9) distributed. Find the probability of students with the mass less than 63 kg.

Answer 1

To find the probability of students with a mass less than 63 kg, we need to calculate the z-score corresponding to a mass of 63 kg and then find the probability associated with that z-score.

First, we calculate the z-score using the formula:

z = (X - μ) / σ

where X is the value we are interested in (63 kg), μ is the mean (68 kg), and σ is the standard deviation (9 kg).

z = (63 - 68) / 9
z = -5 / 9
z = -0.5556

Next, we look up the z-score of -0.5556 in a standard normal distribution table or by using a calculator to find the probability associated with this z-score.

Using a standard normal distribution table, we find that the probability of students with a mass less than 63 kg is approximately 0.2896, or 28.96%.