Assume that the amounts of weight that male college students gain during their freshman year are normally distributed with a mean of $\mu=1.2 \mathrm{~kg}$ and a standard deviation of $\sigma=4.6 \mathrm{~kg}$. Complete parts (a) through (c) below. a. If 1 male college student is randomly selected, find the probability that he gains between $0 \mathrm{~kg}$ and $3 \mathrm{~kg}$ during freshman year. The probability is (Round to four decimal places as needed.)

Step 1 ：We are given that the amounts of weight that male college students gain during their freshman year are normally distributed with a mean of \(\mu=1.2 \mathrm{~kg}\) and a standard deviation of \(\sigma=4.6 \mathrm{~kg}\).

Step 2 ：We are asked to find the probability that a randomly selected male college student gains between 0 kg and 3 kg during their freshman year. This is a problem of finding the probability of a range in a normal distribution.

Step 3 ：We can use the Z-score formula to standardize the weights and find the corresponding probabilities. The Z-score is calculated as \((X - \mu) / \sigma\), where X is the value from the dataset, \(\mu\) is the mean and \(\sigma\) is the standard deviation.

Step 4 ：The probability that the weight gain is between 0 kg and 3 kg is the probability that the Z-score is between Z(0) and Z(3).

Step 5 ：We calculate the Z-score for 0 kg and 3 kg as follows: \[Z(0) = (0 - 1.2) / 4.6\] and \[Z(3) = (3 - 1.2) / 4.6\]

Step 6 ：We find the probabilities corresponding to these Z-scores using a standard normal distribution table.

Step 7 ：The probability that the weight gain is between 0 kg and 3 kg is \(P(Z(3)) - P(Z(0))\).

Step 8 ：Substituting the values, we get \[P_0 = 0.3970965479070302\] and \[P_3 = 0.6522138572609713\]

Step 9 ：Subtracting these probabilities, we get \[P = 0.25511730935394106\]

Step 10 ：Final Answer: The probability that a randomly selected male college student gains between 0 kg and 3 kg during their freshman year is approximately \(\boxed{0.2551}\).