Final answer:
A. The mean weight gain for male college students during their freshman year is 1.2 kg. B. To calculate the z-score for a weight gain of 2.5 kg, we use the formula z = (x - μ) / σ, where x is the weight gain, μ is the mean, and σ is the standard deviation. C. To find the percentage of male college students who gained less than 3 kg, we calculate the area under the normal distribution curve to the left of 3 kg. D. If the weight gain is 10 kg, it is significantly above the mean.
Step-by-step explanation:
A. The mean weight gain for male college students during their freshman year is 1.2 kg. This is given in the question as the mean (μ) of the weight gain distribution.
B. To calculate the z-score for a student who gained 2.5 kg, we use the formula: z = (x - μ) / σ, where x is the weight gain, μ is the mean, and σ is the standard deviation. Substituting the values, we get z = (2.5 - 1.2) / 5.2 ≈ 0.25. So, the z-score is approximately 0.25.
C. To find the percentage of male college students who gained less than 3 kg during their freshman year, we need to calculate the area under the normal distribution curve to the left of 3 kg. First, we calculate the z-score for 3 kg using the formula from part B: z = (3 - 1.2) / 5.2 ≈ 0.35. Using a standard normal distribution table or a calculator, we find that the area to the left of z = 0.35 is approximately 0.6368, or 63.68%. Therefore, approximately 63.68% of male college students gained less than 3 kg during their freshman year.
D. If the weight gain for a male college student is 10 kg, we can compare it to the mean. Since the mean weight gain is 1.2 kg, a weight gain of 10 kg is significantly above the mean.